Department of Mathematics
Annual Report 2001Ð2002
Year in Review: Mathematics Instruction and Research
Cornell University Þrst among private institutions in undergraduates who later earn Ph.D.s.
Ithaca, New York, the home of Cornell University, is located in the heart of the Finger Lakes Region. It offers the cultural activities of a large university and the diversions of a rural environment.
Mathematics study at Cornell is a unique experience. The university has managed to foster excellence in research without forsaking the ideals of a liberal education. In many ways, the cohesiveness and rigor of the Mathematics Department is a reßection of the Cornell tradition.
John Smillie, chair Department of Mathematics Cornell University Telephone: (607) 255-4013 320 Malott Hall Fax: (607) 255-7149 Ithaca, NY 14853-4201 e-mail: [email protected] Table of Contents
The Year in Review 2001–2002...... 1 VIGRE ...... 2 NSF/NIGMS Grant ...... 3 Graduate Program ...... 3 Undergraduate Program ...... 5 Research and Professional Activities...... 5 Support Sta ...... 6 Faculty Changes ...... 6 Gifts ...... 6 Department Prizes and Awards ...... 7 Special Honors and Awards...... 7 Instructional Activities ...... 8 Curriculum Changes ...... 8 Interdisciplinary Instructional Activity ...... 9
Mathematics Course Enrollment Statistics ...... 10
Mathematics Department Directory 2001–2002 ...... 12
New Faculty Members for 2002–2003 ...... 14
Special Programs and Activities ...... 15 The Math Explorers Club ...... 15 Mathematics Awareness Month ...... 15 Expanding Your Horizons ...... 16 Spring Concert Series ...... 16 Cornell Conference on Analysis and Probability on Fractals ...... 17 Cornell Topology Festival...... 17 Preparing Future Professors ...... 18 Special Guest Lectures ...... 18 Research Experiences for Undergraduates Program ...... 19 Summer Program ...... 20 Special Instructional Support ...... 20 Centers for Applied Mathematics ...... 21 Mathematics Library ...... 21 Mathematics Education...... 23 Mathematics Department Endowments ...... 24 Degrees Granted 2001–2002 ...... 25
Department Colloquia ...... 28
2001–2002 Faculty Publications ...... 36
The Faculty and their Research ...... 41
Faculty Pro les...... 42
Visiting Faculty Program Participants ...... 79
Sta Pro les...... 80 The Year in Review 2001–2002
My three-year term as chair is over, and this is the last In December 2001, at our annual holiday party, we Year in Review that I will write. Being department chair awarded the rst annual departmental teaching awards. has been a very interesting experience. There have been Al Schatz won the senior faculty award, Ravi Ramakr- changes: a new building; the VIGRE grant with new ishna won the junior faculty award and Lee Gibson won postdocs, new graduate students and new activities; two the graduate student award. Several graduate student new sta members; a reduced teaching load for H. C. awards were also presented. Fernando Marques received Wangs; and a new department teaching award. On the the Battig Award. Christopher Francisco received the other hand, many things have stayed the same: a helpful York Award. In addition, Dan Ciubotaru, Jean Cortis- and knowledgable sta ; a dedicated faculty; enthusiastic soz, Yuval Gabay and Sam Hsaio received Hutchinson graduate students; dedicated math majors; and a dean Fellowships for the spring semester. who supports our e orts. Daniel Ramras received the annual Kieval Prize from the Searches conducted this year resulted in the hiring of a department at the department’s graduation ceremony in number of new faculty. We hired two H. C. Wang as- May. I am also pleased to report that Peter Clark, a sistant professors: Indira Chatterji (ETH Z urich) and sophomore majoring in mathematics and biology, and a Dan Za ran (Ruhr-Universit at Bochum). We were also college scholar, was one of four Cornell recipients of a fortunate to hire three VIGRE postdocs: Tara Bren- Barry M. Goldwater Scholarship in science and mathe- dle (Columbia University), Alexander Meadows (Stan- matics. ford University) and Brian Smith (Cornell University). We are very happy to have them join us. (See p. 14 to Birgit Speh completed her rst year as director of un- learn more about our new faculty.) dergraduate studies (DUS). Birgit did an exemplary job in this faculty administrative position, and we are very B ela Bajnok and Carolyn DeSilva, both on leave from grateful to her for all her hard work. Gettysburg College in Gettysburg, Pennsylvania, par- ticipated in this year’s visiting program. We appreci- Special thanks to Lou Billera, who nished his term as ate their e orts, and once again our teaching program director of graduate studies (DGS) at the end of June havs bene ted from visiting program participation. (For 2002. Lou was an e ective and energetic DGS who more information about their experiences at Cornell, see served in that capacity since January 2001. We appreci- page 79.) Recruitment e orts have produced four par- ate his dedication to the position and his special talents. ticipants for the 2002–2003 academic year. Michael Stillman has agreed to accept the position be- ginning July 1, 2002. Rick Durrett was recently elected a fellow of the Amer- ican Academy of Arts and Sciences. He is the only This past year the department conducted a review of Cornell professor elected to the prestigious academy’s the graduate program curriculum, the rst in over 25 class of 2002. He joins two department faculty who are years. The e ort was headed up by committee chair previously-elected academy members: Eugene Dynkin Dan Barbasch. Committee members Lou Billera, Ken and Harry Kesten. Founded in 1780, the academy hon- Brown, Rick Durrett, Leonard Gross and Shankar Sen ors distinguished scientists, scholars and leaders in public contributed to this review, along with numerous depart- a airs, business, administration and the arts. The induc- ment faculty members. (See page 9 for more informa- tion ceremony will be held at the academy headquarters tion about this review and the changes generated for the in Cambridge, Massachusetts on October 5, 2002. graduate curriculum.)
Ravi Ramakrishna was awarded the Russell Distin- Once again, Rick Durrett served with distinction as guished Teaching Award from the College of Arts and VIGRE coordinator. Special notice should be taken of Sciences and an AMS Centennial Fellowship. Ravi will the rst VIGRE Faculty Development Workshop, held spend his fellowship year at McGill University (Canada) May 7, 2002, at the Rose Inn. This was an especially in the fall and at Berkeley in the spring. John Guck- successful and exciting mentoring e ort. Topics covered enheimer was elected as Fellow of the American Asso- making the transition from being a graduate student to ciation for the Advancement of Science at the February being an independent researcher, writing NSF proposals 2002 annual meeting in Boston. and delivering good teaching lectures.
The Year in Review 2001–2002 1 Two long-term faculty, Harry Kesten and Richard partment of Theoretical and Applied Mechanics (where Platek, have retired, e ective June 30, 2002. We are she worked with Tim Healey). Two new NSF post- happy to report that Harry Kesten and his wife will re- docs also arrived: Jason Schweinsberg and Alexander main in Ithaca, and he will continue his research and Vladimirsky, both from the University of California at involvement with the department. Richard Platek will Berkeley, Statistics and Mathematics, respectively. be moving to Sarasota, Florida. The recruitment process for fall 2002 took place in Feb- The dean of the College of Arts and Sciences and the ruary. We reached our target of three new postdocs in dean of the Engineering College have both approved a hiring Tara Brendle from Columbia University, Alexan- two-year extension to the current Engineering Restruc- der Meadows from Stanford University, and Brian Smith turing agreement. This agreement was originally nego- from the University of Alabama at Birmingham. tiated in 1996 by then chairman Robert Connelly. The goal of the e ort continues to be to provide outstanding On May 7, 2002, we held our rst ever VIGRE profes- calculus instruction in cooperation with Theoretical and sional development workshop. This event was held at Applied Mechanics by o ering small class sizes. The new the Rose Inn, a bed and breakfast about ten miles north agreement gives our department some additional exibil- of Ithaca; it involved our eight VIGRE/NSF postdocs ity with respect to VIGRE postdocs, which should lead and eight department faculty members. Participants dis- to continued high quality teaching. cussed the road from Ph.D. to tenure, planning research and writing proposals, and issues involved in planning In closing, I would like to thank the sta for their hard courses and delivering good lectures. work, and I would like to thank chair’s assistants Cathy and Linda and my family for putting up with my id- VIGRE Graduate Fellows: Our second group of three iosyncracies during my three-year term. I would like to VIGRE graduate fellows arrived in the fall: Jason Bode thank everyone who said “yes” when I asked them to (Calvin College), Edoardo Carta (University of Puerto do something for the department. In particular, let me Rico) and William Gryc (Amherst College). These stu- thank Ken Brown for agreeing to be my successor. dents were free from teaching responsibilities their entire rst year, making it easier to get through their demand- ing rst-year courses. They will also have one semester VIGRE free in each of the second and third years to allow them The 2001–2002 academic year was the second year of the to broaden their education and explore possible thesis ar- Mathematics Department’s ve-year NSF VIGRE grant. eas. Our recruitment target for fall 2002 was four fellows; The acronym VIGRE is pronounced “vigor” and stands however, a very successful recruiting season yielded six: for Vertically InteGrated Research and Education. At a David Biddle (SUNY at Binghamton), Andrew Cameron recent meeting held by the NSF to judge the successes (University of Virginia), Benjamin Chan (University and chart the future direction of its new program, Bene- of Rochester), Heather Heston (Millersville University), dict Gross (Harvard) quipped, “Like the pill whose name Michael O’Connor (University of Massachusetts) and it resembles, the purpose of the VIGRE grant is varied. Jay Schweig (George Mason University). It is intended to increase the population, revitalize old relationships and allow participants to have more fun.” Graduate Student VIGRE Semesters: Continuing Said less ippantly, the purpose of the VIGRE program graduate students can bene t from the VIGRE grant is (1) to provide more support for postdocs and pre- through VIGRE semesters. In fall 2001, Sarah Spence pare them to take on and balance a broad spectrum of worked to develop course materials for MATH 336 on the faculty duties in research, teaching and service, (2) to applications of algebra to developing codes. Carla Mar- provide support for graduate students to allow them to tin (CAM) was supported in spring 2002 to help develop prepare for the wide range of opportunities available to course materials for a new course on the applications individuals with training in the mathematical sciences, of mathematics to biology (MATH 362/BIOEE 362), and (3) to engage undergraduates in research that will which was taught jointly by John Guckenheimer and enhance their training and increase the chances that they Steve Ellner (Ecology and Evolutionary Biology). Fi- will consider a career in mathematics. nally, Christopher Hardin, a student in logic working with Richard Shore, used his VIGRE semester in spring VIGRE Postdocs: The fall semester brought two new 2002 to take two computer science courses working to- VIGRE postdocs: Matthew Fickus from the Univer- ward a masters in computer science. This year VIGRE sity of Maryland and Anita Mareno from Cornell’s De- also supported graduate students from other institutions
2 The Year in Review 2001–2002 who attended the conference Analysis and Probability the Department of Molecular Biology and Genetics and on Fractals organized by Robert Strichartz, which took Rasmus Nielsen from the newly-formed Department of place at Cornell June 16–20, 2002. Computational Biology and Biological Statistics. Their research concerns problems in probability and statistics Summer Support for Undergraduates: At the under- that arise from two topics. The rst looks for footprints graduate level, the VIGRE grant helped to support the of the xation of advantageous mutations in DNA se- Cornell Research Experiences for Undergraduates pro- qeunce data generated in the Aquadro lab. The second gram in three ways: (1) VIGRE money allowed the pro- is the study of how whole genomes are rearranged by gram to be expanded to include two more Cornell un- large-scale processes that move or invert large segments dergraduates. (2) It provided additional nancial sup- of chromosomes. Awards in the new NSF/NIGMS pro- port for the faculty members who devoted eight weeks gram are quite generous compared to typical mathemat- of their summer to supervising undergraduate projects. ics grants. In each of its ve years, the grant will support (3) It enhanced the program by supporting visitors who a postdoc, a computer programmer, three graduates stu- work with the various projects. dents, and one month of summer support for each of the three investigators. Three undergraduates also received small grants to work directly with Cornell faculty in summer 2001. Debbie Graduate Program Grier worked with Louis Billera, Brian Renne with Anil Nerode and S. Alex Smith with Robert Strichartz. In The Cornell Mathematics Department is rated among most cases, these e orts were preliminary work for a se- the top in the country by the American Mathematical nior thesis, completed during the academic year. Society. The U.S. News and World Report placed Cor- nell ninth in the nation in its 1999 national ranking of Math Explorers Club: The Math Explorers Club graduate mathematics programs. continued this year under the leadership of Robert Strichartz with support from VIGRE. The club endeav- The graduate program included 69 graduate students ors to stimulate an interest in mathematics in local high during the 2001–2002 academic year. Ph.D. degrees school students by exposing them to material not usually were awarded to three students, while nine earned spe- encountered in the high school curriculum. (See p. 15.) cial masters degrees in mathematics, and two received double masters in mathematics and computer science. VIGRE Interdisciplinary Colloquium: The nal activ- The total number of full-time students in the coming ity of the VIGRE grant is the VIGRE Interdisciplinary year will be 72. Due to an especially e ective recuit- Colloquium. In the fall lectures were given by Robert ing season, the entering class this fall will consist of six- Jarrow (Johnson School of Management), Ron Elber teen new Ph.D. students. Ten of the current students (Computer Science), Carlos Castillo-Chavez (a mem- will complete their Ph.D. degrees by August. In addi- ber of both the new Biological Statistics and Computa- tion, three students have dropped out of the program tional Biology department and T&AM), Richard Rand as of June 2002. Five one-year nondegree students will (T&AM) and Viet Elser (Physics). There were no talks be in residence in 2002–2003: one student from Univer- in the spring, as the VIGRE coordinator was doing a lot sity of Paris VII (France) who will be supported un- of travelling. The colloquium will return in the fall. der an exchange agreement with the Cornell Abroad EDUCO Center in Paris, two advanced students from The VIGRE grant partially supported the visit of Duke working with Gregory Lawler, one student from Richard Guy, who gave the Kieval Lecture. (See p. 18.) Marseilles who is working with John Hubbard, and an On the following Monday, he gave a talk for graduate additional student from University of Paris VI who is students and faculty on unsolved problems in combina- visiting Richard Durrett. torial games. Entering students Andrei Maxim, Mauricio Velasco and Jessica Zuniga received one-year fellowships from the NSF/NIGMS Grant Cornell Graduate School; these fellowships will cover full This year Richard Durrett received approval for a grant tuition and stipend. David Biddle, Andrew Cameron, under a joint initiative of the National Science Founda- Benjamin Chan, Heather Heston, Michael O’Connor and tion and the National Institue of General Medical Sci- Jay Schweig received VIGRE fellowships, awarded under ences to support research in the mathematical sciences. our NSF VIGRE grant. After her rst year, Zuniga will His proposal was a joint e ort with Chip Aquadro from also be a VIGRE fellow for three years. Sarah Koch, our
The Year in Review 2001–2002 3 top recruit from last year, is transferring from Berkeley Christopher Francisco — Route 81 Conference on and will enter Cornell with a National Physical Science Cummutative Algebra and AMS meeting Special Consortium Fellowship. The remaining six entering stu- Session on Commutative Algebra in Algebraic Ge- dents — Drew Armstrong, Nikolai Dimitrov, Bradley ometry; Forrest, Timothy Goldberg, Radu Murgescu and James Lee Gibson — Seminar on Finite Markov Chains Worthington — will be supported as teaching assistants. at Oberwolfach and attended the Stochastic Pro- cesses Seminar at Princeton University; Graduate students play an essential role in all aspects of Noam Greenberg — Hebrew University and the the department: teaching, research, mentoring of under- Association for Symbolic Logic; graduates and community outreach programs. Kristin Camenga and Lee Gibson taught mini-courses in local Spencer Hamblen — attended the Canadian Num- schools as part of the Graduate Student School Outreach ber Theory Association VII meeting; Program. For the rst time, three of our students — Matthew Horak — Preparing Future Faculty at Lee Gibson, Todd Kemp and Melanie Pivarski — orga- Ithaca College; nized a recruitment weekend for prospective students. Of Suzanne Hruska — Corning Community College the seven students who attended, ve decided to attend Math Career Day; Cornell. Many students are also active in the Prepar- Sam Hsiao — invited lecture at the 2002 Central ing Future Professors program (p. 18), Expanding Your Section Meeting of the AMS in Ann Arbor, at- Horizons (p. 16) and the Math Explorers Club (p. 15). tended two Eastern Section Meetings of the AMS; Class representatives were G. Christopher Hruska (sixth Henri Johnston — attended the Canadian Number and seventh year), Matthew Horak ( fth year), Nelia Theory Association VII meeting; Charalambous (fourth year), James Belk (third year), Todd Kemp — a short course, “Representation Kristin Camenga (second year) and Henri Johnston ( rst Theory of Compact Lie Groups, Binghamton Uni- year). The graduate and professional student represen- versity, spring 2002; tatives were Gil Rosenberg and Franco Saliola. Melanie Pivarski — Seminar on Finite Markov Chains at Oberwolfach; Awards were given to students for outstanding achieve- Franco Saliola — Eastern Section Meeting of the ment in coursework, research and teaching: AMS; Dan Ciubotaru, Jean Cortissoz, Yuval Gabay and Reba Schuller — Cornell Cognitive Studies; Sam Hsiao received Hutchinson Fellowships. Sarah Spence — invited speaker at the Joint Math- Fernando Marques received the Battig Award. ematics Meeting and AWM Poster Session in San Christopher Francisco received the York Award. Diego; (See Department Prizes and Awards, p. 7.) Jos e Trujillo Ferreras — Seminar on Finite Markov Chains at Oberwolfach. The Olivetti Club is devoted to expository talks on cur- Reba Schuller published a paper with K. Etessami and rent research areas and is organized entirely by graduate T. Wilke, Fair simulation relations, parity games and students. This year the organizers were Noam Green- state space reduction for Buchi Automatia. berg and Evgueni Klebanov in the fall and Todd Kemp and Roland Roeder in the spring. Most of the speak- Between August 2001 and May 2002, three Ph.D. degrees ers were graduate students. (See Department Colloquia, were conferred: p. 32, for a list of talks.) David Brown, assistant professor at Ithaca College; Kathryn Nyman, a postdoc at Texas A&M Uni- Forty-one graduate students gave 88 talks in department versity; seminars. The graduate students were also active in giv- Sarah Spence, assistant professor at Franklin W. ing o -campus research presentations at meetings and Olin College of Engineering. specialized conferences. A sampling of these follows. (See Degrees Granted, p. 25.) Christian Benes — Seminar on Finite Markov Chains at Oberwolfach; Nine others are preparing to complete their degrees in Ryan Budney — Brown University, AMS meeting, August 2002. Of the ten students receiving Ph.D. de- University of Georgia and Ohio State University; grees in May and August 2002, two (Christopher Hruska
4 The Year in Review 2001–2002 and David Revelle) were awarded prestigious NSF Math- UCLA). Daniel Ramras, this year’s Kieval Prize winner, ematical Science Postdoctoral Fellowships (at Chicago won an NSF graduate fellowship as well as a DOD fel- and Berkeley, respectively), two took assistant professor lowship. A few other students attending graduate school positions (one for one year at Cornell) and four secured next year will be getting VIGRE support. postdocs (mostly VIGRE-supported) at various institu- tions around the country (Indiana, Rochester, SUNY Research and Professional Activities Stony Brook, Texas A&M). The remaining two are ar- ranging positions in Europe and India. We expect the Department-sponsored research expenditures for the s- job market for our graduates to continue to be strong for cal year 2001–2002 totaled $1,736,048. This included at least the next several years. 42 grants and contracts from federal, state and private agencies awarded to 39 faculty. Faculty submitted 18 new grant proposals, six of which have been funded to Undergraduate Program date. Editorships included: The Cornell undergraduate program in mathematics in 2001–2002 included 140 majors (including three condi- Dan Barbasch, editor of Proceedings of the AMS; tional acceptances). One of our new majors, Peter Clark, Yuri Berest, editor of the Journal of Nonlinear won a Goldwater Scholarship. (See Special Honors and Mathematical Physics; Awards, p. 7.) Several of our graduating seniors wrote Louis Billera, member of the editorial boards of the senior theses: Scott Bailey, Ari Blinder, Debbie Grier, Journal of Algebraic Combinatorics and Discrete S. Alex Smith and Benjamin Szekely. At least four of and Computational Geometry; our majors applied to study abroad for all or part of next year: Robert Connelly, editor of Beitr age f ur Algebra und Michelle Fullwood (Budapest, fall 2002); Geometrie; Sebastian Mekas (Cambridge, Robinson College); R. Keith Dennis, coeditor of the Jahrbuch Project; Oded Yacobi (Budapest, fall 2002); Richard Durrett, associate editor of Notices of the Paul Young (Moscow, fall 2002). AMS and the Journal of Theoretical Probability; Cli ord Earle, coeditor of Proceedings of the Sec- The majors committee organized a fall reception for po- ond Iberoamerican Congress on Geometry; tential majors, a fairly big event where major and ca- Jos e F. Escobar, member of the editorial boards of reer options were discussed. Robert Strichartz discussed the Electronic Journal of Di erential Equations, REU programs. Study abroad options, particularly the Revista Colombiana de Matem aticas and Inno- Moscow and Budapest programs, were presented to the vaci on y Ciencia; students, and someone from Career Services spoke as well. The reception was announced in classes and in the Leonard Gross, member of the editorial boards school paper; about 15–20 students and over a dozen of the Journal of Functional Analysis, Reviews faculty attended. of Mathematical Physics, Potential Analysis, the Soochow Journal of Mathematics and Revista In the spring, the majors committee organized an advis- Colombiana de Matem aticas and of the advi- ing reception for students interested in upper-level math- sory board of Methods of Functional Analysis and ematics classes. This event highlighted new upper-level Topology; courses, and many of the instructors of these (and other) John Guckenheimer, editor of the Journal of Ex- courses attended. Posters were displayed that included perimental Mathematics, the SIAM Journal of Ap- the instructors’ photographs to make it easier for stu- plied Dynamical Systems and the Moscow Mathe- dents to nd them. This event was advertised like the matical Journal; fall reception with about the same turnout. Yulij Ilyashenko, editor-in-chief of the Moscow Bachelors degrees were awarded to 44 students, including Mathematical Journal, member of the editorial one in August 2001 and six in January 2002. One student boards of Functional Analysis and its Applica- graduated summa cum laude, ve graduated magna cum tions, Dynamical and Control Systems, Ergodic laude, and seven graduated cum laude. Several of our Theory and Dynamical Systems, Proceedings of the graduates are going on to graduate school in mathemat- Moscow Mathematical Society and Mathematical ics (Columbia, Northwestern, Ohio State, Stanford and Enlightenment;
The Year in Review 2001–2002 5 Harry Kesten, member of the editorial boards of reviewed, analyzed and in some cases changed. This the Indiana University Journal of Mathematics, brings the total documented and completed tasks to 34, the New York Journal of Mathematics and Journal for inclusion in the departmental job task manual. Upon d’Analyse Math ematique; completion, this task manual will help with sta cross- Gregory Lawler, associate editor of Combinatorics, training and supervision. Probability and Computing; Anil Nerode, member of the editorial boards of An- Faculty Changes nals of Pure and Applied Logic, Mathematical and Harry Kesten decided to retire at the end of this aca- Computer Modelling, the Journal of Pure and Ap- demic year. The tenured faculty voted unanimously to plied Algebra, the International Journal of Hybrid confer emeritus professor status on him e ective July 1, Systems and Annals of Math & AI ; 2002. Richard Platek also retired e ective July 1, 2002; Michael Nussbaum, member of the editorial boards he is moving to Sarasota, Florida. of Annales de l’Institut Henri Poincar e and Prob- abilit es et Statistiques; John Smillie completed his term of three years as depart- James Renegar, associate editor of the SIAM Jour- ment chairperson on June 30, 2002. The faculty selected nal on Optimization; Kenneth Brown as the next chairperson to serve a three- Laurent Salo -Coste, editor of Mathematische year term beginning July 1, 2002. Zeitschrift, associate editor of Stochastic Processes and their Applications, the European Series of In- The faculty also voted to give Robert Terrell a half-time dustrial and Applied Mathematics (Probability and appointment as senior lecturer to begin July 1, 2002. Statistics) and Annales de la Facult e des Sciences (Other department personnel changes are noted in the de Toulouse; Department Directory, pp. 12–13.) Shankar Sen, member of the editorial board of the On leave for 2001–2002: Journal of the Ramanujan Mathematical Society; Stephen Chase, sabbatical leave, spring 2002 Richard Shore, editor of Studies in Logic and the Peter Kahn, sabbatical leave, fall 2001 Foundations of Mathematics; Harry Kesten, leave, academic year Birgit Speh, editor of the New York Journal of Gregory Lawler, leave, fall 2001 Mathematics and the Journal of Representation Michael Morley, sabbatical leave, spring 2002 Theory; Irena Peeva, leave, academic year Michael Stillman, algebraic geometry editor for Oscar Rothaus, leave, spring 2002 Proceedings of the AMS; Richard Shore, sabbatical leave, spring 2002 Reyer Sjamaar, sabbatical leave, spring 2002 Robert Strichartz, executive editor of the Journal Robert Strichartz, sabbatical leave, spring 2002 of Fourier Analysis and Applications; Lars Wahlbin, editor of Mathematics of Computa- On leave for 2002–2003: tion; Eugene Dynkin, sabbatical leave, spring 2003 James West, associate editor of Fundamenta Math- Cli ord Earle, sabbatical leave, academic year ematicae. Leonard Gross, sabbatical leave, fall 2002 John Guckenheimer, sabbatical leave, fall 2002 Support Sta J. T. Gene Hwang, sabbatical leave, spring 2003 Michael Morley, sabbatical leave, fall 2002 Last summer two new sta members were hired, and Ravi Ramakrishna, leave, academic year many of the sta positions underwent a reorganization Laurent Salo -Coste, sabbatical leave, spring 2003 with new job responsibilities. For those a ected, the past Shankar Sen, sabbatical leave, fall 2002 year has been spent learning new tasks and adjusting to John Smillie, sabbatical leave, academic year new responsibilities. This has been a successful change, and the sta have settled in nicely to their new routines. Gifts The sta task review project continued throughout the As always, we appreciate the kindness and generosity 2001–2002 academic year. Eighteen task meetings were of alumni and other friends of mathematics. During held, wherein key administrative tasks were documented, the 2001–2002 academic year, designated donor gifts in-
6 The Year in Review 2001–2002 creased the principal of various department endowments. tive ability in mathematics. This prize is funded sub- In addition, the department received some unrestricted stantially by contributions solicited from various faculty. gift donations, which are used to supplement departmen- Each year, the high school selects a small group of stu- tal activities for the mathematics community at Cornell. dents; one or two of our faculty interview them and then In many cases, contributions were received in response to select a winner. the department newsletter, Math Matters. By distribut- ing this newsletter, we hope to keep our many friends Daniel Alexander Ramras, who graduated summa cum current on department activities. If you would like to laude in mathematics in May, won the Harry S. Kieval be added to the newsletter mailing list, please contact Prize in Mathematics. The Kieval Prize, established in Catherine Stevens at [email protected]. 1994 by Harry S. Kieval ’36, provides an annual award to an outstanding graduating senior mathematics ma- jor. The student is selected by the Mathematics Depart- Department Prizes and Awards ment’s honors committee on the basis of academic per- Recipients of three new Department Teaching Awards formance, the quality and variety of mathematics courses were announced at the department’s annual holiday taken, and faculty recommendations. party on Friday, December 7. The Teaching Recogni- tion Award was given to Al Schatz, the Junior Faculty The Eleanor Norton York Award for 2001–2002 was Teaching Award to Ravi Ramakrishna and the Graduate awarded to Karen Masters and Britt Scharringhausen in Student Teaching Award to Lee Gibson. Astronomy and Christopher Francisco in Mathematics. The York Award was established by friends of Eleanor The Robert John Battig Graduate Prize was awarded York, who died of cancer in 1993. Each year a student in to Fernando Marques. Recipients of the Battig Prize are the Mathematics Department and a student in the As- graduate students in mathematics at Cornell who have tronomy Department, in which Eleanor was employed, passed their A exam (typically in their second year of are selected to receive this award. The recipients are study). Any such graduate student is eligible regardless chosen from those in the middle of their graduate ed- of social and nancial background. A department com- ucation on the basis of their achievements to date to mittee composed of the chair, the director of graduate encourage them to have even more success in the future. studies and three members of the graduate admissions committee select a recipient each year based on excel- Special Honors and Awards lence and promise in mathematics. Harry Kesten, Gregory Lawler and John Smillie have The department sponsored the third annual Freshman been invited to address the International Congress of Math Prize Exam this year. This is a challenging prize Mathematicians, to be held in August 2002 in Beijing, exam with cash awards open to all freshmen at Cornell. China. The ICM is held once every four years and is The winner this year was Yong-Jae Kwon. Second prize attended by thousands of mathematicians from around went to Shawn Drenning and Guanhan Chew. Other the world. winners were Tomohiko Tanabe, Scott Schi man, Jerry Chiang, Katya Isichenko, Hemanth Srinivas, Jonathan John Guckenheimer was elected a fellow of the Amer- Blender, Wei Yoong Teo and Harikrishna Palaiyanur. ican Association for the Advancement of Science this year. He was recognized for his contributions to the sci- The Hutchinson Fellowship was awarded to Dan Ciub- ences at the February 16th Fellows Forum during the otaru, Jean Cortissoz, Yuval Gabay and Sam Hsiao. AAAS Annual Meeting in Boston, Massachusetts. Awarded to mathematics graduate students who have been outstanding in their work as teaching assistants or John was also appointed to the group of Founders — as students in the graduate program, the Hutchinson a kind of board of trustees — of Cornell’s Computing Fellowship provides one semester of relief from teaching and Information Sciences (CIS). CIS is a new college, to allow the students to work on their thesis problems. run by Dean Robert Constable and the Founders, with Accordingly, it is given to students who have completed responsibility for computer science and for interacting three years of study and are not in their nal year. with other departments on related issues.
Kenneth Brown presented the Ithaca High School Se- Ravi Ramakrishna was honored this year for his commit- nior Prize this year to Zach Cater-Cyker, a senior who ments to both research and teaching. He was awarded a has demonstrated substantial interest and signi cant na- Centennial Research Fellowship by the American Math-
The Year in Review 2001–2002 7 ematical Society, an award which is made annually to year in a row that one of the Cornell recipients was a outstanding mathematicians to help further their careers mathematics major. in research. Ravi was also presented with a Stephen and Margery Russell Teaching Award by the College of Arts Instructional Activities and Sciences for his devotion to teaching. The faculty taught 121 courses in 204 lectures and Richard Durrett was named a Fellow of the American 168 recitations during the 2001–2002 academic year, gen- Academy of Arts & Sciences, the nation’s preeminent erating 22,258 credit hours. They taught 5,690 students learned society. Among the academy’s fellows are schol- aided by 89 teaching assistants and associates. The en- ars in mathematics, the physical and biological sciences, rollment gures are re ected on pp. 10–11. The Dept. medicine, the social sciences and humanities, business, of Theoretical and Applied Mechanics shares the teach- government, public a airs, and the arts, including more ing of engineering calculus and is accredited with 50% of than 160 Nobel Prize laureates and 50 Pulitzer Prize the credit hours for MATH 190 and 191 in the fall and winners. MATH 293 and 294 in the fall and spring; the remaining 18,536 credit hours are accredited to Mathematics. Stephanie van Willigenburg, a visiting assistant pro- fessor, was awarded a University Faculty Award by Curriculum Changes the Natural Sciences and Engineering Research Coun- cil (NSERC) of Canada. NSERC awards 20 of these Two new courses were introduced into the department’s awards annually to talented Canadian female scientists. curriculum during the 2001–2002 academic year. Recipients enjoy a reduced teaching load for 3–5 years thanks to salary contributions from this award. MATH 311, Introduction to Analysis, provides a transi- tion from calculus to theoretical analysis and emphasizes Graeme Bailey, adjunct professor in mathematics and the understanding and construction of proofs in that area director of the computer science MEng program, was of mathematics. It is designed to provide for mathemat- awarded one of the rst Kendall S. Carpenter Memorial ics majors who do not take the honors analysis sequence Advising Awards. The $5,000 award was established MATH 413–414. by Stephen Ashley, a member of the Cornell Board of Trustees, to honor his former advisor; it recognizes “sus- MATH 321 was o ered with the new title Manifolds and tained and distinguished contributions of professorial Di erential Forms and with a completely revised syl- faculty and senior lecturers to undergraduate advising.” labus. Developed and taught by Reyer Sjamaar, it treats vector calculus on manifolds and its applications to par- SIAM awarded the rst (biennial) Moore Prize for Ap- tial di erential equations, uid mechanics and electro- plications of Interval Analysis to Warwick Tucker,an magnetism. H. C. Wang assistant professor, for his paper A rigor- ous ODE solver and Smale’s 14th problem, Foundations Stimulated by a mandate of its ve-year NSF VIGRE of Computational Mathematics 2 no. 1 (2002), 53–117. grant, the Mathematics Department began a compre- The prize was awarded at a ceremony at the SIAM Work- hensive review of its entire curriculum in late 1999 and shop on Validated Computing 2002 in Toronto. continued it the entire 2001–2002 academic year. After reviewing how the department serves students outside Peter Clark, a sophomore majoring in mathematics and the Mathematics Department we decided to introduce biology, and a college scholar, was one of four Cornell re- next year MATH 323, Introduction to Di erential Equa- cipients of a Barry M. Goldwater Scholarship in science tions. It is basically designed for students who wish to and mathematics. The Goldwater Scholarship, estab- learn about basic properties of and methods for both or- lished by Congress in 1986 to honor Senator Barry M. dinary and partial di erential equations in one semester Goldwater, was designed to encourage outstanding stu- (rather than taking one course on each of ordinary and dents to pursue careers in the elds of mathematics, the partial di erential equations, as is presently o ered at natural sciences and engineering. It is a premier un- the 400 level). Considering that the preenrollment is at dergraduate award of its type in these elds. The one- 29, such a course appears to ll a need. and two-year scholarships cover college expenses up to $7,500 per year, including tuition, fees, books and room Graduate Curriculum Review: A committee chaired by and board. This is the seventh year in a row that Cornell Dan Barbasch reviewed the curriculum for new graduate has had three or more Goldwater winners and the third students. Our graduate program has been generally suc-
8 The Year in Review 2001–2002 cessful, but it has not been reviewed in over twenty years. MATH 190, 191 and 192 — were o ered in fall 2001, In the last two years, discussions among Louis Billera, with an average class size of 25 students. director of graduate studies, and the mathematics grad- uate students have uncovered problems with the delivery According to the restructuring agreement, part of the of the four required courses in the Ph.D. program. While instructional resources needed to sta the small classes not questioning the speci c requirements, many gradu- is supplied by faculty recruited from scienti c depart- ate students expressed that the amount of written work ments throughout the university. These faculty, who required in these courses had far outstripped the time are highly quali ed to teach the mathematics relevant available to do it, making “doing the problems” rather to engineering calculus, complement faculty and instruc- than “learning the material” the primary focus of many tional teaching assistants provided by the two core de- students. In this atmosphere, variation in the course partments, Mathematics and T&AM. In fall 2001 we syllabi (as has been the case in 631 and 612) has been a were pleased and fortunate to have recruited the follow- source of particular irritation. ing faculty: Joel Ariaratnam (Mathematics), After an extremely intense rst-year experience, many Bingham Cady (T&AM), students nd the second and third year to be a time without much focus, and they drift without much guid- T. Michael Duncan (Chemical Engineering), ance until they are forced (by policies of the Graduate Chung-Yuen Hui (T&AM), School) to form a committee and take the A exam. Stu- Richard Lovelace (Applied & Engineering Physics), dents indicated that they would like more structure and Anita Mareno (Mathematics), guidance in the program. Jane Wang (T&AM), In general, the graduate committee agreed that the work- Abdul-Aziz Yakubu (Biometrics and T&AM). load for basic courses should be such that a student with This was Prof. Cady’s third year in the program, full teaching assistant duties should be able to take three Prof. Duncan’s fourth, Prof. Hui’s third, Prof. Lovelace’s courses per semester. Special care should be taken that second and Prof. Wang’s third. Professor Cady will con- this is possible for rst-year students. The faculty voted tinue with the program next fall. in favor of creating a canon of six courses with a certain degree of regularity, with TA support and emphasizing that these are important courses for the students, creating two semesters of algebra where there is currently one semester, adding the course on di erentiable manifolds (MATH 652) to the list of required courses. The committee will continue to work on the curriculum next year.
Interdisciplinary Instructional Activity Engineering Restructuring: The Department of Math- ematics, in collaboration with the Department of The- oretical and Applied Mechanics in the College of Engi- neering, completed the fth year of an experimental pro- gram for the restructuring of the teaching of engineering calculus. The object of this program is the delivery of instruction in small classes for the second-semester en- gineering calculus course, MATH 192, during the fall semesters. The program thus continues a process, be- gun in the early 1990s, of replacing large lectures by small classes in all of the rst-year engineering calcu- lus courses. Thirty classes in these three courses —
The Year in Review 2001–2002 9 Mathematics Course Enrollment Statistics
Course and Title Format Instructor Enroll Cr Hrs Semester 103 Mathematical Explorations Lecture Morley, Taimina, A. Solomon 66 198 Fall 2001 103 Mathematical Explorations Lecture B. West, J. West 57 171 Spring 2002 105 Finite Math For the Life and Social Sciences Lec/Sec Durrett 113 339 Fall 2001 106 Calculus For The Life and Social Sciences Lec/Sec Salo -Coste 160 480 Spring 2002 111 Calculus Lecture Bajnok, Coleman, DeSilva, 358 1,432 Fall 2001 Rybnikov, M. Terrell (Czar) 111 Calculus Lecture Cohen (Czar) 112 448 Spring 2002 112 Calculus Lecture Earle (Czar) 178 712 Fall 2001 112 Calculus Lecture Bajnok, DeSilva, Sen (Czar) 200 800 Spring 2002 121 Honors Calculus Lec/Sec Henderson 14 56 Fall 2001 122 Honors Calculus Lec/Sec Mitrea, Strichartz 47 188 Fall 2001 122 Honors Calculus Lec/Sec Salur 20 80 Spring 2002 171 Statistical Theory and Applications Lec/Sec Bendikov, Hwang, Nussbaum 93 372 Fall 2001 171 Statistical Theory and Applications Lec/Sec Bendikov, Hwang, Schweinsberg, Tsai 93 372 Spring 2002 189 FWS: Experiencing Math Through Writing Seminar Cynthia Francisco 16 48 Spring 2002 190 Calculus For Engineers Lec/Sec Hui (T&AM)* 24 96 Fall 2001 191 Calculus For Engineers Lec/Sec Guckenheimer (Czar), Schatz, 259 1,036 Fall 2001 Z. Wang (T&AM)*, Yakubu (T&AM)* 191 Calculus For Engineers Lec/Sec Schatz 6 24 Spring 2002 192 Calculus For Engineers Lec/Sec Bux, Cady (T&AM)*, Connelly (Czar), 460 1,840 Fall 2001 Duncan (ChemE), Lovelace (A&EP), Mareno, Ram rez, Smith, Yakimov 192 Calculus For Engineers Lec/Sec Ramakrishna 283 1,132 Spring 2002 213 Calculus Lec/Sec van Willigenburg 16 64 Fall 2001 213 Calculus Lec/Sec Bendikov 15 60 Spring 2002 221 Linear Algebra and Calculus Lec/Sec Dindos, Limic, Nerode, Sjamaar 100 400 Fall 2001 221 Linear Algebra and Calculus Lec/Sec Lawler, Ram rez, Vogtmann 75 300 Spring 2002 222 Calculus Lec/Sec Back, Qian 47 188 Fall 2001 222 Calculus Lec/Sec Back, Qian, Speh 65 260 Spring 2002 223 Honors Linear Algebra and Calculus Lec/Sec Hubbard, Tucker 43 172 Fall 2001 224 Honors Linear Algebra and Calculus Lec/Sec Tucker 34 136 Spring 2002 231 Linear Algebra Lecture R. Terrell 16 48 Spring 2002 281 Deductive Logic Lecture Hodes (Philosophy) 1 4 Fall 2001 293 Engineering Mathematics Lec/Sec Jenkins (T&AM)*, Stillman 370 1,480 Fall 2001 293 Engineering Mathematics Lec/Sec Burns (T&AM)*, Stillman 450 1,800 Spring 2002 294 Engineering Mathematics Lec/Sec K. Brown, R. Terrell 386 1,544 Fall 2001 294 Engineering Mathematics Lec/Sec Jenkins (T&AM)*, Phoenix (T&AM)* 366 1,464 Spring 2002 311 Introduction to Analysis Lecture Mitrea 26 104 Spring 2002 321 Manifolds and Di erential Forms Lec/Sec Sjamaar 19 76 Fall 2001 332 Algebra and Number Theory Lecture Smithline 39 156 Fall 2001 336 Applicable Algebra Lecture Berest, K. Brown, Rybnikov, 89 356 Spring 2002 van Willigenburg 356 Groups and Geometry Lecture Hatcher 22 88 Spring 2002 362 Dynamic Models in Biology Lecture Ellner (E&EB) / Guckenheimer 9 27 Spring 2002 384 Foundations of Mathematics Lecture Hodes (Philosophy) 10 40 Fall 2001 401 Honors Seminar: Topics In Modern Math. Lecture Barbasch 5 20 Spring 2002 402 Smorgasbord Seminar Seminar Strichartz 4 4 Fall 2001 403 History of Mathematics Lecture Taimina 17 68 Spring 2002 413 Honors Introduction to Analysis Lecture Bendikov, Salo -Coste 57 228 Fall 2001 414 Honors Introduction to Analysis Lecture Wahlbin 32 128 Spring 2002 418 Function Theory of One Complex Var. Lecture Dynkin 11 44 Spring 2002 420 Di erential Equations & Dynamical Systems Lec/Sec Tucker 21 84 Fall 2001 420 Di erential Equations & Dynamical Systems Lec/Sec Vladimirsky 17 68 Spring 2002 422 Applied Complex Analysis Lec/Sec Wahlbin 29 116 Spring 2002 424 Wavelets and Fourier Series Lecture Fickus 36 144 Spring 2002 427 Intro. to Ordinary Di erential Equations Lecture Dindos 5 20 Spring 2002 428 Intro. To Partial Di erential Equations Lecture Ilyashenko 17 68 Fall 2001 431 Introduction To Algebra Lecture Chase 35 140 Fall 2001 432 Introduction To Algebra Lecture Rybnikov 13 52 Spring 2002 433 Honors Introduction To Algebra Lecture Dennis, Tsai 40 160 Fall 2001 434 Honors Introduction To Algebra Lecture Dennis 24 96 Spring 2002 441 Introduction To Combinatorics Lecture Swartz 24 96 Fall 2001 451 Euclidean and Spherical Geometry Lecture Henderson 19 76 Fall 2001 452 Classical Geometries Lecture Connelly 17 68 Spring 2002 453 Introduction To Topology Lecture J. West 10 40 Fall 2001 454 Introduction To Di erential Geometry Lecture Smith 8 32 Spring 2002 455 Applicable Geometry Lecture Billera 6 24 Fall 2001
10 Mathematics Course Enrollment Statistics Course and Title Format Instructor Enroll Cr Hrs Semester 471 Basic Probability Lecture Schweinsberg 20 80 Fall 2001 472 Statistics Lecture Nussbaum 11 44 Spring 2002 483 Intensional Logic Lecture Gra (Philosophy) 1 4 Spring 2002 486 Applied Logic Lecture R. Miller 7 28 Spring 2002 490 Supervised Reading and Research Ind Stud Faculty 9 34 Fall 2001 490 Supervised Reading and Research Ind Stud Faculty 12 43 Spring 2002 500 College Teaching Lecture M. Terrell 15 15 Fall 2001 505 Educ. Issues In Undergraduate Mathematics Lecture Henderson 5 20 Spring 2002 507 Teaching Secondary Mathematics Lecture A. Solomon 10 40 Spring 2002 508 Math. For Secondary School Teachers Lecture A. Solomon 3 3 Fall 2001 508 Math. For Secondary School Teachers Lecture A. Solomon 5 8 Spring 2002 611 Real Analysis Lecture L. Gross 23 92 Fall 2001 612 Complex Analysis Lecture Hubbard 15 60 Spring 2002 613 Topics In Analysis Lecture Hubbard 5 20 Fall 2001 615 Mathematical Methods In Physics Lecture L. Gross 10 40 Fall 2001 617 Dynamical Systems Lecture Ilyashenko 9 36 Fall 2001 619 Partial Di erential Equations Lecture Wahlbin 10 40 Fall 2001 620 Partial Di erential Equations Lecture Mitrea 4 16 Spring 2002 621 Measure Theory and Lebesgue Integration Lecture Fickus 8 32 Fall 2001 631 Algebra Lecture Ramakrishna 21 84 Fall 2001 634 Algebra Lecture Stillman 7 28 Spring 2002 650 Lie Groups Lecture Dynkin 8 32 Spring 2002 651 Introductory Algebraic Topology Lecture Hatcher 15 60 Spring 2002 652 Di erentiable Manifolds Lecture Barbasch 2 8 Fall 2001 661 Geometric Topology Lecture Conant 11 44 Fall 2001 662 Riemannian Geometry Lecture Smith 5 20 Spring 2002 671 Probability Theory Lecture Dynkin 17 68 Fall 2001 672 Probability Theory Lecture Lawler 12 48 Spring 2002 674 Introduction To Mathematical Statistics Lecture Nussbaum 4 16 Spring 2002 681 Logic Lecture Nerode 4 16 Spring 2002 711 Seminar In Analysis Lecture Salo -Coste 14 56 Fall 2001 713 Functional Analysis Lecture L. Gross 12 48 Spring 2002 715 Fourier Analysis Lecture Dindos 5 20 Fall 2001 717 Applied Dynamical Systems Lecture Guckenheimer 5 20 Spring 2002 731 Seminar In Algebra Seminar Billera 10 40 Fall 2001 732 Seminar In Algebra Seminar Dennis 3 12 Spring 2002 735 Topics In Algebra Lecture Barbasch 3 12 Fall 2001 735 Topics In Algebra Lecture Yakimov 4 16 Spring 2002 737 Algebraic Number Theory Lecture Sen 4 16 Fall 2001 739 Topics In Algebra Lecture Bux 11 44 Spring 2002 751 Seminar In Topology Seminar Swartz 4 16 Fall 2001 752 Seminar In Topology Seminar K. Brown 8 32 Spring 2002 753 Algebraic Topology Lecture Hatcher 8 32 Fall 2001 757 Topics In Topology Lecture Cohen 3 12 Fall 2001 758 Topics In Topology Lecture Conant 4 16 Spring 2002 761 Seminar In Geometry Seminar Escobar 5 20 Fall 2001 762 Seminar In Geometry Seminar Escobar 5 20 Spring 2002 767 Algebraic Geometry Lecture Berest 9 36 Spring 2002 771 Seminar In Probability and Statistics Seminar Seminar 0 0 Fall 2001 772 Seminar In Probability and Statistics Seminar Seminar 0 0 Spring 2002 777 Stochastic Processes Lecture Ram rez 7 28 Fall 2001 778 Stochastic Processes Lecture Limic 6 24 Spring 2002 781 Seminar In Logic Seminar Shore 5 20 Fall 2001 782 Seminar In Logic Seminar Nerode 5 20 Spring 2002 783 Model Theory Lecture R. Miller 4 16 Spring 2002 784 Recursion Theory Lecture Shore 8 32 Fall 2001 788 Topics In Applied Logic Lecture Platek 12 48 Fall 2001 790 Supervised Reading and Research Ind Stud Faculty 18 96 Fall 2001 790 Supervised Reading and Research Ind Stud Faculty 16 60 Spring 2002
NOTE: Enrollments in graduate courses may not re ect total attendance. Faculty and graduate students are not required to register.
Dept* Total * The Department of Theoretical and Applied TOTALS Courses Lectures Enroll Cr Hrs Cr Hrs Mechanics shares in the teaching of engineer- Fall Semester 59 115 3,145 10,267 12,357 ing calculus and is accredited with 50% of the Spring Semester 62 89 2,545 8,269 9,901 credit hours for Math 190 and 191 in the fall and Math 293 and 294 in the fall and spring; Academic Year 121 204 5,690 18,536 22,258 the remainder are accredited to Mathematics.
Mathematics Course Enrollment Statistics 11 Mathematics Department Directory 2001–2002
Professors: Assistant Professors: Visiting Faculty: Dan Barbasch Yuri Berest Joel Ariaratnam Louis Billera Irena Peeva Alexander Bendikov Kenneth Brown Ravi Ramakrishna Michael Coleman Stephen Chase Zhongmin Qian Marshall Cohen Acting Professor: Sema Salur Robert Connelly Allen Back Brian Smith R. Keith Dennis Daina Taimina Richard Durrett Adjunct Professor: Stephanie van Willigenburg Eugene Dynkin Graeme Bailey Cli ord Earle Visiting Program Participants: Jos e Escobar Adjunct Associate Professor: Bela Bajnok Leonard Gross Robert Terrell Carolyn DeSilva John Guckenheimer Allen Hatcher Postdoctoral Associate: Visiting Scholars: David Henderson Ricardo Oliva Oleg Chalykh John Hubbard Yasunari Fukai J. T. Gene Hwang H.C. Wang Assistant Professors: Ryuichi Fukuoka Yulij Ilyashenko Kai-Uwe Bux Alexey Glutsyuk Peter Kahn Martin Dindo s Martin Grothaus Harry Kesten Vlada Limic Thomas Rishel Gregory Lawler Irina Mitrea Sue Whitesides Michael Morley Jos e Ram rez Anil Nerode Konstantin Rybnikov Teaching Associate: Michael Nussbaum Jason Schweinsberg Richard Furnas Oscar Rothaus Harrison Tsai Laurent Salo -Coste Warwick Tucker Graduate Students: Alfred Schatz Alexander Vladimirsky Bryant Adams Shankar Sen Milen Yakimov Christian Avart (nondegree) Richard Shore James Belk John Smillie, chair VIGRE Assistant Professors: David Benbennick Birgit Speh James Conant Janet Best Michael Stillman Matthew Fickus Jason Bode Robert Strichartz Anita Mareno Sylvain Bonnot (nondegree) Karen Vogtmann Russell Miller Ryan Budney Lars Wahlbin Lawren Smithline Kristin Camenga James West Edward Swartz Edoardo Carta Nelia Charalambous Professors Emeritus: Senior Lecturers: Dan Ciubotaru James Bramble Avery Solomon Jean Cortissoz Roger Farrell Maria Terrell Alan Robert Demlow G. Roger Livesay Beverly West Amelie DiFabio (nondegree) Lawrence Payne Farkhod Eshmatov Alex Rosenberg Field Members from Christopher Francisco Moss Sweedler Other Departments: Yuval Gabay Timothy Healey (T&AM) Ferenc Gerlits Associate Professors: Dexter Kozen (Computer Science) Lee Gibson Richard Platek Philip Protter (OR&IE) Leah Gold Reyer Sjamaar Richard Rand (T&AM) Noam Greenberg James Renegar (OR&IE) William Gryc
12 Mathematics Department Directory 2001–2002 Pavel Gyrya Administrative Support Sta : Timothy Goldberg Radu Haiduc Linda Clasby Heather Heston Spencer Hamblen Arletta Havlik Sarah Koch Christopher Hardin Joy Jones Andrei Maxim Matthew Horak Michelle Klinger Radu Murgescu Geo rey Christopher Hruska Gayle Lippincott Michael O’Connor Jennifer Suzanne Lynch Hruska Brenda Smith Jay Schweig Samuel Hsiao Donna Smith Mauricio Velasco Henri Johnston Catherine Stevens James Worthington Todd Kemp Colette Walls, manager Jessica Zuniga Evgueni Klebanov Sebastien Krief (nondegree) Computer Consultants: Faculty Departures: JaEun Ku Douglas Alfors Konstantin Rybnikov Dmitriy Leykekhman Robert Terrell Hway Kiong Lim Faculty Retirements: Yi Lin Instructional Computer Lab: Harry Kesten Swapneel Mahajan Allen Back, director Richard Platek Fernando Marques Jason Martin Mathematics Support Center: Faculty Leaves: Je rey Mermin Douglas Alfors, director Eugene Dynkin, spring 2003 Joseph Stephen Miller Richard Furnas Cli ord Earle, academic year Vadims Moldavskis Leonard Gross, fall 2002 Antonio Montalban Mathematics Library Sta : John Guckenheimer, fall 2002 Steven Morris Steven Rockey, librarian J. T. Gene Hwang, spring 2003 Melanie Pivarski Natalie Sheridan Michael Morley, fall 2002 Rajmohan Rajagopalan Ravi Ramakrishna, academic year David Robert Revelle Laurent Salo -Coste, spring 2003 Roland Roeder Changes for 2002–2003 Shankar Sen, fall 2002 Gil Rosenberg John Smillie, academic year Franco Saliola New H.C. Wang Asst. Professors: Everilis Santana-Vega (on leave) Indira Chatterji Hasanjan Sayit Rodrigo Perez Rebecca Schuller Dan Za ran Fernando Schwartz Achilleas Sinefakopoulos New VIGRE Asst. Professors: Steven Sinnott Tara Brendle Serguei Slavnov Alexander Meadows Maria Sloughter Brian Smith Aaron Solo Sarah Agnes Spence New Adjunct Asst. Professors: John Thacker Vlada Limic Jos e Antonio Trujillo Ferreras Warwick Tucker Jonathan Turnes Brigitta Vermesi New Graduate Students: Shawn Walker Drew Armstrong Treven Wall David Biddle Russell Woodroofe Andrew Cameron Yan Zeng Benjamin Chan Yan Zhang Nikolai Dimitrov Huibin Zhou Bradley Forrest
Mathematics Department Directory 2001–2002 13 New Faculty Members for 2002–2003
Tara Brendle Brian Smith VIGRE Assistant Professor VIGRE Assistant Professor Tara Brendle received a Ph.D. in mathematics in May Brian Smith received a Ph.D. in mathematics in August 2002 from Columbia University under the direction of 2001 from the University of Alabama at Birmingham un- Joan Birman. Professor Brendle’s research interests are der the direction of Gilbert Weinstein. Professor Smith’s in geometric topology, 3-manifolds, Heegaard splittings, research interests include di erential geometry, nonlinear Torelli groups, and representations of mapping class partial di erential equations and general relativity. His groups of surfaces. Professor Brendle is especially in- current research interests involve the study of asymptot- terested in the algebraic structure of the Torelli group. ically at Riemannian 3-manifolds of nonnegative scalar curvature.
Indira Chatterji H. C. Wang Assistant Professor Rodrigo Perez H. C. Wang Assistant Professor Indira Chatterji received a Ph.D. in mathematics in Sep- tember 2001 from ETH Z urich in Switzerland under the Rodrigo Perez received a Ph.D. in mathematics in May direction of Marc Burger and Alain Valette. Professor 2002 from SUNY at Stony Brook under the direction of Chatterji’s research area is centered around the Baum- John Milnor. Professor Perez’s research interests are in Connes conjecture, focusing on the aspects related to complex dynamics in both one and several variables. In geometric group theory and topology. Professor Chat- particular, Professor Perez’s work focuses on the combi- terji’s current research interests are in property (RD) natorial structure of orbits and its implications on the and relative property (RD) and the consequences of the geometry of Julia sets. Baum-Connes/Bost related conjectures in many di er- ent elds. Dan Za ran H. C. Wang Assistant Professor Alexander Meadows Dan Za ran received a Ph.D. in mathematics in Decem- VIGRE Assistant Professor ber 2000 from the Universit e de Provence in Marseille, Alexander Meadows received a Ph.D. in mathematics in France, under the direction of Karl Oeljeklaus. Profes- May 2002 from Stanford University under the direction sor Za ran’s research interests are in the area of com- of Leon Simon. Professor Meadows’ research interests plex holomorphic geometry and complex analysis: clas- include nonlinear elliptic partial di erential equations, si cation of compact complex surfaces; Inoue-Hirzebruch geometric measure theory and calculus of variations. His surfaces; Serre problem (holomorphic ber bundles and current research focuses on the geometry of singular sets Stein spaces); holomorphic foliations; singularities of and the regularity of solutions to elliptic PDEs arising complex surfaces; dynamics of H enon automorphisms. in di erential geometry. From 1995 through 2001 he taught at the Universit e de Provence. In 2001–2002 Professor Za ran was in Bochum, Germany, working with A. T. Huckleberry.
14 New Faculty Members for 2002–2003 Special Programs and Activities
The Math Explorers Club The Math Explorers Club, a program for high school Ratio by Robert Strichartz and Geometry and Topology students funded by the department’s VIGRE grant, be- of Surfaces by Edward Swartz. Two modules were of- gan its second full year of operation this fall. The Sat- fered in the spring: Probability and Statistics by Ravi urday meetings are open to all interested students at Ramakrishna and From the Finite to the More Than In- no charge. The goal of the club is two-fold: to stim- nite by James Conant. ulate an interest in mathematics by exposing students The program is run by four graduate students — to material not usually encountered in the high school Sharad Goel (CAM), Todd Kemp, Maria Sloughter and curriculum and to provide a peer group of students who Tiberiu Tomita (CAM) — and has modules taught by share an interest in mathematics. faculty members. It is a great opportunity for graduate Participants choose among modules that provide in- students to interact with faculty in an informal setting struction in interesting areas of mathematics, computer and to gain valuable experience in education and out- lab activities and problem-solving sessions. Two in- reach that will help them in future job searches. Par- tense hour-long sessions are separated by a break, during ticipants enjoy the challenge of communicating the ex- which participants of all modules can gather to relax and citement of mathematics to young and eager minds and talk things over. spreading the word that mathematics is a cool subject. Three modules were o ered this fall: Knot Theory by We expect the program to evolve and grow in response Graeme Bailey, The Fibonacci Sequence and the Golden to the needs and interests of the participants.
Mathematics Awareness Month April is Mathematics Awareness Month, and once In this talk, Tucker showed that there is a narrow (but again the department organized several activities as our non-empty!) region that ts in between these two schools contribution to this national event. The general public of thought. The main underlying idea is to NOT try was invited to come to Malott Hall for the third annual to model the real numbers using a computer’s oating public lecture, aimed at presenting interesting new de- point numbers, but rather to enclose entire sets of real velopments in mathematics to a wider audience. numbers in small intervals with well-de ned endpoints. As it turns out, computers handle this situation rather Public Lecture well, allowing theorems to be proven with mathematical This year’s lecture, Using a Computer to Do Rigorous rigor. Mathematics, was given by Warwick Tucker. The au- dience — composed of high school students, secondary Mathematics Awareness Week at Area Schools math teachers, sta and students from both Cornell and The American Mathematical Society encourages uni- Ithaca College, and members of the general public — versities to support the idea of a math awareness week was quite appreciative. in April at area schools. We have participated in this It is widely understood that mathematics had an im- practice since its inception. We sponsor a T-shirt design portant role in the development of computers, and com- contest, won this year by Joshua Berggren, a sophomore puters have had an enormous in uence on all areas of life at Ithaca High School. The Departments of Mathematics and learning. But the role of computers in mathematics at Cornell University and Ithaca High School underwrote itself is a much more subtle and controversial issue. the cost of producing 90 shirts that were distributed to The general feelings about using computers in science sta and students at Cornell and several area schools. can be divided into two main categories: One group of At Ithaca High, students won the shirts as prizes for researchers considers all problems to be solvable, given solving a math problem of the day, or a more extensive a su ciently large and fast computer. The other group week-long challenge. claims that computers are inherently inexact, and that virtually no results produced by machines are to be trusted.
Special Programs and Activities 15 Expanding Your Horizons Created in 1976, Expanding Your Horizons in Science graduate students) to a game, and by correctly deciding and Mathematics is a national program aimed at en- whether or not to go rst the girls defeated the Expert! couraging middle-school girls’ interest in math and sci- From there the group moved on to two-pile Nim, where ence and motivating them to continue taking math and players take turns removing however many items they science courses throughout high school. Organized and want from exactly one of two piles. The player who takes run by women in mathematics and science, it is held in the last item wins. Soon the girls solved this and moved over 100 locations nationwide. The Math/Science Net- on to the three-pile case. After experimenting with dif- work — a non-pro t membership organization of edu- ferent strategies for a while, the entire group challenged cators, scientists, mathematicians, parents, community and defeated the Expert. leaders, and government and corporate representatives The Center for Applied Mathematics (CAM) also — licenses and coordinates this network of EYH confer- sponsored a session, Symmetry and Tesselations,in ences (www.expandingyourhorizons.org). M/SN’s mis- which Nelia Charalambous and Jean Cortissoz partici- sion is to promote the continuing advancement in math- pated. During the rst part of the presentation, Mer- ematics and science education of all people, with a par- cedes Franco (CAM) showed the girls some examples of ticular emphasis on the needs of women and girls. It tilings from art around the world and proceeded to de- initiates local EYH sites and provides them with tech- scribe the symmetries found in tesselations of the plane. nical assistance and conference and planning materials, With these ideas in mind, the girls were given a square as well as support services such as coordinated publicity with a xed design inside it, and they were asked to ll and public relations posters and buttons. The Network a page with the square and symmetric images of it. The also provides a “networking” link between sites. purpose of the exercise was to create a pattern in the On April 27, 2002, the graduate students of the Cor- plane that could have a number of symmetries. (For ex- nell Mathematics Department once again participated ample, it could be re ected over a line rotated about a in a day of hands-on workshops in mathematics for 7th point.) To make things even more interesting, the co- and 8th grade girls. The Mathematics Department spon- ordinators asked them to color their tiling and see how sored a workshop on game theory, run by several stu- coloring could preserve or completely remove the sym- dents in the department. In the workshop The Secret metry of a pattern. The possibilities were too many to of Nim, Cynthia Bowers Francisco, Leah Gold, Melanie be explored in half an hour, but the girls took some Pivarski, Rajmohan Rajagopalan and Maria Sloughter more pictures home with them to practice on. During worked with a group of girls using M&Ms and pretzels the second part of the session, Nelia demonstrated how to study the game of Nim. They started by having the one could go about nding the symmetries in the work girls pair up to play the 20 game: Starting at the num- of M. C. Escher. The girls were given a few of Escher’s ber 20, each player takes turns subtracting an integer drawings and asked to look for the fundamental region between 1 and 4 until zero remains; the player who ends that the artist used for tiling the plane. Knowing the at zero wins. After playing the game for a bit, the girls basic tile helped in nding many of the symmetries, and found the pattern and generalized it to similar games. all of a sudden a complicated work of art was broken Then the entire group challenged an ‘Expert’ (one of the down into a few simpler patterns.
Spring Concert Series On the evening of Sunday, May 5, 2002, a group of tal- Duo F ur Zwei Gitarren, op. 34 , Fernando Sor: John ented faculty, visitors, graduate students, undergradu- Hubbard and Warwick Tucker — guitar. ates, family and friends of the Mathematics Department Valse Brilliante in A Minor,Fr ed eric Chopin: Diana performed before an appreciative audience in the depart- Dorothy Hubbard — piano. ment’s twelfth annual Spring Concert, held at the A. D. Moj Dilbere, trad. Bosnian: Vlada Limi c — guitar, vo- White House. As the program below shows, perform- cal; Gregory Lawler — guitar, prim, vocal. ers entertained the audience with a variety of selections, Ne Dirajte mi Ravnicu, Miroslav Skoro: Vlada Limi c— ranging from classical to modern. guitar, vocal; Gregory Lawler — guitar, prim, vocal. Ariel’s Song, Robert Strichartz (words from Shake- Prelude in C Major (Book 1 of the Well-Tempered speare’s The Tempest): Kristin Camenga, Todd Clavier), Johann Sebastian Bach: Lawren Smithline Kemp — vocal; Robert Strichartz — piano. — piano. Never Rain, Brian Luko : Brian Luko — piano.
16 Special Programs and Activities Au pays o u se fait la guerre, Henri Duparc (Po eme Nocturne, Opus 9, #2 (in E- at major),Fr ed eric de Th eophile Gautier): Eleanor Hubbard — vocal; Chopin: Noam Greenberg — piano. Graeme Bailey — piano. Piano Quartet, Opus 47 (3rd movement), Robert Schu- Rain-Wheels, Clive James (lyrics) and Pete Atkin (mu- mann: Carla Martin — violin; Graeme Bailey — cello; sic): Noam Greenberg — piano; Christopher Hardin Nancy Sundell — viola; Robert Strichartz — piano. — electric guitar (bass); Steve Morris — electric gui- The Merry Maiden and the Tar (from H.M.S. Pinafore), tar; Treven Wall — vocal. Gilbert and Sullivan: John Hubbard, Todd Kemp — Payday Evening, Clive James (lyrics) and Pete Atkin vocal; Graeme Bailey — piano. (music): Noam Greenberg — piano; Christopher A British Tar (from H.M.S. Pinafore), Gilbert and Sul- Hardin — electric guitar (bass); Steve Morris — elec- livan: John Hubbard, Todd Kemp — vocal; Graeme tric guitar; Treven Wall — vocal. Bailey — piano. Cumbia, traditional Colombian music and dance: Mer- I Am the Very Model of a Modern Major General (from cedes Franco, Ariel Cintron-Arias — dancers. Pirates of Penzance), Gilbert and Sullivan: Todd Piano Quartet, 1st movement (Allegro), Robert Palmer: Kemp — vocal; Graeme Bailey — piano. Carla Martin — violin; Robert Strichartz — piano; I Will Survive, D. Fekaris and F. Perren, Stephanie van Nancy Sundell — viola; Graeme Bailey — cello. Willigenburg (lyrics): Kristin Camenga, Stephanie Waltz in C# Minor,Fr ed eric Chopin: Greg Padowski van Willigenburg — vocal; Todd Kemp — piano. — piano. Concerto in D Minor for Two Violins and Piano, Jo- hann Sebastian Bach: Carla Martin, Sebastian Mekas — violin; Kristin Camenga — piano.
Cornell Conference on Analysis and Probability on Fractals Analysis and probability on fractals is an exciting new intended to bring neophytes up to speed on the subject, area of mathematical research that studies basic analytic starting with basic de nitions and examples, and reach- operators and stochastic processes when the underlying ing to the frontiers of research. space is fractal. The books Di usions on Fractals by Martin Barlow, Jun Kigami, Robert Strichartz and M. Barlow (Lecture Notes 1690, Springer, 1998) and Alexander Teplyaev were the members the organizing Analysis on Fractals by Jun Kigami (Cambridge Uni- committee. Invited speakers were: Martin Barlow, versity Press, 2001) and the expository article Analysis University of British Columbia; Richard Bass, Univer- on fractals by R. Strichartz (Notices AMS 46 (1999), sity of Connecticut; Rostislav Grigorchuk, Steklov In- 1199–1208) give an indication of the accomplishments stitute of Mathematics; Ben Hambly, Oxford Univer- in this area in the recent past. Research in this area is sity; Alf Jonsson, University of Umea; Jun Kigami, closely related to work in analysis and probability when Kyoto University; Takashi Kumagai, Kyoto Univer- the underlying space is manifold or a graph. sity; Michel Lapidus, University of California at River- The purpose of the Cornell Conference on Analysis side; Volker Metz, Bielefeld University; Hirofumi Os- and Probability on Fractals (June 16–20, 2002) was to ada, Nagoya University; Christophe Sabot, University of bring together mathematicians who are already working Paris; Robert Strichartz, Cornell University; Alexander in this area, and also graduate students and researchers Teplyaev, University of California at Riverside. There from related areas who wanted to learn more about it. were about 50 outside attendees. Toward this end, the conference included a mini-course
Cornell Topology Festival The topology/geometry group of the Mathematics De- Science Foundation. In the current era of highly special- partment hosted the fortieth annual Cornell Topology ized conferences, the Cornell Topology Festival is note- Festival on May 3–5 this year. Now an internationally- worthy in that — representing the interests of the cur- known tradition, the Festival was founded in part by rent faculty — it presents a broad spectrum of current Paul Olum in 1963 as a small regional conference that mathematics, usually featuring topics in geometric and celebrated the return of spring and reviewed the out- algebraic topology, geometric group theory and geome- standing results in topology during the preceding year. try. The current festival attracts fty to eighty topologists The festival consists of seven or eight one-hour lectures and geometers annually and is funded by the National interspersed with thirty-minute breaks for discussion of
Special Programs and Activities 17 results, conjectures and new theorems. Other activities Dusa McDu , SUNY at Stony Brook: The Topology of include an opening reception, a dinner, an open house Groups of Symplectomorphisms and a picnic. This format encourages a lively and open Yair Minsky, SUNY at Stony Brook: On Thurston’s exchange of ideas and promotes mathematical collabo- Ending Lamination Conjecture ration. This year’s featured speakers and their topics Peter Ozsvath, Princeton University: Holomorphic Disks were: and Low-Dimensional Topology Guoliang Yu, Vanderbilt University: The Novikov Con- Mladen Bestvina, University of Utah: Measured Lami- jecture and Geometry of Groups nations and Group Theory Daniel Biss, Massachusetts Institute of Technology: The The forty- rst Cornell Topology Festival will be held Combinatorics of Smooth Manifolds: Oriented Ma- May 2–4, 2003. (Next year’s schedule will be posted troids in Topology at www.math.cornell.edu/efestival/) Steve Gersten, University of Utah: Isoperimetric In- equalities for Nilpotent Groups
Preparing Future Professors The department’s Preparing Future Professors pro- Speakers included Matt Horak, Mobius bands, Klein bot- gram continues to prepare graduate students for the pro- tles and knots: an intuitive introduction to topology,at fessorate while it attracts attention from outside admin- Ithaca College; Kristin Camenga, A tale of two proofs, istrative agencies. The program was funded this year by at Rochester Institute of Technology; Joseph Miller, The the O ce of the Dean of the College of Arts and Sci- game of Hex: provably pointless or positively playable?, ences, under the direction of Dr. Maria Terrell. at SUNY Cortland; Noam Greenberg, Paradoxes and the Cornell graduate students gave talks to mixed audi- foundations of mathematics: how to escape the serpent’s ences of faculty and students at nearby colleges and tongue, at Wells College; and Todd Kemp, You can’t universities. This experience a orded participants the comb a coconut, unless it’s odd (dimension), at SUNY opportunity to talk about their work in ways that an- Binghamton. Graduate students Sarah Spence, Lee Gib- ticipate both professional meetings and job searches. son and Roland Roeder coordinated the talks.
Special Guest Lectures Kieval Lecture Math Club Guest Lecture Richard Guy, Emeritus and Faculty Professor of the Professor Jordan Ellenberg gave a special guest lec- University of Calgary delivered the 2001 Kieval lecture, ture in April titled The mathematics of Set -or- Every- Fun from Mathematics and Mathematics from Fun,in thing I know about Fourier analysis I learned from play- November. The lecture was an autobiographical history ing cards , sponsored by the Student Activities Finance of combinatorial games. Combinatorics is the branch of Commission. mathematics that includes the enumeration of compli- Set is a fairly popular card game. (To learn about Set, cated con gurations and patterns. visit www.cabinfevergames.com/cf set.html.) Prof. El- Professor Guy has taught mathematics at all levels lenberg spoke about how “sets” in the game correspond from kindergarten to post-graduate in Britain, Singa- to “lines” in various geometries and gave an exposition pore, India and Canada. He has published over 250 pa- of how many cards guarantee that a set will occur. pers and a dozen books, including Winning Ways with Prof. Ellenberg received his A.B. and Ph.D. degrees in Elwyn Berlekamp and John Conway. mathematics from Harvard University. He is currently The Kieval lecture, designed for undergraduate stu- on the faculty of the Princeton University Mathematics dents and members of the public who have a basic sci- Department and is a frequent contributor to the online enti c and mathematical knowledge, is funded through magazine slate.com, writing on issues from baseball to a bequest of the late Dr. Harry S. Kieval ’36. Kieval, politics and how mathematics applies to understanding a longtime professor of mathematics at Humboldt State them. University in Arcata, CA, died in 1994.
18 Special Programs and Activities Research Experiences for Undergraduates Program The Cornell Research Experiences for Undergraduates what is generally thought of as fractal geometry and (REU) program, funded through a grant from the Na- makes contact with many classical areas such as par- tional Science Foundation and supplemented by the de- tial di erential equations, harmonic analysis, analysis on partment’s VIGRE grant, is one of the nation’s leading manifolds and numerical analysis. The students carry summer programs for undergraduate research. During out computer experiments to explore new problems. the summer of 2001, the eighth summer for this program, This summer, the students explored the sampling fourteen undergraduates from across the country, includ- problem: recover a function from just a nite set of its ing such well-known institutions as Harvard, Chicago values, under appropriate spectral hypotheses. The ex- and Cornell and some lesser-known institutions as Uni- perimental results suggest that this problem is actually versity of Missouri at Rolla and North Central College, much better behaved than the classical Shannon sam- came here to work on research projects in three areas: pling theorem. They began work on de ning a nonlinear analysis on fractals, directed by Robert Strichartz, ge- di erential operator, the p-Laplacian, on the Sierpinski ometry of numbers, directed by Konstantin Rybnikov, gasket fractal, and on de ning a standard Laplacian on and discrete geometry, directed by K aroly Bezdek, a vis- the octagasket fractal, which has a more complicated iting professor from E otv os University, Budapest, Hun- structure than the fractals previously studied. They also gary. Graduate students Todd Kemp, Melanie Pivarski continued work begun in summer 2000 in developing a and Franco Saliola assisted with the program. nite element method numerical analysis scheme on the During the past eight years, this program has served pentagasket fractal and using it to help understand the 87 students (20 female) and produced over two dozen re- spectrum of the Laplacian in this case. search papers, published in such journals as Transactions of the AMS, Indiana University Mathematics Journal, Geometry of Numbers Geometria Dedicata and Experimental Mathematics.In Students working with Prof. Konstantin Rybnikov a typical year, the department receives over one hun- studied the geometry of quadratic forms over the in- dred applications. The students in the program receive tegers, or equivalently lattices in high-dimensional Eu- a generous stipend, although some students have come clidean spaces, and certain geometric objects associated with funding from outside sources. One student from with them: the Delaunay polytopes and the Voronoi the program received the Morgan Prize for Undergradu- polyhedron in Sym(n, R). In particular, they studied ate Research, a prestigious national award, and another an in nite series of integer polytopes, introduced by Er- has been nominated for this award based on work done dahl and Rybnikov, called supertopes. They gathered during the program. a great deal of combinatorial information about the su- Students work individually or in small groups on prob- pertopes and made progress toward proving their con- lems that have been carefully chosen to be accessible to jectured Delaunay property. In addition, one of the stu- undergraduate, but are still of interest to the general dents, Kirsten Wickelgren, was successful in proving a mathematical community. Often these problems involve conjecture of Shtogrin and Ryshkov, dating to 1974, con- computer experimentation. At the end of the program, cerning the group of the Voronoi polyhedron. the students give public lectures on their results at an Undergraduate Research Forum, and many go on to give Discrete Geometry talks at various conferences. The students get to hone Students worked with Prof. K aroly Bezdek on a num- their lecturing skills at a weekly jam session in which ber of problems concerning sets of points in nite- they discuss their work with other participants. They at- dimensional vector spaces, not just with respect to the tend the Smorgasbord Seminar, a lecture series in which usual Euclidean distance but more general distances de- members of the department dish out small tastes of what ned by arbitrary norms. One of the students was able research is like in many di erent areas of mathematics. to nd the largest surface density of faces of Voronoi cells in unit sphere packings in Euclidean 3-space. An- Analysis on Fractals other student found estimates for the largest number of Students working with Prof. Strichartz in the program equidistant points that can be placed in a given normed since 1996 have already made important contributions to space and related questions. Other problems studied this developing area, the goal of which is to create the included estimating the minimum diameter of a set of analogs of calculus and di erential equations for func- seven points in a plane (with arbitrary norm) when the tions de ned on fractals. This theory goes far beyond points are at least a distance of one from each other.
Special Programs and Activities 19 Summer Program In summer session 2001, the Mathematics Department Even for traditional calculus courses, the special char- o ered 12 courses in the three-week, eight-week and six- acteristics of summer study allow for a much greater in- week sessions, among them Statistical Theory and Ap- teraction between students and faculty, creating a more plication in the Real World, Applicable Algebra, Calcu- exciting educational experience for both. The Mathe- lus and Engineering Mathematics. Students can choose matics Department enrolled a total of 227 students in from a variety of courses and take whatever they need to summer 2001, including students from Cornell, other col- ful ll their graduation requirements or just get ahead. leges and high schools. High school students who come Mathematical Explorations (MATH 103) is a very pop- to Cornell in the summer are able to experience the vi- ular o ering, both in summers and during the academic tality of mathematical life here. Many of these students year, and is taught in the three-week and six-week ses- apply for undergraduate study at Cornell the following sions. The instructor chooses the topic. In the three- year. In addition to our own faculty, visiting faculty from week session, Prof. Zoran Sunik’s topic was Mathemat- other colleges and universities join us to teach summer ics and Politics; Prof. Thomas Barr taught Cryptology classes. Mathematics graduate students appointed as in the six-week session. teaching assistants provide support to our instructors.
Special Instructional Support Computer Lab Mathematics Support Center Classes that made signi cant use of the lab this An academic support wing of the Mathematics De- year were Statistical Theory (MATH 171), Mathemat- partment, the Mathematics Support Center provides free ical Explorations (MATH 103), Teaching Secondary one-on-one and small-group tutoring, workshops and re- Mathematics (MATH 507) and Multivariable Calculus view sessions on topics of common concern in mathemat- (MATH 222). Classical Geometry (MATH 452), Applied ics, approximately fty brief printed capsules on various Dynamical Systems (MATH 717), Di erential Equa- mathematical topics, and advice, encouragement or re- tions/Dynamical Systems (MATH 420) and several sec- ferrals for students. Although the Center focuses on the tions of elementary Calculus (MATH 112) also made lim- support of introductory courses, it employs both under- ited use of the lab. graduates and postgraduates (about eight each year) of The Math Explorers Club for high school students diverse backgrounds and provides some limited tutoring continued to be a heavy user of the lab many Satur- even in upper-level courses. Douglas S. Alfors directs the day mornings. Students working on senior theses and operations of the MSC and coordinates its e orts with Research Experiences for Undergraduates program par- the instructors of the introductory calculus sequence. ticipants were also signi cant users of the lab. The MSC is located on a main thoroughfare of Malott The frontline resources of the lab currently center on Hall and is consequently quite visible and accessible to the thirteen 1.4 gigahertz Pentium 4 computers dual- students. We have several tutoring areas that are suf- booting Windows 2000 and Redhat Linux. The linux ciently separated from one another to address privacy sides of these machines were improved this year to sup- and noise issues, yet are not so widely separated that port widespread REU and potential classwide dynamical we lose contact with someone who is working on some- systems use. These Pentium 4 machines are supported thing. Our ‘reception area’ can adequately accommodate by the two one-year-old fast Pentium 3 SCSI servers. students who are waiting for their turn to be tutored, We continued to use three older 266 megahertz NT ma- and we have a couple of sites that work nicely for small chines, to meet our course capacity of 30 students work- groups. The small library of texts that we maintain can ing in partners at 15 machines. be accessed easily by tutors and tutees, and mathemat- A new system of networking charges at Cornell raised ics computer programs provide additional support when the share of our budget for this purpose from around needed. We anticipate having a more visible web pres- 2% to 22%, with a further rise to 32% scheduled in the ence soon and plan to replace some antiquated computer next scal year. We had to restrict opening hours dur- equipment. ing the spring by more than 20 hours per week and will Management of the facility, strictly speaking, re- apparently need continuing cuts during the summer and mains as before. We continue weekday hours of ser- o -semester times. vice (10 AM–5 PM), as well as Sunday hours (1:30 PM– 5:30 PM).
20 Special Programs and Activities Learning Strategies Center a ninety-minute weekly lecture held on either Sunday, The Learning Strategies Center (LSC) provides aca- Monday or Wednesday evening, which reviewed mate- demic support in a variety of subjects across campus, rial covered in the parent course, with an emphasis on including biology, chemistry, physics, economics, writ- problem solving and prelim preparation. In addition, ing, study skills, mathematics and statistics. The mis- extensive tutoring hours were provided by the supple- sion of the LSC is to provide academic assistance to stu- mental course instructors and their assistants. dents during their transition from high school students Support for MATH 171, as well as other undergrad- to accomplished Cornell students. Studies have shown uate statistics courses, was also provided by the LSC that students who successfully complete their freshman in the Center for Learning and Teaching Support In- year generally go on to graduate from Cornell. There- structional Lab. The tutor-sta ed lab was open three fore, most of the LSC’s e orts are directed to supporting evenings and two afternoons per week, equipped with large, primarily freshmen, courses. statistical software and respective problem sets for the In the 2001–2002 academic year, the LSC pro- courses supported. vided academic support for MATH 105, MATH 106, During the 2002–2003 academic year, support will con- MATH 111 and MATH 112. Support included re- tinue to be provided as described above for MATH 105, spective supplemental courses MATH 005, MATH 006, MATH 106, MATH 111, MATH 112 and MATH 171. MATH 011 and MATH 012. These courses consisted of
Center for Applied Mathematics Cornell’s Center for Applied Mathematics (CAM) was scienti c computations, and its students are among the established to promote research and advanced study in best at Cornell. The 80 center faculty are drawn from the applied mathematics and to bring together students and Department of Mathematics and 14 other departments professors with interests in various branches of the sub- in engineering and the sciences. ject. Terrence L. Fine was appointed director of CAM The following Mathematics Department faculty are e ective July 1, 1999. members of CAM: L. Billera, R. Connelly, R. Durrett, The environment for applied mathematics at Cornell E. B. Dynkin, J. F. Escobar, L. Gross, J. Guckenheimer, today is rich and varied. Viewed nationally, Cornell is J. H. Hubbard, H. Kesten, A. Nerode, L. Salo -Coste, a major center of activity in applied mathematics and A. H. Schatz, J. Smillie, M. Stillman and L. B. Wahlbin.
Mathematics Library The Mathematics Library continues to have a high An increasing portion of the journals in the library level of use that often nds most of the library computers collection is now available either on paper in the library and many seats full. Paintings and items of interest are or online to all Cornell users. A small number of titles on display in the library. Most notable is a collection of are now available only online; the University Library oil paintings of early faculty of the department, including has negotiated some site license contracts that make a large portrait of James Edward Oliver, who started the online-only option nancially favorable and provide the department colloquium series in 1891. This year, archival reliability. New online resources are important, wireless networking service was added inside the library but they are not less expensive than the printed resources via Cornell’s RedRover. they will eventually replace. A crisis is looming because The Mathematics Library collection at Cornell is one one publisher, Elsevier, is poised to signi cantly increase of the nest in the nation and supports research and in- their prices. Elsevier represents only 6% of our current struction in mathematics and statistics for the Cornell journal subscriptions but consumes 30% of our budget. community. The research collection consists of works It is likely that we will have to signi cantly retrench our on mathematics, statistics, applied mathematics, math- collection of their titles, canceling subscriptions and pay- ematics education and the history of mathematics. For ing for online use on an article by article basis. undergraduates with an interest in mathematics, the li- Gifts to the library endowment and improved endow- brary is a wonderful resource for materials to support ment payout have made endowment income a very sig- instructional and career needs as well as expository and ni cant source of funding for the purchase of library ma- recreational reading. The library collection has great terials. The university-appropriated budget for the li- historic depth and breadth, and includes materials from brary continues to grow but not as fast as the cost of around the world in many languages. library materials. Thanks to the continued support of
Special Programs and Activities 21 our donors, endowment income has grown from 1.5% of covery beginning next year. Marketing the journal pack- our budget in 1990 to 21.5% for the coming scal year. age to libraries is a priority in this regard. Euclid’s gov- Gifts are the di erence between an excellent library and ernance structure for the cost-recovery phase is under a mediocre one. discussion. The Mathematics Library encourages and welcomes Project Euclid is managed by Zsuzsa Koltay, CUL’s all patrons in the Cornell community to use its resources. coordinator of electronic publishing. More informa- Reciprocal interlibrary loan agreements with other in- tion about Project Euclid is available on the web at stitutions make Cornell’s resources available throughout euclid.library.cornell.edu/project/; Zsuzsa Koltay can the world and open the world to Cornell researchers. answer questions at (607) 255-7964 or [email protected]. The need for quanti cation, analysis and more mathe- matical sophistication in the social, biological and en- Cornell University Mathematics Collection gineering sciences attracts a spectrum of patrons from The Cornell University Mathematics Collection across the campus and generates frequent use of the col- (library5.library.cornell.edu/math.html) is a collection of lection. A full range of reference, circulation, printing 577 digitized books that were scanned from originals held and photocopy services are available in person and via by the Mathematics Library as part of an early CUL- phone, e-mail or the world wide web. Xerox collaboration on digital preservation techniques. The library sta consists of Steven Rockey, the direc- The titles can be viewed electronically, and the Mathe- tor of the library, Natalie Sheridan, branch manager, and matics Library also does a brisk (cost-recovery) business approximately a dozen part-time undergraduate student selling bound paper facsimiles to libraries and individ- employees. The veteran professional sta and the com- uals. Over the decade during which the reprints have petent student employees are always ready to serve the been o ered, sales have averaged roughly 100 books per public, and they welcome feedback. A primary goal is year; the program has been so successful, in fact, that to make the library experience for the sta and patrons the printers used for producing the reprints are burning interesting, productive and enriching in a small and per- out. sonal environment. The Math Books collection consists mostly of pre- The Mathematics Library’s world wide web home 1914 titles, originally selected according to these crite- page (www.math.cornell.edu/elibrary/) has information ria: the books were out-of-print; there were no copy- about the library’s services and hours of operation with right restraints on digitizing; they were not otherwise pointers to relevant databases such as MathSciNet, links available in reprint or microform; and they represented to mathematical science resources, and an extensive bib- important research in mathematics. The electronic ver- liography of “collected works” of mathematicians. Li- sion of the rst reviewing journal in mathematics, Die brary personnel are always adding new and relevant Jahrbuchuber die Fortschritte der Mathematik (1868– links. Visit our library, our home page, or contact us 1942) (www.emis.de/projects/JFM) has links to most of electronically or by telephone to nd out how the Math- these books, as well as other retrodigitized mathemat- ematics Library can serve you. ical publications. The digital Math Books collection is slated to migrate to Project Euclid in the near future. Project Euclid The roles of the two projects may already be merging. Project Euclid (projecteuclid.org) is Cornell Univer- sity Library’s electronic publishing initiative in mathe- Distributed Digital Library of Mathematical Mono- matics. With support from the Mellon Foundation and graphs (NSF/DFG) SPARC (Scholarly Publishing and Academic Resources This collaboration among Cornell University Library, Coalition), Euclid provides a shared web platform for so- the University of Michigan Library, and the State and ciety and independent publishers of mathematics jour- University Library Goettingen (Germany) is funded by nals, easing their transition to the electronic environ- the NSF and the DFG (Deutsche Forschungsgemein- ment and allowing them to compete with large commer- schaft). Interoperability is the goal of the NSF/DFG cial publishers. At present, Euclid provides current jour- project: to nd a viable common protocol that will al- nal content, but some publishers have expressed interest low access to three bodies of material. When nished, in retrodigitizing. Euclid is now in production. It is the system should deliver easy, searchable, electronic ac- currently partnering with 14 journals in theoretical and cess to several thousand mathematics books from the applied mathematics and statistics, and further partner- three universities. The new protocol is derived from the ships are being negotiated. Dienst protocol and draws on the Open Archives Ini- Euclid is in a period of transition, still doing system tiative. To date, cross-collection searching between the development work, on one hand, but aiming for cost re- CUL and UM collections has been set up.
22 Special Programs and Activities Digital Mathematics Library (DML) transition to electronic-only publishing. EMANI will not The NSF has tentatively funded a two-year plan- be a “dark archive.” Springer has declared its intention ning process for the initiative in which CUL will to make its archived materials accessible in a relatively serve as the coordinator of a working group of math- short time after publication. EMANI is expected to be ematicians, publishers, and librarians. The DML an important component in the broader Digital Mathe- proposal responds to a white paper prepared by matics Library initiative if Springer can in fact o er a John Ewing, the executive director of the American model for other publishers of an open and collaborative Mathematics Society, Twenty centuries of mathemat- approach to issues of archiving and access provision. ics: digitizing and disseminating the past mathematical The normalization of TEX (the default standard mark- literature (www.ams.org/ewing/Twenty centuries.pdf). up language for mathematical notation) is seen as key Prof. Keith Dennis convened an uno cial session during to the success of EMANI, and Goettingen is taking the the Joint Mathematics Meetings in San Diego in Febru- lead on this. Springer has promised to normalize TEX ary to discuss the proposal. It was attended by scholars, for all its publications according to library speci cations. publishers and librarians from Europe and North Amer- There is also an interest in the development of MathML ica involved in mathematics digitization e orts, as well as an alternative. as by representatives from the NSF. The rst o cial meeting of the DML advisory committee will take place Zentralblatt MATH and EMIS Mirror Sites July 29 and 30 in Washington, DC. Questions involv- Cornell University Library provides one of nine inter- ing the scope and content of the collection, as well as is- national mirrors for the online Zentralblatt MATH data- sues of standards and interoperability, are on the agenda. base (euclid.library.cornell.edu). Zentralblatt publishes Keith Dennis will deliver a report from the DC meeting abstracts and reviews of the international mathematics to the August meeting of the International Mathematics literature drawn from more than 2,300 serials and jour- Union in Beijing. A second planning meeting will follow nals, going back as far as 1931. The Ithaca site is not in 2003. electronically synchronized with the main site; instead, Zentralblatt’s policy is to send updates in the form of Electronic Mathematics Archives Initiative (EMANI) CDs, which are loaded manually at CUL. Consequently, EMANI is a collaborative e ort between the German coverage at the mirrors is frequently one issue behind scienti c publisher Springer and the libraries at Cornell, the main site. Goettingen, Tsinghua (Beijing), and Orsay (Paris) that CUL also mirrors the European Mathematical Soci- focuses on the archiving of digital mathematics litera- ety’s EMIS (European Mathematical Information Ser- ture and also addresses repository and dissemination is- vice) site. The EMIS mirror (emis.library.cornell.edu) sues. Springer wishes to establish its reputation as a provides outside links to several mathematics databases leader in digital archiving in a public-spirited fashion and stores the content of 62 mathematics journals. An- and hopes to bene t from the good will this can gen- nual user hits to the EMIS mirror number in the thou- erate. Springer also hopes that a systematic and col- sands. Unlike Zentralblatt, the EMIS mirror is updated laborative approach to digital archiving will speed their “live.”
Mathematics Education Cornell/Schools Mathematics Resource Program research that show how the mathematics we teach The Cornell/Schools Mathematics Resource Program in schools is being explored and applied. Among was initiated in 1985 by Cornell’s Committee on Edu- those making presentations were John Hubbard, Lawren cation and the Community. Developed and facilitated Smithline, David Henderson and Daina Taimina of Cor- by David Henderson and Avery Solomon, it has received nell. continued funding and support from Cornell. The CSMRP also initiated an NSF proposal to form The CSMRP is aimed at improving the state of math- a ve-year partnership with local schools to help them ematics teaching and learning by providing in-service to solve several problems in curriculum, new testing re- mathematics courses and workshops for teachers, re- quirements, and at-risk students. searching and developing materials for the classroom that follow a broader approach to mathematics, and ini- Cornell Teacher Education tiating and supporting cooperative e orts between Cor- Sponsored jointly by the departments of Mathematics nell University and local schools. and Education, this ve-year program seeks to recruit The focus of the Saturday workshops during 2001– and prepare students to become secondary mathemat- 2002 has been to present teachers with new areas of ics teachers, allowing participants to attain a Master of
Special Programs and Activities 23 Arts in Teaching and New York State certi cation. This in Mathematics Education in the Education department year we sought to improve student and faculty aware- and active interest among several members of the Math- ness of the program, through discussions with several ematics Department, we hope Cornell will soon be able other university departments, preparation and dissemi- to assume a leadership role in addressing the critical na- nation of informational materials, and open forums for tional need for mathematics teachers. interested students. With the creation of a new position
Mathematics Department Endowments The department is thankful to alumni, friends and dowment is used to provide annual prizes to a continuing family who support the department endowments. With- graduate student at Cornell. out their generosity, we would be unable to provide many The Faculty Book Endowment is dedicated to pro- of the o erings that make our department unique. viding the Cornell community with immediate access to The Cornell University Department of Mathemat- one of the world’s nest collections of mathematics books ics Award is presented to an Ithaca High School student and publications. who has excelled in mathematics and who has demon- The Israel Berstein Memorial Fund was established strated originality and innovative power in mathematics. in honor of Israel Berstein, who was a professor in this The recipient of this award is selected by interviews with department from 1962 through 1991. The memorial fund members of the Department of Mathematics. has as its central purpose helping young mathemati- We have recently instituted new departmental teach- cians in the eld of topology. An award has been estab- ing awards for graduate students and faculty. We would lished for an outstanding graduate student in topology like to endow the Teaching Award for Graduate Stu- or neighboring areas. dents so that a generous prize can accompany it. The Logic Endowment was established as the direct The Colloquium Endowment Fund was instituted to result of a very generous gift from a former Cornell un- invite distinguished scientists to speak at Cornell. Earn- dergraduate. This endowment seeks to actively sup- ings from this endowment are used to pay for honoraria port promising logic students in the areas of institutional and travel expenses for guest lecturers who speak at the memberships and travel expenses to the Association for Oliver Club seminars during the academic year. The Symbolic Logic meetings and events, as well as other Oliver Club was founded (as the Mathematical Club of activities in the eld of logic. Cornell University) in January 1891 by James E. Oliver, The Robert John Battig Endowment was established who was then chair of the department. by his parents in December 1997, after the untimely The Eleanor Norton York Endowment was estab- death of Robert Battig, a graduate student in mathe- lished in honor of Eleanor Norton York, with the intent matics. The current purpose of this fund is to provide of recognizing outstanding graduate students in both As- an annual prize to an outstanding continuing graduate tronomy and Mathematics. The income from this en- student in Mathematics at Cornell.
24 Special Programs and Activities Degrees Granted 2001–2002
Doctoral Degrees
August 2001 David Anthony Brown Using Spider Theory to Explore Parameter Spaces MS Special, Cornell University, 1999 neighborhood of the attracting cycle. BS, Ithaca College, 1995 Since the image of a univalent mapping completely Committee: Hubbard, Earle, Smillie determines the mapping, we visualize these maps con- First Position: assistant professor, Ithaca College cretely on the Riemann sphere; with discs for feet and curves as legs connected at in nity, these maps conjure Abstract: For a xed integer d 2, consider the family a picture of fat-footed spiders. Isotopy classes of these d of polynomials Pd, (z)= (1 + z/d) , where is a com- spiders form a Teichm uller space, and the tools found plex parameter. In this work, we study the location of in Teichm uller theory prove useful in understanding the parameters for which Pd, has an attracting cycle of a Spider Space. By de ning a contracting holomorphic given length, multiplier, and combinatorial type. mapping on this spider space, we can iterate this map- Two main tools are used in determining an algorithm ping to a xed point in Teichm uller space which in turn for nding these parameters: the well-established the- determines the parameter we seek. ories of external rays in the dynamical and parameter Finally, we extend the results about these polynomial z planes and Teichm uller theory. External rays are used families to the exponential family E (z)= e . Here, to specify hyperbolic components in parameter space of we are able to constructively prove the existence and lo- the polynomials and study the combinatorics of the at- cation of hyperbolic components in the parameter space tracting cycle. A properly normalized space of univalent of E . mappings is then employed to determine a linearizing
Kathryn Louise Nyman Enumeration in Geometric Lattices and the Symmetric Group MS Special, Cornell University, 1998 We also show that all ag Whitney numbers are simul- BS, Carthage College, 1995 taneously minimized by the lattice corresponding to the Committee: Billera, Stillman, Renegar near pencil arrangement of points in Rn. Next we focus First Position: postdoctoral position, Texas A&M Uni- on rank 3 geometric lattices and give a collection of in- versity equalities which imply all the linear inequalities satis ed by the ag Whitney numbers of rank 3 geometric lat- Abstract: This work primarily deals with questions re- tices. We further describe the smallest closed convex set lating to the enumeration of chains in geometric lattices. containing the ag Whitney numbers of rank 3 lattices The study of geometric lattices arose in the process of corresponding to oriented matroids. characterizing the lattices of subspaces formed by a nite The ab-index is a polynomial associated to a lattice set of points in projective or a ne space, and ordered which contains all of the information regarding the ag by inclusion. More generally geometric lattices encode Whitney numbers. We give a recurrence relation for the the structure of matroids (or combinatorial geometries), ab-index of families of lattices satisfying a particular set which take an axiomatic approach to the concept of de- of conditions. We also give a collection of inequalities pendence. for the ab-index of geometric lattices. The ag Whitney numbers of a geometric lattice count Finally, we turn our attention to the group algebra of the number of chains of the lattice with elements having the symmetric group. The peak set of a permutation speci ed ranks. We are interested in the linear inequali- is the set {i : (i 1) < (i)> (i+1)}. We prove the ties satis ed by the ag Whitney numbers. existence of a subalgebra of Solomon’s descent algebra We present a lower bond on the ag Whitney numbers in which elements are sums of permutations that share of a lattice in terms of its rank and number of atoms. a common peak set.
Degrees Granted 2001–2002 25 May 2002
Sarah Agnes Spence Subspace Subcodes and Generalized Coset Codes MS Special, Cornell University, 2000 We next consider generalized coset codes, which are BS, University of Richmond, 1997 built using partitions of signal space codes. We ex- Committee: Kozen, Wicker, Billera tend the concepts of generalized coset codes in Euclidean First Position: assistant professor, Franklin W. Olin space by de ning generalized coset codes in Lee space. College of Engineering We prove that all linear codes over Zm are realizable as these new Lee-generalized coset codes. This implies Abstract: This dissertation considers codes that are that linear codes over Zm have desirable symmetry prop- formed using certain subsets of algebraic error-control erties. We also discuss some relationships among inte- codes and signal space codes. We rst consider subspace ger lattices, linear codes over Z4, and generalized coset subcodes of Reed-Solomon (SSRS) codes. We prove a codes. conjecture of Hattori concerning how to identify sub- spaces that give an SSRS code whose dimension exceeds a certain lower bound.
Master of Science Special (No Thesis Required) August 2001 Lee R. Gibson, Mathematics Samuel Hsiao, Mathematics BS, University of Louisville, 1999 BS, Haverford College, 1995 Committee: Salo -Coste, Durrett, K. Brown, Lawler Committee: Billera, Stillman, K. Brown Todd A. Kemp, Mathematics January 2002 BS, University of Calgary (Canada), 2000 Christopher A. Francisco, Mathematics Committee: L. Gross, Salo -Coste, Sjamaar BS, University of Illinois at Urbana-Champaign, 1999 Committee: Stillman, Billera, K. Brown Rajmohan Rajagopalan, Mathematics BA, Oberlin College, 1998 Dmitriy A. Leykekhman, Mathematics Committee: Shore, Kleinberg, Nerode, Kozen BA, New York University, 1998 Committee: Wahlbin, Schatz, Vavasis Gil Rosenberg, Mathematics BA, Swarthmore College, 2000 Rajmohan Rajagopalan, Computer Science Committee: J. West, Sen, Speh BA, Oberlin College, 1998 Committee: Shore, Kleinberg, Nerode, Kozen Timothy A. Roughgarden, Mathematics BS, Stanford University, 1997 Russell S. Woodroofe, Mathematics Committee: Tardos, Kleinberg, Shmoys, Billera BS, University of Michigan, 1998 Committee: K. Brown, Dennis, Billera Rebecca Schuller, Mathematics and Computer Science BA, Grinnell College, 1998 May 2002 Committee: Nerode, Hartmanis, Caruana James M. Belk, Mathematics BS, Binghamton University, 1998 Maria T. Sloughter, Mathematics Committee: K. Brown, Cohen, Salo -Coste BA, Carleton College, 1999 Committee: Connelly, Billera, Stillman
26 Degrees Granted 2001–2002 Bachelor of Arts
August 2001 Supap Kirtsaeng † Christopher Michael Snyder Cum Laude in Mathematics Vince Lee January 2002 Justin Ryan Matis Anna Allegra Angus † William John Meakem Ziv Feldman † Douglas Christopher Mitarotonda † Scott Matthew Kramer † Cum Laude in Asian Studies Christopher R e Lauren A. Moskowitz † Michael Anthony Savalli Akshay Murthy † Jennifer Marie Zimmer Summa Cum Laude in Economics Hui Khoon Ng † May 2002 Magna Cum Laude in Mathematics Ryan Shay Babcock † Summa Cum Laude in Physics Scott Michael Bailey † Timofei Piatenko Magna Cum Laude in Mathematics Daniel Alexander Ramras † Jordan Michael Barry † Kieval Prize in Mathematics Cum Laude in Mathematics Summa Cum Laude in Mathematics Magna Cum Laude in Economics Scott Michael Seliko Ari Zev Blinder † Daniel Simone † Cum Laude in Mathematics Scott Alexander Smith † James Chen Magna Cum Laude in Mathematics Tingting Chen Jay Alexander Sorenson P. Devin Corr Julie Ann Staub Melissa Chatanay DiBella Michael Andrew Suppe Jason Flannick † Benjamin Haber Szekely † Cum Laude in Mathematics Cum Laude in Mathematics Summa Cum Laude in Physics Joon Leng Tan Han Pin Goh † Linda Tieu Cum Laude in Mathematics Raciel Valle † Summa Cum Laude in Physics Magna Cum Laude in Mathematics Debbie Sara Grier † Samuel Joseph Wald Cum Laude in Mathematics Brian Zhong-Hua Wong Paul Ezra Katz Janet Suzie Yoon † Justin Block Kinney Homa Shaghaghi Zarghamee † Magna Cum Laude in Mathematics Summa Cum Laude in Physics † Distinction in all subjects
Degrees Granted 2001–2002 27 Department Colloquia
Analysis Seminar September 2001 January 2002 Matthew Fickus, Cornell University: Finite normalized Natasa Pavlovic, University of Illinois at Chicago: tight frames A cheap Ca arelli-Kohn-Nirenberg inequality for the Martin Dindo s, Cornell University: Hardy spaces and Navier-Stokes equations with hyper-dissipation potential theory on C1 domains Craig Sutton, Dartmouth College: Constructing simply- Irina Mitrea, Cornell University: The Dirichlet problem connected isospectral Riemannian manifolds via for the Laplacian on rough domains Sunada’s method Laurent Salo -Coste, Cornell University: Hypoellipticity in in nite dimension February 2002 Alexander Bendikov, Cornell University: Ultracontrac- October 2001 tivity of semigroups obtained by subordination Brian Smith, Cornell University: On the connectedness Zhongmin Qian, CNRS (France) and Cornell Univer- of the space of initial data for the Einstein equations sity: Extremal metric, unitary group and holomorphic Robert Strichartz, Cornell University: Analysis on frac- Dirichlet form tals (some new results) John Hubbard, Cornell University: The Farey basis of Zhongmin Qian, CNRS (France) and Cornell University: Sobolev H1 Curvature-dimension inequality and the heat equation Cli ord Earle, Cornell University: The world’s greatest Jos e F. Escobar, Cornell University: New results on con- Schwarz-Pick metric formal deformation of metrics March 2002 November 2001 Florin Catrina, Rochester University: Weighted elliptic Yulij Ilyashenko and Vadims Moldavskis, Cornell Uni- equations with critical Sobolev exponents versity: Rotation numbers and moduli of elliptic Irina Mitrea, Cornell University: Boundedness criteria curves: good and bad news about an Arnold’s conjec- for singular integral operators of Calderon-Zygmund ture type Marius Mitrea, University of Missouri at Columbia: Smoothness spaces and elliptic PDEs in nonsmooth do- April 2002 mains Martin Dindo s, Cornell University: Stationary Navier- Robert Strichartz, Cornell University: p-energy and p- Stokes equation on Lipschitz domains harmonic functions on the Sierpinski gasket Guozhen Lu, Wayne State University: Convex functions on the Heisenberg and strati ed groups December 2001 Allan Greenleaf, Rochester University: Uniqueness in Alexander Kiselev, University of Chicago: Enhancement the Calder on problem for conormal potentials and con- and quenching of combustion by uid ow ductivities Martin Grothaus, Cornell University: Reverse hypercon- Tadeusz Iwaniec, Syracuse University: Smooth approxi- tractivity for subharmonic functions mation and the degree formula for mappings between manifolds
Combinatorial and Algebraic Geometry Seminar September 2001 October 2001 Stephanie van Willigenburg, Cornell University: Pieri Ezra Miller, MIT: Determinantal ideals and the combi- operators and Eulerian enumeration natorics of Schubert polynomials John Hubbard, Cornell University: Resolving the singu- Eva-Maria Feichtner, ETH Z urich (Switzerland): Inci- larities of Hilbert modular surfaces: a dynamical point dence combinatorics of resolutions of view Louis Billera, Cornell University: Quasisymmetric func- Sara Billey, MIT: A root system description of pattern tions, Hopf duality and Eulerian enumeration avoidance with applications to G/B Frank Sottile, University of Massachusetts at Amherst: Common transversals and tangents in P 3
28 Department Colloquia November 2001 February 2002 Geanina Tudose, York University (Canada): On the Harrison Tsai, Cornell University: Baum-Sell algorithm combinatorics of the Verlinde algebra for maximizing polynomials Oleg Chalykh, Moscow State University (Russia) and Edward Swartz, Cornell University: 101 uses for a bro- Cornell University: Macdonald polynomials and a new ken circuit (in two parts) proof of the Macdonald conjectures Marcelo Aguiar, Texas A&M University: Loday’s types March 2002 of algebras and Rota’s types of operators Weiqiang Wang, University of Virginia and MSRI: Hilbert schemes and wreath products: a comparison December 2001 Lawren Smithline, Cornell University: Compact opera- Swapneel Mahajan, Cornell University: On the Hopf al- tors with rational generating functions gebra of permutations of Malvenuto and Reutenauer April 2002 January 2002 Steve Sinnott, Cornell University: Factoring ordinary Christopher Francisco, Cornell University: Some conjec- di erential operators with Laurent polynomial coe - tures on lex-plus-powers ideals cients Swapneel Mahajan, Cornell University: Operads + Hopf algebras + Coxeter groups ?
Discrete Geometry and Graph Theory Seminar September 2001 John Hubbard, Cornell University: Andreev’s theorem: Andrei Raigorodskii, University of Moscow (Russia): is it true? Measuring the di erence between bases of Zn Konstantin Rybnikov, Cornell University: Delaunay February 2002 tilings and Dirichlet-Voronoi polytopes of lattices Konstantin Rybnikov, Cornell University: Abelian gain Franco Saliola, Cornell University: Forbidden minors graphs and their application in discrete geometry Franco Saliola, Cornell University: The Colin de Verdi ere graph invariant April 2002 Walter Whiteley, York University (Canada): Inductive October 2001 techniques for plane frameworks Maria Sloughter, Cornell University: Polytopes and the Daniel Dix, University of South Carolina: Discrete struc- Colin de Verdi ere number tures for biomolecular geometry Sue Whitesides, McGill University (Canada) and Cor- Tom Zaslavsky, SUNY at Binghamton: Semi-unique rep- nell University: Fixed parameter tractability results for resentation of a cute kind of matroid crossing minimization problems in layered graphs (in Ileana Streinu, Smith College: On the number of embed- two parts) dings of minimally rigid graphs
November 2001 May 2002 Robert Connelly, Cornell University: The Kneser- Jason Cantarella, University of Georgia: Rope length Pousen conjecture: an update critical curves -or- on a kind of continuous tensegrity David Benbennick, Cornell University: Unfolding convex theory polytopes (in two parts)
Dynamics and Geometry Seminar September 2001 Roland Roeder, Cornell University: Hamiltonian me- John Hubbard, Cornell University: Escalle-Voronin in- chanics of a tokamak’s magnetic eld variants in 1 and 2 dimensions (in two parts) Ricardo Oliva, Cornell University: Overview of some as- pects of complex dynamics October 2001 Michael Coleman, Cornell University: A stable walking November 2001 toy that cannot stand still Yulij Ilyashenko, Cornell University: Restricted versions Vadim Kaloshin, MIT: Dynamics of the oil spill of Hilbert’s 16th problem
Department Colloquia 29 December 2001 March 2002 Alexander B. Vladimirsky, Cornell University: Anisotropy John Hubbard, Cornell University: How to nd all roots in front propagation and control theory of complex polynomials by Newton’s method
January 2002 April 2002 Sebastian Wieczorek, Vrije Universiteit (Netherlands): Sylvain Bonnot, Cornell University and Universit ede Nonlinear dynamics and bifurcations of an optically Marseille (France): A proof of Jakobson’s theorem (in injected semiconductor laser (in two parts) two parts)
February 2002 Nikola Petrov, University of Texas at Austin: Regularity of conjugacies between critical circle maps: numerical results
Group Theory Seminar September 2001 November 2001 R. Keith Dennis, Cornell University: Commutators, Gerhard Michler, University of Essen (Germany): The characters and the Casimir element (in three parts) Brauer-Fowler theorem and the existence and unique- ness of the sporadic simple groups October 2001 Kenneth Brown, Cornell University: The coset poset Laurent Salo -Coste, Cornell University: Random walks Russ Woodroofe, Cornell University: Shellings and the on nite groups coset poset
Lie Groups Seminar September 2001 January 2002 Milen Yakimov, Cornell University: Symplectic leaves in Tara Holm, MIT: A hint at di erential topology on complex reductive Poisson-Lie groups graphs Tom Graber, Harvard University: Rational points of curves over function elds February 2002 Laurent Salo -Coste, Cornell University: Analysis on October 2001 high dimensional compact Lie groups Eckhart Meinrenken, University of Toronto (Canada): Farkhod Eshmatov, Cornell University: Projective mod- The Du o homomorphism for subalgebras ules over Dixmier algebras and quiver varieties Paula Cohen, Lille University (France): On special Milen Yakimov, Cornell University: Poisson Lie groups points and some hyperbolic distribution problems via symplectic (Marsden-Weinstein) reduction Yuri Berest, Cornell University: Cherednik algebras and di erential operators on quasi-invariants March 2002 Oleg Chalykh, Moscow State University (Russia) and Alex Feingold, SUNY at Binghamton: Perspectives on Cornell University: Schroedinger operators with trivial vertex operator algebra local monodromy and deformed root systems Jacques Hurtubise, McGill University (Canada): Elliptic Sklyanin integrable systems November 2001 Stephen Bullock, University of Michigan: Bueler’s con- Catherine O’Neil, MIT: Moduli of ‘n-prepared’ genus one jecture and inadmissible weights curves (with no points) Ludmil Katzarkov, University of California at Irvine: April 2002 Symplectic geometry and quivers Swapneel Mahajan, Cornell University: Deformation Birgit Speh, Cornell University: On the Arthur Selberg quantization for operads trace formula Charles Dunkl, University of Virginia: Nonsymmet- ric Jack polynomials, commuting self-adjoint operators December 2001 and norm evaluations Michael Thaddeus, Columbia University: Mirror sym- Dan Barbasch, Cornell University: Hecke algebras and metry and Higgs bundles the Plancherel theorem
30 Department Colloquia Logic Seminar September 2001 December 2001 Michael Morley, Cornell University: In nitary formulas Andre Nies, University of Aukland (New Zealand): Ran- Noam Greenberg, Cornell University: Precipitous and domness and lowness properties of sets saturated ideals Joseph Miller, Cornell University: Computable in nitary February 2002 formulas Russell Miller, Cornell University: Introduction to O- Yuval Gabay, Cornell University: Barwise compactness minimal theory (in four parts) Noam Greenberg, Cornell University: Sharps and pro- Noam Greenberg, Cornell University: Stationary towers jective ordinals (in two parts) (in ve parts) Joseph Miller, Cornell University: Hyperarithmetic sets of formulas March 2002 Vivian Morley, Cornell University: Semi-analytic sets October 2001 Vivian Morley, Cornell University: Subanalytic sets (in Russell Miller, Cornell University: Some automorphisms two parts) of the lattice of c.e. sets Noam Greenberg, Cornell University: Measurability and Yuval Gabay, Cornell University: Applications of barwise inaccessability compactness Christopher Hardin, Cornell University: Barendregt on Julia Knight, Notre Dame University: Complicated rela- combinatory logics and algebras tions in computable structures Julia Knight, Notre Dame University: n-diagrams April 2002 Christopher Hardin, Cornell University: Computable lin- Russell Miller, Cornell University: Ritt’s algorithm for ear orderings (in two parts) systems of algebraic di erential equations (in two Richard Shore, Cornell University: Invariants, reverse parts) mathematics and Boolean algebras (in two parts) Christopher Hardin, Cornell University: Combinatory Christopher Hardin, Cornell University: Computable logic according to Barendregt (in two parts) Boolean algebras Russell Miller, Cornell University: Ritt’s algorithm for arbitrary systems of algebraic PDEs November 2001 Antonio Montalban, Cornell University: Model theory of Antonio Montalban, Cornell University: Completeness di erential algebra (in two parts) and forcing (in three parts) Noam Greenberg, Cornell University: A measurable and May 2002 saturation imply Not CH, e ectively (in three parts) Sergey Slavnov, Cornell University: Multiplicative linear Shai Ben-David, Technion (Israel): On the inability to logic and symplectic manifolds resolve the P versus NP question Vivian Morley, Cornell University: The Ash-Nerode the- orem (in two parts) Oliver Club September 2001 Milen Yakimov, Cornell University: Geometry of Andrei M. Raigorodskii, Moscow State University (Rus- Poisson-Lie groups and representation theory of Hopf sia): On the Borsuk partition problem algebras Warwick Tucker, Cornell University: Using a computer Askold Khovanskii, University of Toronto (Canada): to do rigorous mathematics Parshin’s symbols, toric geometry and product of the Tom Graber, Harvard University: Rationally connected roots of a system of equations varieties November 2001 October 2001 James Yorke, University of Maryland: Plato’s problem: Victor Palamodov, Tel Aviv University (Israel): Inverse can we understand reality when seeing only shadowy problems and Gabor analysis images Alexey Glutsyuk, Ecole Normale Sup erieure de Lyon Ludmil Katzarkov, University of California at Irvine: (France): Simultaneous uniformization New examples of non-K uhler homotopy types
Department Colloquia 31 Alexei Sossinski, Independent University of Moscow March 2002 (Russia): Could the Poincare conjecture be false? Jacques Hurtubise, McGill University (Canada): Inte- Sorin Popescu, SUNY at Stony Brook: Geometry and grable systems and surfaces algebra of modular varieties Irina Mitrea, Cornell University: On the spectral radius conjecture in two dimensions December 2001 Sigurdur Helgason, MIT: Eigenspace representations Michael Thaddeus, Columbia University: Mirror sym- metry and Langlands duality April 2002 Morris Hirsch, University of California at Berkeley: Solv- January 2002 able Lie group actions on surfaces Peter Ozsvath, Princeton University: Holomorphic disks Daniel Dix, University of South Carolina: Protein fold- and low-dimensional topology ing from a dynamical systems viewpoint Sue Whitesides, McGill University (Canada) and Cornell Charles Dunkl, University of Virginia: Complex re ec- University: Recent themes in algorithmic graph theory tion groups and nonsymmetric Jack polynomials Shuguang Wang, University of Missouri at Columbia: February 2002 Gauge theory and real structures Gregory Lawler, Cornell University: Conformally invari- ant measures May 2002 Bruce Kleiner, University of Michigan: Quasiconformal Dusa McDu , SUNY at Stony Brook: The topology of geometry in metric spaces groups of symplectomorphisms Stephanie van Willigenburg, Cornell University: The al- gebra of card shu ing Yves Le Jan, Universit e Paris Sud (France): Brownian ows
Olivetti Club September 2001 December 2001 Sam Hsiao, Cornell University: The upper bound conjec- Todd Kemp, Cornell University: Integrals and deriva- ture and the importance of being Cohen-Macauley tives G. Christopher Hruska, Cornell University: Hyperbolic groups and their boundaries January 2002 Noam Greenberg, Cornell University: The constructible Joseph Miller, Cornell University: Computable analysis: universe and the continuum hypothesis Brouwer’s theorem and xable sets David Revelle, Cornell University: There ain’t no way to October 2001 measure that there table! Sarah Spence, Cornell University: Generalized coset codes and lattices February 2002 Kristin Camenga, Cornell University: Ramsey theory on Jason Martin, Cornell University: An algebraic version graphs and hypergraphs of Dynkin’s theorem Nelia Charalambous, Cornell University: A classi ca- James Belk, Cornell University: Amenability and the tion of three-dimensional noncompact manifolds with Banach-Tarski paradox nonnegative curvature Lee Gibson, Cornell University: The rabbit in the woods, Ryan Budney, Cornell University: Symmetry in topology or the method of enlargement of obstacles
November 2001 March 2002 Leah Gold, Cornell University: The number of lines on G. Christopher Hruska, Cornell University: Isolated a nonsingular cubic surface ats, or nearly hyperbolic spaces Fernando Schwartz, Cornell University: Soap bubbles Serguei Slavnov, Cornell University: Between logic and Steve Morris, Cornell University: J-holomorphic curves mathematics and bubbling in symplectic topology Treven Wall, Cornell University: A survey of some good Suzanne Hruska, Cornell University: A tour of the Man- elliptic curve cryptosystems, -or- Wow, algebra really delbrot set can be useful!
32 Department Colloquia April 2002 Fernando Schwartz, Cornell University: The Riemann- Todd Kemp, Cornell University: Vector elds on ian Penrose conjecture and some other cool stu from spheres: an analytic approach general relativity Alan Demlow, Cornell University: Localization in nite Gil Rosenberg, Cornell University: Frege structures: bal- element methods, -or- How local can you go? ancing the axiom of abstraction with the rules of logic Will Gryc, Cornell University: Wavelets and multireso- lution analysis Probability Seminar September 2001 January 2002 Jason Schweinsberg, Cornell University: Applications of Pierre Tarres, Ecole Polytechnique F ed erale de Lausanne the continuous-time ballot theorem to Brownian excur- (Switzerland): Reinforced random walks sions and fragmentation processes Richard Durrett, Cornell University: Rigorous results for February 2002 the NK model Richard Durrett, Cornell University: Shu ing chromo- Jeremy Staum, Cornell University: Importance sampling somes with non-equivalent measures Philip Protter, Cornell University: Pricing American op- tions with the Longsta Schwartz algorithm October 2001 Zhongmin Qian, CNRS (France) and Cornell University: Jan Hannig, Colorado State University: Integrated Stochastic calculus for some Gaussian processes Brownian motions and exact L2-small balls March 2002 Vadim Kaloshin, MIT: Dynamics of the oil spill Gregory Lawler, Cornell University: The scaling limit of David Revelle, Cornell University: Heat kernel asymp- loop-erased walk on the square lattice totics on the lamplighter group Thomas Mikosch, University of Copenhagen (Denmark): Some estimation problems for GARCH models November 2001 Gena Samorodnitsky, Cornell University: Tails of solu- Alexander Bendikov, Cornell University: The dichotomy tions of certain nonlinear stochastic di erential equa- problem for Gaussian measures on groups tions driven by heavy tailed L evy motions Philip Protter, Cornell University: Complete nancial markets with hidden arbitrage April 2002 Vlada Limic, Cornell University: A threshold routing Esa Nummelin, University of Helsinki (Finland): Large queueing system in heavy tra c deviations of price equilibria of random economic sys- Arnaud de la Pradelle, University of Paris VI (France): tems The Ito-Skorohod formula for fractional Brownian mo- Lee Gibson, Cornell University: The method of enlarge- tion ment of obstacles Dan Stroock, MIT: Di erential geometry of the space of December 2001 probability measures Shane Henderson, Cornell University: Nonexistence of a David Revelle, Cornell University: Rate of escape of ran- class of random variable generation schemes dom walks on groups Akira Saskai, University of British Columbia (Canada): Sylvie M el eard, Universit e Paris X (France): Conver- Mean- eld critical behavior for the contact process gence from Boltzmann to Landau processes with soft potential and particle approximations
Smorgasbord Seminar (MATH 402) September 2001 Russell Miller, Cornell University: Noncomputable sets Laurent Salo -Coste, Cornell University: Shu ing cards and unsolvable problems and random walks on nite groups Ravi Ramakrishna, Cornell University: A geometric October 2001 proof of the 4 squares theorem Edward Swartz, Cornell University: Introduction to ma- Richard Durrett, Cornell University: Evolution on ran- troids dom landscapes Konstantin Rybnikov, Cornell University: Perfect lat- tices and perfect ellipsoids
Department Colloquia 33 John Guckenheimer, Cornell University: The forced van Jos e F. Escobar, Cornell University: Introduction to the der Pol equation calculus of variations Robert Strichartz, Cornell University: Scales that specify Yulij Ilyashenko, Cornell University: Bifurcations and the smoothness of functions systems with di erent time scales
November 2001 December 2001 Cli ord Earle, Cornell University: How to build a Rie- Michael Stillman, Cornell University: Computing in al- mann surface gebraic geometry James Conant, Cornell University: Euler’s formula and regular polyhedra
Topology and Geometric Group Theory Seminar September 2001 January 2002 Kai-Uwe Bux, Cornell University: Finiteness properties Peter Ozsvath, Princeton University: Holomorphic disks of Korelli groups and invariants of low-dimensional manifolds Ferenc Gerlits, Cornell University: Counting graphs with combinatorial species and Feynmann rules February 2002 G. Christopher Hruska, Cornell University: The relative Ryan Budney, Cornell University: The Lawrence- hyperbolicity of groups with isolated ats Krammer representation is unitary Bruce Kleiner, University of Michigan: Euclidean lami- October 2001 nations in 3-manifolds Arthur Bartels, University of Muenster (Germany): Martin Bridson, Imperial College, Oxford (England): Groups of nite asymptotic dimension and algebraic Curvature and decision processes K-theory David Benbennick, Cornell University: Algorithms in G. Christopher Hruska, Cornell University: The relative knot theory hyperbolicity of groups with isolated ats Dmitri Kozlov, KTH Stockholm (Sweden) and the Uni- March 2002 versity of Bern (Switzerland): Combinatorics of reso- Matthew Horak, Cornell University: Ribbon graph sub- nances complexes of outer space Sue Whitesides, McGill University (Canada) and Cornell Dev Sinha, University of Oregon and Brown University: University: Embedding problems for paths and cycles New perspectives on (self-)linking with direction constrained edges Allen Hatcher, Cornell University: Topological moduli James Conant, Cornell University: In nitesimal opera- spaces for knots tions on graphs April 2002 November 2001 Dan Ramras, Cornell University: Connectivity of the Peter Kahn, Cornell University: Pseudohomology and coset poset homology Marshall Cohen, Cornell University: The Freiheitsatz Ryan Budney, Cornell University: Electrostatic poten- Tobias Ekholm, Uppsala University (Sweden): Embed- tials on con guration spaces: CW decompositions and dedness of minimal surfaces of total boundary curva- compacti cations ture less than 4 James Conant, Cornell University: Graph homology, Tadeusz Januszkiewicz, SUNY at Binghamton: Equi- con guration spaces and Vassiliev invariants variant cohomology of buildings Laura Anderson, SUNY at Binghamton: Combinatorial John Hubbard, Cornell University: A proof of Thurston’s construction of bundles hyperbolization theorem for 3-manifolds which ber over the circle December 2001 G. Christopher Hruska, Cornell University: Convergence Kai-Uwe Bux, Cornell University: Finiteness properties groups and isolated ats of Houghton braid groups Ryan Budney, Cornell University: Representations of May 2002 mapping class groups Thang Le, SUNY at Bu alo: On quantum and nite type invariants of integral homology 3-spheres
34 Department Colloquia Undergraduate Mathematics Club September 2001 January 2002 John Hubbard, Cornell University: Newton’s method as Robert Strichartz, John Guckenheimer and John Hub- an approach to di erential calculus bard, Cornell University: Research Experiences for Undergraduates information session October 2001 Scott Bailey, Cornell University: The Jacobian of a February 2002 graph Sarah Spence, Cornell University: Coding theory and Daniel Ramras, Cornell University: Algebra and combi- cryptography: putting mathematics to work! natorial topology S. Alex Smith, Cornell University: Harmonic structures March 2002 on fractals Richard Durrett, Cornell University: Shu ing chromo- Edward Swartz, Cornell University: Embedding graphs somes in surfaces April 2002 November 2001 Eva Tardos, Cornell University: Games on networks Birgit Speh, Cornell University: Why I like Lie groups Walter Whiteley, York University (Canada): To see like a mathematician December 2001 Jordan Ellenberg, Princeton University: The mathemat- Warwick Tucker, Cornell University: An introduction to ics of ’Set’ -or- Everything I know about Fourier anal- interval arithmetic ysis I learned from playing cards
VIGRE Interdisciplinary Colloquium In connection with the department’s VIGRE grant, October 2001 this monthly colloquium is held with the purpose of in- Ron Elber, Cornell University (Computer Science): The troducing graduate students and professors in the de- design and application of folding potentials partment to some of the possible applications of math- Carlos Castillo-Chavez, Cornell University (Biometrics ematics, by inviting faculty from other departments at and T&AM): Questions and challenges posed by the Cornell to give talks. Since the idea of the talk is to ex- transmission dynamics of tuberculosis pose the audience to research possibilities, speakers are asked to talk about something that has not yet reached November 2001 a de nitive nal form and to indicate open problems. Richard Guy, University of Calgary (Canada): Unsolved problems in combinatorial games September 2001 Richard Rand, Cornell University (T&AM): Recent ad- Robert Jarrow, Cornell University (Johnson School vances in parametric excitation of Management): Second generation Heath-Jarrow- Morton term structure models December 2001 Viet Elser, Cornell University (Physics): Dynamical sys- tems approach to phase retrieval
Department Colloquia 35 2001–2002 Faculty Publications
Yuri Berest and George Wilson, Ideal classes of the Weyl Richard Durrett and Nancy Sundell, Exponential dis- algebra and noncommutative projective geometry (with tance statistics to detect the e ects of population sub- G. Wilson), IMRN 26 (2002), 1347–1397. division, Theor. Pop. Biol. 60 (2001), 107–116. Louis Billera, Susan Holmes and Karen Vogtmann, Ge- Richard Durrett, Mutual invadability implies coexistence ometry of the space of phylogenetic trees, Advances in in spatial models, Memoirs of the AMS 156 no. 740 Applied Mathematics 27 (2001), 733–767. (2002). Louis Billera and Persi Diaconis, A geometric interpre- K. Y. Chen, Richard Durrett and Steve Tanksley, A tation of the Metropolis-Hastings algorithm, Statistical simple formula useful for positional cloning, Genetics Science 16 (2001), 335–339. 160 (2002), 353–355. Louis Billera, Sam Hsiao and Stephanie van Willigen- Richard Durrett, Harry Kesten and Vlada Limic, Once burg, Peak quasisymmetric functions and Eulerian edge-reinforced random walk on a tree, Probab. Theory enumeration, Advances in Mathematics, to appear. Rel. Fields, to appear. Kai-Uwe Bux, Finiteness properties of soluble S- Linda Buttel, Richard Durrett and Simon Levin, Com- arithmetic groups — a survey; in Proceedings of the petition and species packing in patchy environments, conference “Groups: Geometric and Combinatorial Theor. Pop. Biol., to appear. Aspects,” Bielefeld, 1999, to appear. Ted Cox and Richard Durrett, The stepping stone model: James Conant, On a theorem of Goussarov, J. Knot new formulas expose old myths, Ann. Appl. Prob., to Theory Rami cations, to appear. appear. K aroly Bezdek and Robert Connelly, The Kneser- Eugene Dynkin, Branching exit Markov systems and su- Poulsen conjecture in the plane, Crelle’s Journal, to perprocesses, Annals of Probability 29 no. 4 (2001), appear. 1833–1858. Robert Connelly and N. Khamsemanan, Unit distance Eugene Dynkin, Di usions, Superdi usions and Par- preserving functions from Euclidean spaces, Beitr age tial Di erential Equations, Colloquium Publications, zur Algebra und Geometrie, to appear. American Mathematical Society, 2002. Robert Connelly, Konstantin Rybnikov and Stanislav Cli ord Earle and Nikola Lakic, Variability sets on Rie- Volkov, Percolation and the loss of tension in an in- mann surfaces and forgetful maps between Teichm uller nite triangular lattice, J. Statist. Phys. 105 no. 1–2 spaces, Ann. Acad. Sci. Fenn. Math., to appear. (2001), 143–171. Cli ord Earle, Schwarz’s lemma and Teichm uller con- K aroly Bezdek, Grigoriy Blekherman, Robert Connelly traction, Contemporary Math., to appear. and B. Csikus, The polyhedral Tammes problem, Arch. Cli ord Earle, Vladimir Markovic and Dragomir Saric, Math. (Basel) 76 no. 4 (2001), 314–320. Barycentric extension and the Bers embedding for as- Martin Dindos, Existence and uniqueness for a semilin- ymptotic Teichm uller space, Contemporary Math., to ear elliptic problem on Lipschitz domains in Riemann- appear. ian manifolds, Comm. PDE 27 (2002), 219–281. Cli ord Earle, L. A. Harris, John Hubbard and Martin Dindos and Marius Mitrea, Semilinear Poisson Sudeb Mitra, Schwarz’s lemma and the Kobayashi problems in Sobolev-Bessov spaces on Lipschitz do- and Carath eodory pseudometrics on complex Banach mains, Publicacions Mathematiques, to appear. manifolds; in Kleinian Groups and Hyperbolic Three- Richard Durrett and Vlada Limic, On the quantity and Manifolds, Cambridge University Press, to appear. quality of single nucleotide polymorphisms in the hu- John Benedetto and Matthew Fickus, Finite normalized man genome, Stoch. Proc. Appl. 93 (2001), 1–24. tight frames, Advances in Computational Mathemat- Persi Diaconis and Richard Durrett, Chutes and ladders ics, to appear. in Markov chains, J. Theor. Prob. 14 (2001), 899–926. Vesselin Gasharov, Takayuki Hibi and Irena Peeva, Res- Arkendra De, Richard Durrett, Michael Ferguson and olutions of a-stable ideals, J. Algebra, to appear. Suzanne Sindi, The equilibrium distribution for a Marc Chardin, Vesselin Gasharov and Irena Peeva, generalized Sanko -Ferretti model accurately predicts Maximal Betti numbers, PAMS, to appear. chromosome size distributions in a wide variety of Vesselin Gasharov, Irena Peeva and Volkmar Welker, species, J. Appl. Prob. 38 (2001), 324–334. Coordinate subspace arrangements and monomial Chip Aquadro, Peter Calabrese and Richard Durrett, ideals, Proceedings of the Osaka Meeting on Computa- Dynamics of microsatellite divergence under stepwise tional Commutative Algebra and Combinatorics, Ad- mutation and proportional slippage/point mutation vanced Studies in Pure and Applied Mathematics, to models, Genetics 159 (2001), 839–852. appear.
36 2001–2002 Faculty Publications Fernando Galaz-Fontes, Leonard Gross and Stephen John Hubbard, Dierk Schleicher and Scott Sutherland, Sontz, Reverse hypercontractivity over manifolds, How to really nd roots of polynomials by Newton’s Arkiv f ur Mathematik 39 (2001), 283–309. method, Inventiones Mathematicae 146 (2001), 1–33. Thomas Deck and Leonard Gross, Hankel operators over Xavier Bu , Christian Henriksen and John Hubbard, complex manifolds, Paci c J. Math., to appear. Farey curves, J. Exper. Math. 10 no. 4 (2001). John Guckenheimer, Kathleen Ho man and Warren John Hubbard and Ralph Oberste-Vorth, Linked Weckesser, Global analysis of periodic orbits in the solenoid mappings and the non-transversality locus in- forced van der Pol equation; in Global Analysis of Dy- variant, Indiana Math. J. 50 no. 1 (2001). namical Systems (H. Broer, B. Krauskopf and G. Veg- John Hubbard, A rst look at di erential Galois the- ter, eds.), IOP Press, 2001, pp. 261–276. ory, Gazette de la Soci et e Math ematique de France, John Guckenheimer and Yulij Ilyashenko, The duck and to appear. the devil: canards on the staircase, Moscow Mathe- John Hubbard and Karl Papadantonakis, Exploring the matical Journal 1 no. 1 (2001), 27–47. parameter space for H enon mappings, Experimental John Guckenheimer, Review of Stephen Smale biog- Mathematics, to appear. raphy by Steve Batterson, Am. Math. Monthly 108 John Hubbard, A proof of Kolmogorov’s theorem on the (2001), 107–109. conservation of invariant tori, Journal of Nonlinearity, John Guckenheimer, Computing periodic orbits;in to appear. Fluid Mechanics and the Environment: Dynamical J. T. Gene Hwang and Ming Yang, An optimality theory Approaches (J. Lumley, ed.), 2001, pp. 107–120. for mid p-values in 2 2 contingency tables, Statistica John Guckenheimer, Numerical analysis of dynamical Sinica 11 (2001), 807–826. systems, Handbook of Dynamical Systems, Elsevier, J. T. Gene Hwang and Dan Nettleton, Investigating 2002. the probability of sign inconsistency in the regression John Guckenheimer, Bifurcation and degenerate decom- coe cients, Genetics 160 (2002), 1697–1705. position in multiple time scale dynamical systems;in J. T. Gene Hwang and Shyamal D. Peddada, Classi - Nonlinear Dynamics and Chaos: Where do we go from cation of pixels in a noisy grayscale image of polar ice, here?, IOP Press, 2002. IEEE Trans. Geoscience & Remote Sensing, to appear. John Guckenheimer and Ricardo Oliva, Chaos in the Yulij Ilyashenko and A. Panov, Some upper estimates of Hodgkin-Huxley model, SIAM J. App. Dyn. Systems the number of limit cycles of planar vector elds with (2002). applications to Lienard equation, Moscow Mathemat- Allen Hatcher, Algebraic Topology, Cambridge Univer- ical Journal 1 no. 4 (2001), 1–17. sity Press, 2002. F. Dumortier, Yulij Ilyashenko and Christiane Gabor Domokos and Timothy Healey, Hidden symmetry Rousseau, Normal forms near a saddle-node and appli- of global solutions in twisted elastic rings, J. Nonlinear cations to nite cyclicity of graphics, Ergodic Theory Science 11 (2001), 47. and Dynamical Systems, to appear. Timothy Healey, Material symmetry and chirality in Yulij Ilyashenko, Centennial history of Hilbert’s 16th nonlinearly elastic rods, Math. Mech. Solids, to ap- problem, Bulletin of the AMS, to appear. pear. Harry Kesten and J. van den Berg, Randomly coalescing Timothy Healey and Kevin MacEwen, A simple ap- random walk in dimension 3 ; in In and Out of Equi- proach to the 1:1 resonance bifurcation in follower-load librium, Proceedings of a Conference in Mambucaba, problems, Nonlinear Dynamics, to appear. Brazil, to appear. David Henderson and Daina Taimina, Geometry (in- Gregory Lawler, Oded Schramm and Wendelin Werner, vited signed article), Hutchinson Encyclopedia of Values of Brownian intersection exponents I: half- Mathematics. plane exponents, Acta Math. 187 (2001), 237–273. David Henderson, Review of Geometry: Euclidean and Gregory Lawler, Oded Schramm and Wendelin Werner, Beyond by Robin Hartshorne, Bull. AMS, to appear. Values of Brownian intersection exponents II: plane David Henderson, Review of Where Does Mathematics exponents, Acta Math. 187 (2001), 275–308. Come From? by Lako and Nunez, Mathematical In- Gregory Lawler, Oded Schramm and Wendelin Werner, telligencer 24 no. 1, to appear. The dimension of the Brownian frontier is 4/3 , Math. David Henderson, Di erential geometry (invited signed Res. Let. 8 (2001), 401–411. article), Encyclopedia Britannica, to appear. Gregory Lawler, Oded Schramm and Wendelin Werner, David Henderson and Daina Taimina, Non-Euclidean Values of Brownian intersection exponents III: two- geometry (invited signed article), Encyclopedia Bri- sided exponents, Ann. Inst. Henri Poincar e 38 (2002), tannica, to appear. 109–123.
2001–2002 Faculty Publications 37 Gregory Lawler, Oded Schramm and Wendelin Werner, Richard Rand, Igor Rozhkov and Alexander Vakakis, One arm exponent for critical 2D-percolation, Journal Nonlinear modal interactions in the oscillations of a of Probability 7 no. 2 (2002). liquid drop in a gravitational eld, Int’l Journal of Gregory Lawler, Oded Schramm and Wendelin Werner, Nonlinear Mechanics 36 (2001), 803–812. Sharp estimates for Brownian non-intersection prob- Richard Rand and Randolph Zounes, Subharmonic reso- abilities; in In and Out of Equilibrium, Birkh auser, nance in the nonlinear Mathieu equation, Int’l Journal 2002. of Nonlinear Mechanics 37 (2002), 43–73. Gregory Lawler, Oded Schramm and Wendelin Werner, Leslie Ng and Richard Rand, Bifurcations in a Mathieu Analyticity of intersection exponents for planar Brown- equation with cubic nonlinearities, Chaos, Solitons and ian motion, Acta Math., to appear. Fractals 14 (2002), 173–181. Irina Mitrea, On the spectra of elastostatics and hydro- Waldemar Hebisch and Laurent Salo -Coste, On the re- statics layer potentials on curvilinear polygons, Jour- lation between elliptic and parabolic Harnack inequal- nal of Fourier Analysis and Applications 8 (2002). ities, Annales de l’Institut Fourier 51 (2001), 1437– Vladimir Brayman, Wolf Kohn and Anil Nerode, Con- 1481. trol synthesis in hybrid systems with Finsler dynam- Alexander Bendikov and Laurent Salo -Coste, Central ics, invited paper for Chern volume, Houston Journal Gaussian semigroups of measures with continuous den- of Mathematics 28 no. 2 (2002), 353–375. sities, J. Functional Analysis 186 (2001), 206–268. Bakhadyr Khoussainov and Anil Nerode, Automata the- Alexander Bendikov and Laurent Salo -Coste, On the ory and its applications, to appear. absolute continuity of Gaussian measures on locally Grigori Milstein and Michael Nussbaum, Maximum compact groups, J. Theoretical Probability 14 (2001), likelihood estimation of a nonparametric signal in 887–898. white noise by optimal control, Statistics and Prob- Thierry Coulhon, Ilkka Holopainen and Laurent Salo - ability Letters 55 no. 2 (2001), 193–203. Coste, Harnack inequality and hyperbolicity for subel- Ion Grama and Michael Nussbaum, Asymptotic equiv- liptic p-Laplacians with applications to Picard type the- alence of nonparametric regression, Mathematical orems, Geometric and Functional Analysis 11 (2001), Methods of Statistics 11 no. 1 (2002), to appear. 1139–1191. Karen Ames, Lawrence Payne and J. C. Song, Spatial Laurent Salo -Coste, Probability on groups: random decay in the pipe ow of a viscous uid interfacing a walks and invariant di usions, Notices of the AMS porous medium, Math. Models and Methods in Appl. 48 no. 9 (2001), 968–977. Sciences 11 (2001), 1547–1562. Laurent Salo -Coste, Aspects of Sobolev Type Inequal- Lawrence Payne and P. W. Schaefer, Eigenvalue ities, London Mathematical Society Lecture Note Se- and eigenfunction inequalities for elastically supported ries 289, Cambridge University Press, 2002. membranes, ZAMP 52 (2001), 888–895. Alexander Grigor’yan and Laurent Salo -Coste, Dirich- Lawrence Payne and P. W. Schaefer, Decay results for let heat kernel in the exterior of a compact set, Comm. the heat equation under radiation boundary conditions, Pure and Applied Mathematics LV (2002), 93–133. Math. Ineq. and Appl. 4 (2001), 573–584. Alexander Bendikov and Laurent Salo -Coste, Gauss- Changhao Lin and Lawrence Payne, Continuous depen- ian bounds for derivatives of central Gaussian semi- dence on spatial geometry for the generalized Maxwell- groups on compact groups, Transactions of the AMS Caltaneo system, Math. Methods in Appl. Sci. 24 354 (2002), 1279–1298. (2001), 1113–1124. Alexander Grigor’yan and Laurent Salo -Coste, Hit- Lawrence Payne and J. C. Song, Growth and decay ting probabilities for Brownian motion on Riemannian in generalized thermoelasticity, Int. J. Eng. Sci. 40 manifolds, Journal de Math ematiques Pures et Ap- (2002), 385–400. pliqu ees 81 (2002), 115-142. Irena Peeva and Michael Stillman, Toric Hilbert Christophe Pittet and Laurent Salo -Coste, On ran- schemes, Duke Math. J. 111 (2002), 419–449. dom walk on wreath products, Annals of Probability, Irena Peeva, Resolutions and lattices, Special Issue for to appear. Jan-Erik Roos’s anniversary in Homology Homotopy Christophe Pittet and Laurent Salo -Coste, Random Appl., to appear. walk on abelian-by-cycle groups, Proceedings of the Ravi Ramakrishna, Deforming global Galois representa- AMS, to appear. tions, Annals of Mathematics, to appear. Alexander Bendikov and Laurent Salo -Coste, On the Deepak Ramani and Richard Rand, Nonlinear normal hypoellipticity of sub-Laplacians on in nite dimen- modes in a system with nonholonomic constraints, sional compact groups, Forum Mathematicum, to ap- Nonlinear Dynamics 25 (2001), 49–64. pear.
38 2001–2002 Faculty Publications W. Ho mann, Alfred Schatz, Lars Wahlbin and G. Wit- David Eisenbud, Daniel Grayson, Michael Stillman and tum, Asymptotically exact a posteriori estimators for Bernd Sturmfels, eds., Computations in Algebraic Ge- the pointwise gradient error on each element in ir- ometry with Macaulay 2 , Springer-Verlag, 2001. regular meshes; Part I: A smooth problem with glob- Michael Stillman, Bernd Sturmfels and Rekha Thomas, ally quasi-uniform meshes, Math. Comp. 70 no. 235 Algorithms for the Toric Hilbert Scheme, Springer- (2001), 897–909. Verlag, 2001. Alfred Schatz and Lars Wahlbin, Asymptotically exact Nina Huang and Robert Strichartz, Sampling theory for a posteriori estimators for the pointwise gradient er- functions with fractal spectrum, Experimental Mathe- ror on each element in irregular meshes; Part II: the matics 10 (2001), 619–638. piecewise linear case, to appear. Robert Strichartz, Harmonic mappings of the Sierpinski Alfred Schatz and Lars Wahlbin, Pointwise error esti- gasket to the circle, Proceedings American Mathemat- mates for di erences in piecewise linear nite element ical Society 30 (2001), 619–638. approximation, to appear. Robert Meyers, Robert Strichartz and Alexander Jason Schweinsberg, Applications of the continuous- Teplyaev, Dirichlet forms on the Sierpinski gasket,Pa- time ballot theorem to Brownian motion and related ci c Journal of Mathematics, to appear. processes, Stoch. Process. Appl. 95 (2001), 151–176. Scott Bailey, Theodore Kim and Robert Strichartz, Jason Schweinsberg, An O(n2) bound for the relax- Inside the L evy dragon, American Mathematical ation time of a Markov chain on cladograms, Random Monthly, to appear. Struct. Alg. 20 (2002), 59–70. Bryant Adams, S. Alex Smith and Robert Strichartz, James P. Hobert and Jason Schweinsberg, Conditions The spectrum of the Laplacian on the pentagasket, for recurrence and transience of a Markov chain on Conference Proceedings, to appear. Z+ and estimation of a geometric success probability, Anders Oberg, Robert Strichartz and Andrew Q. Ann. Statist., to appear. Yingst, Level sets of harmonic functions on the Sier- Richard Shore and Ted Slaman, A splitting theorem pinski gasket, Arkiv f ur Matematik, to appear. for n-REA degrees, Proc. Amer. Mathematical Soci- Robert Strichartz, Function spaces on fractals, Journal ety 129 (2001), 3721–3728. of Functional Analysis, to appear. Samuel Buss, Alexander Kechris, Anand Pillay and Edward Swartz, Matroids and quotients of spheres, Richard Shore, The prospects for mathematical logic Mathematische Zeitschrift (2002). in the twenty- rst century, Bulletin of Symbolic Logic James Sethian and Alexander Vladimirsky, Ordered up- 7 (2001), 169–196. wind methods for static Hamilton-Jacobi equations, Denis Hirschfeldt, Bakhadyr Khoussainov, Richard Proc. Nat’l Acad. Sci. USA 98 no. 20 (2001), 11069. Shore and A. Slinko, Degree spectra and computable James Sethian and Alexander Vladimirsky, Ordered up- dimension in algebraic structures, Annals of Pure and wind methods for hybrid control, Proceedings of the Applied Logic 115 (2002), 71–113. 5th International Workshop on Hybrid Systems: Com- Richard Shore and Yue Yang, A nonlow2 r.e. degree with putation and Control, Stanford, CA, USA, March 25– the extension of embeddings properties of a low2 de- 27, 2002 (LNCS 2289). gree, Mathematical Logic Quarterly 48 (2002), 131– Martin Bridson and Karen Vogtmann, The symmetries 146. of Outer space, Duke Mathematical Journal 106 no. 2 Richard Shore, Computable structures: presentations (2001), 391–409. matter, Proceedings of the Int’l Cong. LMPS, Krakow, Sava Krstic, Martin Lustig and Karen Vogtmann, An Poland, to appear. equivariant Whitehead algorithm, Proceedings of the Chi-Tat Chong, Richard Shore and Yue Yang, Interpret- Edinburgh Mathematical Society 44 (2001), 117–141. ing arithmetic in the r.e. degrees under 4-induction; Karen Vogtmann, Automorphisms of free groups and in Reverse Mathematics (S. Simpson, ed.), Lecture Outer space, Geometriae Dedicata, to appear. Notes in Logic, 2001. Ricardo Nochetto and Lars Wahlbin, Positivity preserv- Victor Guillemin, Lisa Je rey and Reyer Sjamaar, Sym- ing nite element approximation, Math. Comp., to ap- plectic implosion, Transformation Groups, to appear. pear. Eric Bedford and John Smillie, Polynomial di eomor- Nikolai Bakaev, Vidar Thom ee and Lars Wahlbin, phisms of C2 VIII: Quasi-expansion, Amer. J. Math- Maximum-norm estimates for resolvents of elliptic - ematics 124 (2002), 221–271. nite element operators, Math. Comp., to appear. J urgen Rohlfs and Birgit Speh, Pseudo Eisenstein Jerry Farlow, James Hall, Jean Marie McDill and Bev- series and the cohomology of arithmetic groups I , erly West, Di erential Equations and Linear Algebra, Manuscripta Mathematica, to appear. Prentice Hall, 2002.
2001–2002 Faculty Publications 39 Milen Yakimov, Symplectic leaves of complex reductive Nikolai Reshetikhin and Milen Yakimov, Quantum in- Poisson-Lie groups, Duke Mathematical Journal 112 variant measures, Comm. Math. Phys. 224 (2001), (2002), 453–509. 399–426. F. Alberto Gr unbaum and Milen Yakimov, Discrete Timothy Hodges and Milen Yakimov, The double and Darboux transformations from Jacobi polynomials,Pa- dual of a quasitriangular Lie bialgebra, Math. Res. ci c J. Math. 204 (2002), 395–431. Lett. 8 (2001), 91–105.
40 2001–2002 Faculty Publications The Faculty and their Research
Dan M. Barbasch, Professor; Ph.D. (1976) University of David W. Henderson, Professor; Ph.D. (1964) Univer- Illinois; Representation theory of reductive Lie groups. sity of Wisconsin; Geometry, educational mathemat- Yuri Berest, Assistant Professor; Ph.D. (1997) Univer- ics. sit e de Montreal (Canada); Mathematical physics and John H. Hubbard, Professor; Doctorat d’Etat (1973) algebraic geometry. Universit e de Paris Sud; Analysis, di erential equa- Louis Billera, Professor; Ph.D. (1968) City University of tions, di erential geometry. New York; Geometric and algebraic combinatorics. J.T. Gene Hwang, Professor; Ph.D. (1979) Purdue Uni- James H. Bramble, Professor Emeritus; Ph.D. (1958) versity; Statistics, con dence set theory. University of Maryland; Numerical solutions of partial Yulij Ilyashenko, Professor; Ph.D. (1969) Moscow State di erential equations. University; Dynamical systems. Kenneth S. Brown, Professor; Ph.D. (1971) Mas- Peter J. Kahn, Professor; Ph.D. (1964) Princeton Uni- sachusetts Institute of Technology; Algebra, topology, versity; Symplectic topology/geometry. group theory. Harry Kesten, Goldwin Smith Professor; Ph.D. (1958) Stephen U. Chase, Professor; Ph.D. (1960) University Cornell University; Probability theory, limit theorems, of Chicago; Non-commutative algebra, homological al- percolation theory. gebra, Hopf algebras, group theory. Dexter Kozen, Professor of Computer Science; Ph.D. Marshall M. Cohen, Professor; Ph.D. (1965) University (1977) Cornell University; Computational theory, of Michigan; Topology, geometric (and combinatorial) computational algebra and logic, logics and semantics group theory. of programming languages. Robert Connelly, Professor; Ph.D. (1969) University of Gregory Lawler, Professor; Ph.D. (1979) Princeton Uni- Michigan; Discrete geometry, computational geometry versity; Probability, statistical physics. and the rigidity of discrete structures. G. Roger Livesay, Professor Emeritus; Ph.D. (1952) R. Keith Dennis, Professor; Ph.D. (1970) Rice Univer- University of Illinois; Di erential topology, group ac- sity; Commutative and non-commutative algebra, al- tions. gebraic K-theory, group theory, mathematical bibliog- Michael D. Morley, Professor; Ph.D. (1962) University raphy. of Chicago; Mathematical logic, model theory. Richard Durrett, Professor; Ph.D. (1976) Stanford Uni- Anil Nerode, Goldwin Smith Professor; Ph.D. (1956) versity; Problems in probability theory that arise from University of Chicago; Mathematical logic, recursive ecology and genetics. functions, computer science, mathematics of AI, con- Eugene B. Dynkin, A. R. Bullis Chair and Professor; trol engineering. Ph.D. (1948), Dr. of Science (1951) Moscow Univer- Michael Nussbaum, Professor; Ph.D. (1979) Academy sity; Probability theory, Lie groups. of Sciences Berlin (Germany); Mathematical statistics. Cli ord J. Earle, Professor; Ph.D. (1962) Harvard Uni- Lawrence E. Payne, Professor Emeritus; Ph.D. (1950) versity; Complex variables, Teichm uller spaces. Iowa State University; Partial di erential equations, Jos e F. Escobar, Professor; Ph.D. (1986) University of ill-posed and nonstandard problems. California at Berkeley; Partial di erential equations; Irena Peeva, Assistant Professor; Ph.D. (1995) Brandeis di erential geometry. University; Commutative algebra and algebraic geom- Roger H. Farrell, Professor Emeritus; Ph.D. (1959) Uni- etry. versity of Illinois; Mathematical statistics, measure Richard Platek, Associate Professor; Ph.D. (1966) Stan- theory. ford University; Mathematical logic, recursion theory, Leonard Gross, Professor; Ph.D. (1958) University of set theory, computer science. Chicago; Functional analysis, constructive quantum Philip Protter, Professor of Operations Research and In- eld theory. dustrial Engineering; Ph.D. (1975) University of Cali- John M. Guckenheimer, Professor; Ph.D. (1970) Uni- fornia at San Diego; Stochastic analysis, stochastic nu- versity of California at Berkeley; Dynamical systems. merical analysis, stochastic nance theory and Markov Allen Hatcher, Professor; Ph.D. (1971) Stanford Uni- processes. versity; Geometric topology. Ravi Ramakrishna, Assistant Professor; Ph.D. (1992) Timothy Healey, Professor and Chair of Theoretical and Princeton University; Algebraic number theory. Applied Mechanics; Ph.D. (1985) University of Illinois; Richard Rand, Professor of Theoretical and Applied Me- Nonlinear elasticity, nonlinear analysis, partial di er- chanics; Sc.D. (1967) Columbia University; Applied ential equations. mathematics and di erential equations.
The Faculty and their Research 41 James Renegar, Professor of Operations Research and Michael E. Stillman, Professor; Ph.D. (1983) Harvard Industrial Engineering; Ph.D. (1983) University of University; Algebraic geometry, computational alge- California at Berkeley; Optimization algorithms. bra. Oscar S. Rothaus, Professor; Ph.D. (1958) Princeton Robert S. Strichartz, Professor; Ph.D. (1966) Prince- University; Several complex variables, combinatorics, ton University; Harmonic analysis, partial di erential Sobolev inequalities. equations, analysis on fractals. Laurent Salo -Coste, Professor; Ph.D. (1983) and Doc- Moss E. Sweedler, Professor Emeritus; Ph.D. (1965) torat d’Etat (1989) Universit e Paris VI; Analysis, po- Massachusetts Institute of Technology; Algebra, algo- tential theory, stochastic processes. rithms. Alfred H. Schatz, Professor; Ph.D. (1964) New York Karen Vogtmann, Professor; Ph.D. (1977) University University; Numerical solutions of partial di erential of California at Berkeley; Topology, geometric group equations. theory. Shankar Sen, Professor; Ph.D. (1967) Harvard Univer- Lars B. Wahlbin, Professor; Ph.D. (1971) University of sity; Algebraic number theory. G oteborg, Sweden; Numerical solutions of partial dif- Richard A. Shore, Professor; Ph.D. (1972) Mas- ferential equations. sachusetts Institute of Technology; Mathematical James E. West, Professor; Ph.D. (1967) Louisiana State logic, recursion theory, set theory. University; Geometric topology, in nite-dimensional Reyer Sjamaar, Associate Professor; Ph.D. (1990) Rijk- topology. suniversiteit te Utrecht (RUU), the Netherlands; Sym- plectic geometry. John Smillie, Professor and Chair; Ph.D. (1977) Univer- sity of Chicago; Dynamical systems. Birgit E. Speh, Professor; Ph.D. (1977) Massachusetts Institute of Technology; Lie groups, automorphic Faculty on sabbatical or other leave during all or part of forms, representation theory. the 2001–2002 academic year.
42 The Faculty and their Research Faculty Pro les
Allen Back Acting Professor of Mathematics Director of the Mathematics Instructional Computing Lab My original training was primarily in di erential ge- Invited Lectures: Mathematicians and Education Re- ometry and secondarily in topology. The most interest- form, Ithaca (1995). SIAM Special Session on Dynami- ing portion of my earlier work was related to the role of cal Systems Software, Philadelphia (1993). Oberwolfach compact Lie group actions in di erential geometry, es- Equivariant Di erential Geometry Conference (1983). pecially curvature realizability questions. I’ve been im- Syracuse Topology Conference (1981). AMS Special Ses- pressed by a variety of recent progress in this area (e.g. sion on Equivariant Geometry, San Francisco (1980). Einstein metrics and positive Ricci curvature on many University of Waterloo Math Colloquium (1979). cohomogeniety one manifolds) and have been working on what further directions may now be fruitful. Selected Publications: Besides equivariant di erential geometry, other areas Mathematics and tensegrity (with R. Connelly), Ameri- of past work and interest include transformation groups, can Scientist, March-April (1998), 142–151. homotopy theory, dynamical systems, some parts of dstool: computer assisted exploration of dynamical sys- mathematical physics, geometric modeling and robotics. tems (with J. Guckenheimer, M. Myers, F. J. Wicklin My work as director of the Instructional Computing Lab and P. Worfolk), Notices Amer. Math. Soc. 39 (1992), has also meshed with a longstanding interest in the use 303–309. of computers for mathematical enrichment. Equivariant geometry and Kervaire spheres (with Wu Yi Hsiang), Trans. Amer. Math. Soc. 304 no. 1 (1987), Awards and Honors: Putnam Exam Honorable Mention 207–227. (1969 and 1970). NSF Graduate Fellowship (1971). NSF Pontryagin forms on homogeneous spaces, Comment. Research Grant (1980). Math. Helv. 57 no. 3 (1982), 349–355. Rational Pontryagin classes and killing forms, J. Di er- Professional Activities: Assist in REU Program (1994– ential Geom. 16 no. 2 (1981), 191–193. present). Assist in Math Explorers Club Program (2000– Involutions on Grassmann manifolds, Ph.D. Thesis, present). Berkeley, 1977.
Graeme Bailey Professor of Computer Science Director of the Computer Science MEng Program Adjunct Professor of Mathematics Originally working in low-dimensional topology and point in collaborating with molecular pharmacologists combinatorial group theory, through an odd mixture and structural biologists has already yielded some in- of circumstances I have become actively involved in re- triguing insights. With the recent successes at Syracuse search in mathematics and medicine. One of two ongoing in determining scroll waves with the thickness of car- research projects in this area is the modelling of lung in- diac muscle, I’ve become interested again in modelling ation, together with a research group at the Class One dynamic aspects of cardiac electrophysiology. Trauma Center in Syracuse. This is in the early stages of Outside the primarily research front, this past year a program to extend to various pathologies a ecting elas- I’ve given a number of invited talks to student and ticity and aimed towards e ective clinical treatments. alumni groups, was voted ACSU “Faculty of the Year,” We’ve been fortunate to have made some signi cant ad- received the Kenneth A. Goldman Excellence in Teach- vances in answering some questions which had remained ing award, served on the Rhodes, Marshall, Churchill unsolved for over 30 years. The other project is in and Fulbright Fellowship committees for the nth year understanding deformations of transmembrane proteins — again the university was successful in having several used in cell-signalling processes. This is a carefully con- winners — was involved in continuing university discus- strained version of the protein-folding problems which sions on developing more vital faculty/student interac- have been exciting the mathematical biology community tions (serving on the University Program House Com- in recent years; the application of a topological view- mittee and the North Campus Committee), was the fac-
Faculty Pro les 43 ulty advisor for the Judo Club, remained involved with bright Committee, the Downtown Partnership COPC, Cornell EMS, enjoyed my eleventh year as a Faculty Fel- the Advisory Committee for Health Careers, the Arts’ low at Risley and gave the usual plethora of concerts. College’s Chairs Committee, the Slope Day Commit- tee and the Advisory Board for CURIE (persuading Awards and Honors: Kendall S. Carpenter Advising high school girls to consider engineering). Risley Fac- Award, 2002. ulty Fellow. Advisor to the Cornell Lunatics Club, the Administrative Activities: Member of the Board of Di- Judo Club. Contributor to the Math Explorer’s Club, rectors for Engineers Without Borders, the West Cam- the Association for Undergraduate Computer Scientists pus Housing Operations Committee, the Faculty in Res- [ACSU]. One of the invited fascilitators for ENG College idence Committee, the Marshall and Rhodes Scholarship Summer LEADER-SHAPE Program. One of the judges Selection Committees, the Masters of Engineering Com- for last year’s rst o ering of the graduate research sym- mittee, the Full Tuition Awards Committee, the Full- posium (Engineering College graduate students).
Dan Barbasch Professor of Mathematics My research is in the eld of representation theory of Selected Publications: reductive Lie groups. I am particularly interested in the The dual reductive pairs correspondence for complex classi cation of the unitary dual for groups over local groups (with J. Adams), J. Func. Anal. 132 (1995). elds, and its relation to the orbit structure of the Lie The dual reductive pairs correspondence for odd orthog- algebra. Furthermore I am interested in the relation of onal groups (with J. Adams), J. Func. Anal. (1996). these representations to problems arising from number Unitary spherical spectrum for split classical p-adic theory, more precisely automorphic forms. groups, Acta Applicandae Mathematicae 44 (1996). The spherical dual for p-adic groups (with A. Moy), Professional Activities: Referee for Transactions of the Proc. of Conf. in Cordoba, Argentina. AMS, American Journal of Mathematics and the Na- Local character expansions (with A. Moy), Ann. Sci. de tional Science Foundation. L’Ecole Norm. Sup. (1997). The associated variety of an induced representation Invited Lectures: (with M. Bozicevic), Proc. AMS (1998). Unitary representations and endoscopy, AMS Regional The associated variety of unipotent representations, Conference, Maryland. preprint. Classi cation of 1-K type representations (with A. Moy), Proc. AMS, to appear.
Yuri Berest Assistant Professor of Mathematics My interests are in mathematical physics, algebraic lem still remains unsolved even in the simplest cases (for geometry and noncommutative algebra. To be a bit more example, for analytic wave operators on at spaces). speci c, let me mention a few di erent topics that I am Integrable Systems. This eld has seen remarkable trying to bring together in my research. development during the past thirty years. ‘Integrable The Nature of Wave Fronts. The mathematical systems’ is an imprecise term, covering ordinary and par- problem has a practical origin: to understand what hap- tial di erential equations, statistical mechanics models, pens when a short signal (light or sound, say) is omitted Yang-Mills theories, string theory, random matrices — from point A, travels through a medium and arrives at almost any problem that ‘looks complicated’ but can be point B. There are many possibilities. There could be solved more or less explicitly. Miraculously, the explana- focusing, di raction, persistence of faint echoes or still tions for solvability always turn out to be related, even a short (‘clean-cut’) signal at B. Analysis is di cult when the underlying (physical or mathematical) models because explicit solutions are usually not available, and appear to have nothing in common. because the wave front may have complicated geometry. Noncommutative Algebra and Algebraic Ge- My e orts in this direction focus on the study of propa- ometry. In recent years, there have been a number of gation of ‘clean-cut’ wave signals (in particular, the con- important applications of techniques and ideas from al- ditions under which such signals could exist). Posed by gebraic geometry to noncommutative algebra. By e orts J. Hadamard more than 80 years ago, this classical prob- of M. Artin and his collaborators a far-reaching noncom-
44 Faculty Pro les mutative version of projective algebraic geometry has Selected Publications: been developed. Roughly speaking, the key idea behind Hadamard’s problem and Coxeter groups: new exam- this generalization is to view the category of graded mod- ples of Huygens’ equations (with A. P. Veselov), Func. ules modulo torsion over a noncommutative graded ring Anal. and Appl. 28 no. 1 (1994), 3–12. as the noncommutative analogue of a projective vari- Huygens’ principle and integrability (with A. P. Veselov), ety. This intuition has led to a remarkable number of Russian Math. Surveys 49 no. 6 (1994), 7–77. nontrivial results in noncommutative algebra and rep- Lacunae of hyperbolic Riesz kernels and commutative resentation theory. It turns out that the geometry of rings of partial di erential operators, Lett. Math. noncommutative projective surfaces is intrinsically re- Phys. 41 no. 3 (1997), 227–235. lated to certain integrable systems. My current research Huygens’ principle in Minkowski spaces and soliton solu- project (pursued jointly with G. Wilson) is aimed at clar- tions of the Korteweg-de-Vries equation (with I. Lout- ifying this relation. Remarkably, the link to integrable senko), Comm. Math. Phys. 190 no. 1 (1997), 113–132. systems sheds new light on some old and (traditionally Hierarchies of Huygens’ operators and Hadamard’s con- perceived as) di cult questions in algebraic geometry. jecture, Acta Appl. Math. 53 no. 2 (1998), 125–185. One of our recent results is a complete classi cation of Classi cation of rings of di erential operators on a ne rings of global di erential operators on a ne algebraic curves (with G. Wilson), Internat. Math. Res. Notices curves. 2 (1999), 105–109. The problem of lacunas and analysis on root systems, Awards and Honors: Canadian Mathematical Society Trans. Amer. Math. Soc. 352 no. 8 (2000), 3743–3776. Doctoral Prize (1998). A. P. Sloan Research Fellowship Automorphisms and ideals of the Weyl algebra (with (2001). G. Wilson), Math. Ann. 318 no. 1 (2000), 127–147. Ideal classes of the Weyl algebra and noncommuta- Professional Activities: Editor of the Journal of Non- tive projective geometry (with G. Wilson), IMRN 26 linear Mathematical Physics. Reviewer for Mathematical (2002), 1347–1397. Reviews. Referee for the NSF and several journals.
Louis J. Billera Professor of Mathematics Director of Graduate Studies For some time, my research has centered on combina- More recently, my attention has turned to applying torial properties of convex polytopes and their relations these ideas to an interesting problem arising in biology to algebraic and geometric questions. Some problems (structure of phylogenetic trees) and to connections, via are related to the facial structure of polytopes, for ex- duality of Hopf algebras, with various algebras of qua- ample, enumeration of faces or identi cation of their lat- sisymmetric functions. tice structure. Others have to do with subdivisions of polytopes, how they might depend on the geometry (as Professional Activities: Member of the editorial boards opposed to the combinatorics) of the underlying set, or of Discrete and Computational Geometry and the Jour- how the algebraic properties of objects related to a given nal of Algebraic Combinatorics. Served on the NSF subdivision, for example the algebra of smooth piecewise Panel for grants in combinatorics from the Algebra, polynomial functions (splines) de ned on it, might de- Number Theory and Combinatorics Program. pend on both combinatorial and geometric issues. A common theme in much of this has been the con- Invited Lectures: Delivered lectures on quasisymmetric struction of polytopes to given speci cations: for exam- functions and Eulerian enumeration at: AMS regional ple the construction with Carl Lee of polytopes satisfying meeting (Williamstown, Virginia, October 2001), Uni- the conditions of McMullen’s g-conjecture, showing these versity of Miami (March 2002), CombinaTexas (Denton, conditions to be su cient to describe the enumeration of Texas, March 2002), University of Washington (Seattle, faces of all simplicial convex polytopes; or the construc- April 2002), University College (London, England, May tion with Bernd Sturmfels of ber polytopes, showing 2002). that certain sets of polyhedral subdivisions of polytopes Delivered colloquium talks on geometry of the space of themselves had the structure of convex polytopes; or the phylogenetic trees at: University of Miami (March 2002), construction with A. Sarangarajan of faces of the trav- MIT (March 2002), University of Washington (Seattle, eling salesman polytope, showing this polytope to have April 2002). every possible 0-1 polytope as a low-dimensional face.
Faculty Pro les 45 Selected Publications: Geometry of the space of phylogenetic trees (with Linear inequalities for ags in graded partially ordered S. Holmes and K. Vogtmann), Advances in Applied sets (with G. Hetyei), J. Comb. Theory, Series A, 89 Mathematics 27 (2001), 733–767. (2000), 77–104. A geometric interpretation of the Metropolis-Hastings Monotonicity of the cd-index for polytopes (with R. Ehren- algorithm (with P. Diaconis), Statistical Science 16 borg), Math. Z. 233 (2000), 421–441. (2001), 335–339. Noncommutative enumeration in graded posets (with Peak quasisymmetric functions and Eulerian enumera- N. Liu), J. Algebraic Combinatorics 12 (2000), 7–24. tion (with S. Hsiao and S. van Willigenburg), Ad- Decompositions of partially ordered sets (with G. Het- vances in Mathematics, to appear. yei), Order 17 (2000), 141–166.
James H. Bramble Professor Emeritus of Mathematics For the past 25 years I have been interested in the de- Professional Activities: Distinguished Professor of velopment of the theoretical foundation of nite-element Mathematics at Texas A&M University. methods for the approximation of solutions of elliptic and parabolic partial di erential equations. Recently I Invited Lectures: have concentrated on questions concerning rapid solution Interpolation between subspaces of Hilbert spaces and of large-scale systems that result from such approxima- multilevel scales and norms, invited address, sympo- tions. Such a question is: Among all the theoretically sium honoring John Osborn, University of Maryland, good approximations to a general class of problems, are College Park, September 2000. there some that can be solved e ciently by taking ad- vantage of modern computer architectures such as par- Selected Publications: allelism? Answers to questions like this one can bring Multigrid methods (with X. Zhang); a chapter in the many problems into the realm of practical feasibility. My Handbook for Numerical Analysis (P. Ciarlet and J. L. current research interest is the design of approximations Lions, eds.), North Holland, 2001. to solutions to problems in partial di erential equations that adequately describe the problem and that can be e ciently solved using modern computing power.
Kenneth Brown Professor of Mathematics Until recently my main interests have been algebra Professional Activities: Referee for various journals and and topology. I have especially enjoyed using topological government agencies. Served on the committee to select methods to study in nite discrete groups. In some of my algebra speakers for the 1982 Int’l Congress of Mathe- early work, for instance, I studied Euler characteristics maticians and on the organizing committees for many of groups. I obtained formulas relating the Euler charac- conferences on topological methods in group theory. teristic (a topological concept) to purely algebraic prop- Invited Lectures: erties of groups. When applied in special cases, these Cohomology of in nite groups, International Congress of formulas unexpectedly led to new results in algebraic Mathematicians, Helsinki (1978). number theory. Later, I found topological methods for Buildings lecture series, Univ. Hong Kong (June 1999). studying two interesting families of groups: in nite sim- ple groups, and groups which can be presented by means Selected Publications: of a complete rewriting system. Euler characteristics of discrete groups and G-spaces, In- I have recently incorporated methods of probability vent. Math. 27 (1974), 229–264. theory into my research. In work with L. Billera and Cohomology of Groups, Springer-Verlag, New York, 1982 P. Diaconis, for example, we combine tools from geom- (Graduate texts in mathematics 87). etry, topology, and probability to analyze an interesting Buildings, Springer-Verlag, New York, 1989. family of random walks. Random walks and hyperplane arrangements (with P. Di- aconis), Ann. Prob. 26 (1998), 1813–1854. Awards and Honors: Clark Teaching Award, Cornell Semigroups, rings and Markov chains, J. Theoretical University (1987). Probability 13 (2000), 871–938.
46 Faculty Pro les Kai-Uwe Bux H. C. Wang Assistant Professor of Mathematics The underlying idea of geometric group theory is that invariants — niteness properties and geometric invari- groups are meant to act on geometric objects. The prop- ants extend and re ne the notions of nite generation erties of the action can be used to study both the group and nite presentability of groups. and the geometry. From this point of view, the rst step in understanding a group is to nd a space on which it Invited Lectures: Last year, I gave invited talks at Bing- acts “nicely.” Classical examples of this technique in- hamton University (December 2001) and at the Univer- clude the work on arithmetic and S-arithmetic groups sity of Virginia at Charlottesville (April 2002). by means of buildings and symmetric spaces, the study of mapping class groups via Teichm uller theory, and the Selected Publications: results about outer automorphism groups of free groups Finiteness properties of some metabelian S-arithmetic via their actions on Culler-Vogtmann spaces. groups, Proceedings of the London Mathematical So- Once a space X and an action G → Aut(X) are cho- ciety 75 (1997), 308–322. sen, there is still the problem of understanding the space. The Bestvina-Brady construction revisited — geomet- In this context, combinatorial Morse theory is an impor- ric computation of -invariants of right angled Artin tant tool: If there is a real-valued function f : X → R groups (with C. Gonzalez), Journal of the London on the space, whose level sets are invariant with respect Mathematical Society (2) 60 (1999), 793–801. to the group action, then the homotopy type of the space Orbit spaces of subgroup complexes and Morse theory, and of the sublevel sets f 1( ∞,t] can be understood Topology Proceedings 24 (Spring 1999), 39–51. in terms of incremental changes as the value of t varies. Finiteness properties of soluble S-arithmetic groups – I have applied some of these ideas to solvable S- a survey; in Proceedings of the conference “Groups: arithmetic groups over global function elds in order Geometric and Combinatorial Aspects,” Bielefeld, to determine their niteness properties and geometric 1999, to appear.
Stephen U. Chase Professor of Mathematics With the exception of my early work on module the- pure algebra; these involve primarily Hopf algebras (es- ory, homological algebra, and abelian groups, the endur- pecially quantum groups and Tannakian reconstruction) ing theme of my mathematical interests and research has and, more recently, nite groups (especially the structure been the Galois theory of rings and elds, and variations of p-groups). of these theories in which the role of the classical Galois group is played by some related algebraic structure such Selected Publications: as a restricted Lie algebra, group scheme, Hopf alge- Galois theory and Galois cohomology of commutative bra, or groupoid. This work impinges upon and utilizes rings (with D. K. Harrison and A. Rosenberg), Amer. techniques from other areas in which I also have strong Math. Soc. Memoir 52 (1965). interests, such as category theory and homological al- Hopf Algebras and Galois Theory (with M. E. Sweedler), gebra, group theory, group schemes and Hopf algebras, Lecture Notes in Math 97, Springer-Verlag, 1969. representation theory, algebraic K-theory, and algebraic In nitesimal group scheme actions on nite eld exten- number theory. sions, Amer. J. Math. 98 (1976), 441–480. Following a period in my career in which the main fo- Rami cation invariants and torsion Galois module struc- cus of my research was the Galois module structure of ture in number elds, J. Algebra 91 (1984), 207–257. algebraic integers, I have returned to investigations in
Marshall M. Cohen Professor of Mathematics I work in the closely related elds of geometric topol- ric problems or geometric themes into combinatorial and ogy, combinatorial group theory and geometric group algebraic problems. The work has involved the inter- theory. Much of my work has dealt with the introduc- mingling of topological manifolds, combinatorial topol- tion of combinatorial and algebraic themes into geomet- ogy, the foundations of piecewise linear topology, simple-
Faculty Pro les 47 homotopy theory, automorphisms of free groups, and A Course in Simple-Homotopy Theory, Graduate Texts spaces of length functions on groups. Currently the sec- in Mathematics 10, Springer Verlag, 1973. ond best description of me is geometric group theorist. Whitehead torsion, group extensions and Zeeman’s con- The title which I most covet is that of teacher. The jecture in high dimensions, Top. 16 (1977), 79–88. writing of a research paper and the teaching of fresh- What does a basis of F (a, b) look like? (with W. Metzler man calculus, and everything in between, falls under this and A. Zimmermann), Math. Ann. 257 (1981), 435– rubric. Happy is the person who comes to understand 445. something and then gets to explain it. On the dynamics and the xed subgroup of a free group In addition to research and teaching, I deeply value automorphism (with M. Lustig), Inv. Math. 96 (1989), and enjoy my role as a faculty advisor to undergraduates. 613–638. Very small group actions on R-trees and Dehn twist au- Awards and Honors: Winner of the Dean’s Award for tomorphisms (with M. Lustig), Topology 34 (1995), Advising in 1992, the rst year in which this award was 575–617. given. (It is now called the Robert A. and Donna B. The conjugacy problem for Dehn twist automorphisms Paul Award for Excellence in Advising.) of free groups (with M. Lustig), Commentarii Mathe- Professional Activities: Member of the AMS and MAA. matici Helvetici 74 (1999), 179–200. The surjectivity problem for one-generator, one-relator Selected Publications: extensions of torsion-free groups (with C. Rourke), Simplicial structures and transverse cellularity, Annals Geometry and Topology 5 (2001), 127–142. of Math. (2) 85 (1967), 218–245.
James Conant VIGRE Assistant Professor of Mathematics I am interested in essentially all areas of mathematics Awards and Honors: Member of the Max-Planck- although I tend to do research in areas closely related Institut, Bonn (summer 2001). to low-dimensional topology, and especially to Vassiliev knot and three-manifold invariants. One of my favorite Administrative Activities: Organizer of the Topology results, which is joint with Peter Teichner, is a character- Seminar (spring 2002). ization of when two knots share Vassiliev invariants up Invited Lectures: Junge Topologen conference, Univer- to a given degree in terms of ambient cobordism by cer- sity of Munster (Sep. 2001). AMS special session in low tain 2-complexes called gropes. This can be found in our dimensional topology, San Diego (Jan. 2002). Confer- preprint Grope cobordism of classical knots, available at ence on quantum topology, University of Warwick, Eng- arxiv.org. I am currently thinking about graph homol- land (Mar. 2002). ogy and operads. Karen Vogtmann and I have a preprint on the subject, A Lie bialgebra structure on graphs and Selected Publications: graph homology, which is also available at arxiv.org. On a theorem of Goussarov, J. Knot Theory Rami ca- tions, to appear.
Robert Connelly Professor of Mathematics Discrete geometry, with emphasis on the geometry of Another subject of interest is the theory of exible rigid and exible structures, is my main area of interest. surfaces. There are triangulated surfaces that ex, keep- A tensegrity is a structure composed of sticks held in ing their edges at a xed length, and it has recently mid-air with strings which, nevertheless, holds its shape. been shown that such surfaces maintain a xed volume This can be modeled very nicely as a con guration of while they ex. There is no perfect mathematical bel- points with upper and lower bounds on the distances be- lows. This is also related to a polynomial that relates the tween certain pairs of points. This in turn leads to inter- volume of the surface to the lengths of its edges. This is esting problems in, and applications to, distance geome- at the intersection of discrete geometry, algebraic geom- try and the theory of packings and coverings of spheres etry and topology. as well as applications to robotics, protein folding, mo- tion planning and percolation problems in physics and Professional Activities: Member of the AMS and the probability. MAA. Reviewer for the Mathematical Reviews. Ref-
48 Faculty Pro les eree for various journals. Editor for Beitr age f ur Algebra Selected Publications: und Geometrie. Organized the Fourth Geometry Fes- Rigidity; Chapter 1.7 in Handbook of Convex Geometry tival (with K. Bezdek, A. Bezdek and K. Boroczky), (P. M. Gruber and J. M. Wills, eds.), North Holland, Budapest, Hungary (1999). Organized a workshop on 1993, pp. 223–271. discrete geometry (with B. Erdahl, W. Whiteley and Higher-order rigidity — What is the proper de nition? M. Senechal) at the AMS Conference in Lowell, MA (with H. Servatius), Discrete Comput. Geom. 11 (Apr. 2000). (1994), 193–200. Finite and uniform stability of sphere coverings (with Invited Lectures: A. Bezdek and K. Bezdek), L. Fejes T oth Festschrift, The bellows conjecture, Conference on Discrete and Special Volume of Discrete and Comput. Geom. 13 Computational Geometry, Ascona, Switzerland (June no. 3–4 (1995), 313–319. 1999); Case Western, Ohio (Aug. 1999); University of Globally rigid symmetric tensegrities (with M. Terrell), Illinois at Urbana-Champaign (Aug. 1999). Structural Topology 21 (1995), 59–78. Symmetric tensegrities, ICAAM Conference at Edin- Second-order rigidity and prestress stability for tenseg- burgh, Scotland (July 1999), University of Laramie rity frameworks (with W. Whiteley), SIAM J. Discrete (Aug. 1999). Mathematics 9 no. 3 (1996), 453–491. Two-distance functions, Budapest, Hungary (July The bellows conjecture (with I. Sabitov and A. Walz), 1999). Contrib. to Alg. and Geom. 38 no. 1 (1997), 1–10. Two-distance preserving functions, University of Illinois Finite and uniform stability of sphere packings (with at Urbana-Champaign (Aug. 1999); Western Washing- A. Bezdek and K. Bezdek), Discrete and Comput. ton University (Nov. 1999); Technical University of Vi- Geom. 20 (1998), 111–130. enna, Austria (Dec. 1999). Mathematics and tensegrity (with A. Back), American Tension percolation, Geometry Festival at Budapest, Scientist March-April (1998), 142–151. Hungary (Nov. 1999); ETH Zurich, Switzerland (Dec. Tensegrity structures: why are they stable?; in Rigidity 1999). Theory and Appl. (M. F. Thorpe and P. M. Duxbury, Several talks on Rigidity and The carpenter’s rule prob- eds.), Kluwer Academic/Plenum, 1999, 47–54. lem, Workshop on Discrete and Computational Geom- Tension percolation (with K. Rybnikov and S. Volkov), etry (associated with McGill Univ., Canada) at Bar- submitted. bados (Jan.–Feb. 2000). Straightening polygonal arcs and convexifying polygonal The carpenter’s rule problem, Reed College (2000). cycles (with E. Demaine and G. Rote), in preparation.
R. Keith Dennis Professor of Mathematics Most of my research has been in the eld of algebraic While I was executive editor of Mathematical Reviews, K-theory. This eld is, in some sense, a fancy gener- I became interested in problems dealing with mathemat- alization of linear algebra to arbitrary rings. As such, ical communication, databases and mathematical bibli- it has applications in many other areas of mathematics ography, and how to convert the older mathematical lit- such as topology, algebraic geometry, and even the the- erature into searchable electronic form. I have mainly ory of Markov processes. I have been most interested in been involved with these issues during the last several the computational aspects of the subject, in particular years. the computation of quotients of rings of algebraic inte- gers and in the computation of the Whitehead group for Professional Activities: Served on the board of ad- nite abelian groups. visors for the American Institute of Mathematics Parts of this work have involved the use of computers (AIM). Chaired the AIM Library Board. Part of to understand a number of examples before formulating the project to digitize the Duke Mathematics Jour- and proving the general results. This work has led to nal. Coeditor with B. Wegner on the Jahrbuch Project the study of questions about group rings, number theory, (www.eims.de/projects/JFM). Served on the committee and theory of nite groups. My current interest lies in to arrange digitization of the Paci c Journal of Math- studying a number of problems relating to commutators, ematics. Co-organizer of the workshop “Linking and structure, and invariants of nite groups which can be Searching in Distributed Digital Libraries,” University investigated by computer computations. of Michigan, Ann Arbor, March 18–20, 2002.
Faculty Pro les 49 Administrative Activities: Worked with the University Selected Publications: Librarian on Project Euclid. Noncommutative Algebra (with B. Farb), Springer-Ver- lag, 1993. Invited Lectures: A global mathematics library: how Homogeneous functions and algebraic K-theory (with to get there?, CEIC meeting, Vancouver, Quebec, Reinhard Laubenbacher), to appear. Canada (Feb. 2002). The number of groups of order N, to appear. An international project to construct a global mathemat- Totally non-abelian nite groups, in preparation. ics library, workshop in Ann Arbor, Michigan (Mar. Generic product decompositions of nite groups,in 2002). preparation.
Martin Dindo s H. C. Wang Assistant Professor of Mathematics In my research I study problems that originate in har- ical assumptions previously thought to be necessary in monic analysis and partial di erential equations. In par- Rn. Recently I began to work on problems related to ticular, I am interested in problems that contain inter- uid mechanics. play of both of these elds, such as use of harmonic anal- ysis to study elliptic linear and nonlinear partial di er- Selected Publications: ential equations. Harmonic analysis is well suited for Limits of trans nite convergent sequences of derivatives, studying PDE on rough domains and with rough coe - Real Analysis Exchange 22 no. 1 (1996/97), 338–345. cients where others (less powerful tools) fail. On series with alternating signs in the Euclidean metric, Sometimes I am interested in questions that originate Real Analysis Exchange 25 no. 2 (1999/2000), 599– purely in harmonic analysis such as in my thesis where I 616. studied Hardy spaces on manifolds. In this setting many Existence and uniqueness for a semilinear elliptic prob- new phenomena not seen in Rn appear due to the pres- lem on Lipschitz domains in Riemannian manifolds, ence of non-Euclidean metric. The study of harmonic Comm. PDE 27 no. 1–2 (2002), 219–281. functions and various spaces on manifolds also brings Semilinear Poisson problems in Sobolev-Besov spaces certain unexpected bene ts. For example the develop- on Lipschitz domains (with M. Mitrea), Publicacions ment of layer potential theory on domains in Riemannian Mathematiques, to appear. manifolds helped to remove certain super cial topolog-
Richard Durrett Professor of Mathematics My research concerns problems in probability theory to understand how genomes involve due to large scale that arise from ecology and genetics. Most of my ef- processes: inversions, translocations, and chromosome forts in the rst direction have been with Simon Levin ssions and fusions. This topic is not only important for in Ecology and Evolutionary Biology at Princeton, with comparative genomics but also leads to some unexpected whom I have collaborated since 1987. My recent work connections between random walks on the permutation primarily concerns applications to genetics, which these group and the Erdos-Renyi theory of random graphs. days is more fashionably called genomics. As the re- cent publications cited below indicate, I have worked Professional Activities: Associate Editor of Notices of with Chip Aquadro in Molecular Biology and Genet- the American Mathematical Society and the Journal of ics on microsatellites (DNA repeat sequences), helped Theoretical Probability. Elected fellow of the American Steve Tanksley in Plant Breeding to solve a problem he Academy of Arts and Sciences, 2002. was interested in, and have worked on various topics with Ted Cox at Syracuse, NSF postdoc Vlada Limic, Selected Publications: graduate student Nancy Sundell, and REU particpants Stochastic spatial models, SIAM Review 41 (1999), 677– Arkendra De, Mike Ferguson, and Suzanne Sindi. In be- 718. tween these numerous trips to the dark side, I have on Distribution and abundance of microsatellites in the occasion worked on problems in pure mathematics in col- yeast genome can be explained by a balance between laboration with Persi Diaconis or Vlada Limic and Harry slippage events and point mutations (with C. F. Kesten. The nal two publications are on the topic that Aquadro, S. Kruglyak and M. Schug), Mol. Biol. Evol. is the center of my current research: building models 17 (2000), 1210–1219.
50 Faculty Pro les Probability Theory: An Introduction to its Applications; Chutes and ladders in Markov chains (with P. Diaconis), in Mathematics Unlimited 2001 and Beyond, Springer- J. Theor. Prob. 14 (2001), 899–926. Verlag New York, 2001, pp. 393–405. Mutual invadability implies coexistence in spatial models, Dynamics of microsatellite divergence under stepwise Memoirs of the AMS 156 no. 740 (2002). mutation and proportional slippage/point mutation A simple formula useful for positional cloning (with models (with P. Calabrese and C. F. Aquadro), Ge- K. Y. Chen and S. D. Tanksley), Genetics 160 (2002), netics 159 (2001), 839–852 353–355. On the quantity and quality of single nucleotide polymor- Competition and species packing in patchy environments phisms in the human genome (with V. Limic), Stoch. (with L. A. Buttel and S. A. Levin), Theor. Pop. Biol., Proc. Appl. 93 (2001), 1–24. to appear. Exponential distance statistics to detect the e ects of Once edge-reinforced random walk on a tree (with population subdivision (with N. Sundell), Theor. Pop. H. Kesten and V. Limic), Prob. Th. Rel. Fields, to Biol. 60 (2001), 107–116. appear. The equilibrium distribution for a generalized Sanko - The stepping stone model: new formulas expose old Ferretti model accurately predicts chromosome size dis- myths (with J. T. Cox), Ann. Appl. Prob., to appear. tributions in a wide variety of species (with A. De, Shu ing chromosomes, J. Theor. Prob., to appear. M. Ferguson and S. Sindi), J. Appl. Prob. 38 (2001), Bayesian estimation of the number of inversions in the 324–334. history of two chromosomes, J. Comp. Bio., submit- ted.
Eugene B. Dynkin Professor of Mathematics A. R. Bullis Chair Lie groups were the main subject of Dynkin’s earlier Professional Activities: Served on the advisory board research. “Dynkin’s Diagrams” are widely used by math- of Probability Theory and its Applications and Mathe- ematicians and physicists. After 1954, probability theory matics in Operations Research. Scienti c advisor of the became the central eld of his interests. Principal e orts International Center for Mathematical Sciences, Edin- were devoted to Markov processes and their connections burgh, Great Britain. with potential theory and partial di erential equations. Other work includes research in mathematical statistics Invited Lectures: Delivered an invited lecture at the In- (su cient statistics, exponential families), optimal con- ternational Conference on Potential Theory and Related trol (optimal stopping, control with incomplete data) Fields, Bielefeld, Germany, March 2001. Gave a plenary and mathematical economics (economic growth and eco- address at the conference “Perspectives in Partial Dif- nomic equilibrium under uncertainty). More recently, he ferential Equations and Probability,” Minneapolis, Min- has been working on the relationship between Markov nesota, May 2001. processes and random elds which arise in statistical physics and quantum eld theory. Since 1988, branching Selected Publications: measure-valued processes have become the main subject Fine topology and ne trace on the boundary associated of his research (the name “superprocesses” suggested by with a class of semilinear di erential equations (with him for these processes is now standard in mathemati- S. E. Kuznetsov), Comm. Pure Appl. Math. 51 (1998), cal literature). He established connections between su- 897–936. perdi usions and a class of nonlinear partial di erential Probability and nonlinear analysis, Canadian Mathemat- equations that makes it possible to apply powerful ana- ical Society Conference Proceedings 28 (2000), 139. lytic tools for investigating the path behavior of superdif- Rough boundary trace for solutions of Lu = (u) (with fusions and that provides a new probabilistic approach S. Kuznetsov), Probability Theory and its Applica- to problems on nonlinear PDEs. Since 1996 the main tions 45 (2000), 740. e orts were devoted to new directions in this eld: the Selected Papers of E. B. Dynkin with Commentary, AMS description of all positive solutions of a certain class of and International Press (A. Onishchik, G. Seitz and nonlinear equations and the study of boundary singu- A. Yushkevich, eds.), 2000. larities of such solutions. A systematic and improved Branching exit Markov systems and superprocesses, An- presentation of the results is contained in a monograph nals of Probability 29 no. 4 (2001), 1833–1858. published in 2002 in the Colloquium Publications Series Di usions, Superdi usions and Partial Di erential by the American Mathematical Society. Equations, Colloquium Publications, AMS, 2002.
Faculty Pro les 51 Cli ord Earle Professor of Mathematics Most of my research concerns invariants belonging to University of Warwick, England (Feb. 2002). Mathemat- Riemann surfaces. I am especially interested in learning ics Colloquium, University of Warwick, England (Feb. how these invariants change when the complex structure 2002). Mathematics Colloquium, University of South- of the Riemann surface is modi ed. A useful technique ern California (Apr. 2002). Topology Seminar, Califor- is to consider a family of Riemann surfaces depending nia Institute of Technology (Apr. 2002). holomorphically on some parameters and to study how the invariants of the surface change as we move about in Selected Publications: the parameter space. Quasiconformal maps and Kleinian A bre bundle description of Teichm uller theory (with groups have proved to be fundamental tools for the con- J. Eells), J. Di erential Geometry 3 (1969), 19–43. struction of good parameter spaces, so I have studied A xed point theorem for holomorphic mappings (with and used them extensively. R. S. Hamilton), Global Analysis, Proc. Symp. Pure Math., Vol. XVI, Berkeley, Calif. (1968), Amer. Math. Professional Activities: Managing editor of Proceedings Soc., Providence, 1970, pp. 61–65. of the American Mathematical Society through Janu- Conformally natural extension of homeomorphisms of ary 31, 2001. One of three U.S. members of the organiz- the circle (with A. Douady), Acta Math. 157 (1986), ing committee for the Second Iberoamerican Congress 23–48. on Geometry, Guanajuato, Mexico, January 2001. Quasiconformal Isotopies (with C. McMullen), Holo- morphic functions and moduli, Vol. I, Math. Sci. Administrative Activities: Served on the Arts College Res. Inst. Publ. 10, Springer, New York-Berlin, 1988, Ad Hoc Committee on Faculty Salaries. pp. 143–154. Teichm uller disks and Veech’s F-structures (with F. P. Invited Lectures: Symposium on Kleinian groups and Gardiner), Extremal Riemann surfaces, Contemp. hyperbolic geometry, University of Warwick, England Math. 201 (1997), 165–189. (Sep. 2001). Analysis and hyperbolic geometry seminar,
Jos e F. Escobar Professor of Mathematics My research has focused on the study of linear and Awards and Honors: Presidential Faculty Fellowship non-linear partial di erential equations arising in dif- (1992–1999), created by President Bush to be given to ferential geometry. The basic purpose of geometry is 15 scientists in the nation each year. Colciencias Award, to give a good description of a class of geometric ob- Category A (1996). Alejandro Angel Escobar Founda- jects. The geometric objects I study are the so-called tion: Mention of Excellence in Science (1995). Riemannian manifolds. These are spaces endowed with analytical structures, like the metric which provide us Professional Activities: Member of the AMS and the with a way to measure lengths and angles. It is natu- Colombian Mathematical Society. Correspondent mem- ral to study deformations of these structures to realize ber of the Colombian Academy of Sciences. Chairman of what properties in the space remain stable under such III Escuela de Verano en Geometr a Diferencial, Ecua- perturbations. The description of all these deformations ciones en Derivadas Parciales y An alisis Num erico, Uni- is usually governed by di erential equations. The cur- versidad de los Andes, Bogot a, Colombia (1995). Chair- vature tensor of a Riemannian manifold (a measure for man of Physical Sciences, Mathematics and Engineering the “non-euclideanness” of a Riemannian space) usually Panel for the 1995, 1996, 1997 & 1998 Ford Foundation makes such equations non-linear, although as in physics, Dissertation and Postdoctoral Fellowships. most of them are of variational nature. I have been able Editorial Board of the Electronic Journal of Di eren- to develop the existence theory of solutions to semilinear tial Equations since 1993 and Revista Colombiana de elliptic equations with non-linear boundary conditions. Matem aticas since 1992. International editor of Inno- These equations appear in the problem of conformal de- vaci on y Ciencia since 1992. Referee for the Journal of formation of a Riemannian metric on a manifold with the AMS, Journal of Di . Geometry, Duke Mathemati- boundary and in some non-linear problems in physics. cal Journal, Indiana Mathematical Journal, Proceedings
52 Faculty Pro les of the AMS, Communications in Analysis and Geometry, Selected Publications: among others, and the NSF. Conformal metrics with prescribed scalar curvature (with R. Schoen), Invent. Math. 86 (2) (1986), 243– Invited Lectures: 254. Conformal geometry, US-Chinese Conference on Recent Uniqueness theorems on conformal deformations of met- Developments in Di erential Equations and Applica- rics, Sobolev inequalities and an eigenvalue estimate, tions, Hangzhou, P. R. China (1996). Comm. on Pure and Appl. Math. 43 no. 7 (1990), 857– The geometry of the rst Steklov eigenvalue, Southern 883. California Geometry Analysis Seminar, Irvine, Cali- Conformal deformation of a Riemannian metric to a fornia (1998). scalar at metric with constant mean curvature on the An isoperimetric inequality and the Steklov eigenvalue, boundary, Ann. Math. 136 (1992), 1–50. Brazilian School of Geometry, Belo Horizonte, Brazil The Yamabe problem on manifolds with boundary,J. (1998). Di . Geom. 25 (1992), 21–84. New results on conformal deformation of metrics, Work- A comparison theorem for the rst non-zero Steklov shop on Geometric Partial Di erential Equations, Pa- eigenvalue, J. Funct. Analysis 178 (2000), 143–155. ci c Institute, UBC, Vancouver, Canada (2001). Conformal metrics on the ball with zero scalar curvature and prescribed mean curvature on the boundary (with G. Garcia), preprint 2002.
Roger Farrell Professor Emeritus of Mathematics Retired as of July 1, 1999, I am still semi-active in the Selected Publications: department and try to come in most days to audit classes Multivariate Calculation, Springer-Verlag, 1985. and work some in the Math Support Center. I am not Proof of a necessary and su cient condition for admis- active in research. sibility in discrete multivariate problems (with L. D. My research concerned the application of decision the- Brown), J. Mult. Anal. 24 (1988), 46–52. ory methods to statistical problems to try and charac- All admissible linear estimators of the vector of Gam- terize completely good and bad methods of estimation ma state parameters with application to random ef- and testing. Useful decision theory methods can involve fects models (with W. Klonecki and S. Zontek), Ann. development of inequalities, compacti cation of spaces, Statist. 17 (1989), 268–281. and study of the way sequences of measures converge. A lower bound for the risk in estimating the value of a probability density (with L. D. Brown), Jour. Amer. Professional Activities: Member of the IMS, AMS and Statist. Assoc. 85 (1990), 1147–1153. ASA. Occasional reviews for Mathematical Reviews and Estimations of accuracy in testing (with J. T. G. Hwang, occasional refereeing. G. Casella, C. Robert and M. T. Wells), Ann. Statist. 20 (1992), 490–509. Spitzer and Bohnenblust, revisited (1997), preprint.
Matthew C. Fickus VIGRE Assistant Professor of Mathematics The eld of harmonic analysis is composed of many compositions may be used to build error correction di- branches. In the same way one may decompose a har- rectly into Fourier and wavelet transforms, and thus help mony into pure tones, linear algebra provides a formal- bridge the gap between channel and source coding. ism for breaking vectors apart into basis elements. My interests lie in further developing the theory of bases in Invited Lectures: AMS Spring Southeastern Sectional both the pure and applied (signal processing) setting. Meeting (Mar. 2002). DIMACS Workshop on Source Speci cally, I am studying bases of complex exponen- Coding and Harmonic Analysis (May 2002). tial functions on fractal measures with the goal of gen- eralizing Fourier series. I also am interested in frames, a Selected Publications: way of performing basis-type decompositions which al- Finite normalized tight frames (with J. Benedetto), Ad- low redundancy. My hope is that redundant frame de- vances in Computational Mathematics, to appear.
Faculty Pro les 53 Vesselin Gasharov H. C. Wang Assistant Professor of Mathematics My work is in commutative algebra and algebraic com- On the Neggers-Stanley conjecture and the Eulerian poly- binatorics. I am especially interested in the interplay of nomials, J. Combin. Theory (A) 82 (1998). ideas and the rich connections between these two elds. Factoring the Poincar e polynomials for the Bruhat order More speci cally, I am interested in Hilbert functions, on Sn, J. Combin. Theory (A) 83 (1998). symmetric functions, free resolutions, total positivity, Hilbert functions and homogeneous generic forms II , Schubert varieties, toric varieties, Gr obner bases theory Compositio Mathematica 116 (1999). and monomial ideals. The lcm-lattice in monomial tesolutions (with I. Peeva and V. Welker), Math. Res. Lett. 6 (1999). Professional Activities: Coorganizer of a special session Rationality for generic toric rings (with I. Peeva and in Algebraic and Geometric Combinatorics at the AMS V. Welker), Mathematische Zeitschrift 233 (2000). Meeting in Providence, RI (1999). Referee for various Deformations of codimension 2 toric varieties (with journals. I. Peeva), Compositio Mathematica 123 (2000), 225– 241. Selected Publications: Su ciency of Lakshmibai-Sandhya singularity conditions Incomparability graphs of (3 + 1)-free posets are s- for Schubert varieties, Compositio Mathematica 126 positive, Discrete Math. 157 (1996). (2001), 47–56. Complete intersection dimension (with L. Avramov and Resolutions of a-stable ideals (with T. Hibi and I. Peeva), I. Peeva), Publ. Math. IHES 86 (1997). J. Algebra, to appear.
Leonard Gross Professor of Mathematics My research could, for the most part, be described organizer of satellite of IMP, Warwick, UK (July 2000). as analysis over in nite dimensional spaces. This has Co-organizer of satellite of ICM, Beijing (Aug. 2002). sometimes been motivated by problems of mathematical physics, speci cally statistical mechanics and the prob- Invited Lectures: lem of existence of quantum elds. There is usually a Quantization on compact Lie groups and the universal naturally arising probability measure on the in nite di- enveloping algebra, Von Neumann Symposium, MIT mensional space of interest to me which links functional (1994). analytic questions to probability theory. In recent years, Hilbert spaces of holomorphic functions on complex Lie I have been interested in properties of the Dirichlet form groups, Taniguchi Symposium, Warwick, England associated to pinned Brownian motion on loop groups. (1994). A long range goal is proof of a Hodge-deRham theorem The mathematical rami cations of Wiener’s program for these manifolds of maps. This has led, most recently, in statistical physics, Wiener Centenary Symposium, to a study of Dirichlet forms in holomorphic function Lansing, MI (1994). spaces over a complex manifold. Hall’s transform via the Segal-Bargmann Map, London Mathematical Society (1995). Awards and Honors: Guggenheim Fellow (1974–75). Hall’s transform and quantum mechanics, Probability Humboldt Prize (1993). Bourbaki Lecture, Paris, France Towards 2000, Columbia University (1995). (1998). Hilbert spaces of holomorphic functions on complex Lie groups, Paris, France (1996); Bochum, Germany Professional Activities: Editorial boards of the Jour- (1996); Mannheim, Germany (1996). nal of Functional Analysis, Reviews in Mathematical Hypercontractivity over complex manifolds, Paris (1998); Physics, Potential Analysis, Soochow Journal of Math- London (1998). ematics, Revista Colombiana de Matem ematicas and Analysis on loop groups, Kusadaci, Turkey (1998). Electronic Research Announcements of the American Dirichlet forms in holomorphic function spaces, North- Mathematical Society. Board of Governors of the In- western University (June 2000), University of Warwick stitute of Mathematics and Its Applications, Minnesota (July 2000), New Orleans AMS meeting (Jan. 2001), (1989–91). Co-organizer of special session at Ameri- Washington University (March 2001). can Mathematical Society meeting (Apr. 1998). Co-
54 Faculty Pro les Selected Publications: A Poincar e lemma for connection forms, J. Func. Anal. Abstract Wiener spaces, Proceedings of 5th Berkeley 63 (1985), 1–46. Symposium on Mathematical Statistics and Probabil- Logarithmic Sobolev inequalities on loop groups, J. Func. ity, Vol 2, pt. 1 (1965), 31–41. Anal. 102 (1991), 268–313. The Cauchy problem for the coupled Maxwell and Dirac Uniqueness of ground states for Schr odinger operators equations, Comm. Pure App. Math. 19 (1966), 1–15. over loop groups, J. Func. Anal. 112 (1993), 373–441. Existence and uniqueness of physical ground states,J. A local Peter-Weyl theorem, Trans. AMS 352 (1999), Func. Anal. 10 (1972), 52–109. 413–427. Logarithmic Sobolev inequalities, Amer. J. Math. 97 Hypercontractivity over complex manifolds, Acta Math. (1975), 1061–83. 182 (1999), 159–206. Convergence of U(1)3 lattice gauge theory to its contin- uum limit, Comm. Math. Phys. 92 (1983), 137–162.
John Guckenheimer Professor of Mathematics Dynamical systems theory studies long time behavior Administrative Activities: Faculty on Computing and of systems governed by deterministic rules. Even the Information Founders Committee. Transition Commit- simplest nonlinear dynamical systems can generate phe- tee, Biological Statistics and Computational Biology De- nomena of bewildering complexity. Formulas that de- partment. Faculty Senate. University Appeals Panel. scribe the behavior of a system seldom exist. Computer Chair of Mathematics Department Education Commit- simulation is the way to see how initial conditions evolve tee. for particular systems. In carrying out simulations with many, many di erent systems, common patterns are ob- Invited Lectures: Gave invited lectures at the Univer- served repeatedly. One of the main goals of dynamical sity of Arizona (Feb. 2001), the Howes Memorial Confer- systems theory is to discover these patterns and charac- ence, Berkeley (March 2001), the University of California terize their properties. The theory can then be used as a at Davis (three talks, Feb. and May 2001), the Colston basis for description and interpretation of the dynamics Conference, Bristol, England (June 2001), the SIAM An- of speci c systems. It can also be used as the foundation nual meeting, San Diego (July 2001), the Fields Institute for numerical algorithms that seek to analyze system be- (two talks in di erent workshops, Dec. 2001) and IMPA havior in ways that go beyond simulation. Throughout (three talks, Jan. 2002). the theory, dependence of dynamical behavior upon sys- tem parameters has been an important topic. Bifurca- Selected Publications: tion theory is the part of dynamical systems theory that Global analysis of periodic orbits in the forced van der systematically studies how systems change with varying Pol equation (with K. Ho man and W. Weckesser); parameters. in Global Analysis of Dynamical Systems (H. Broer, My research is a blend of theoretical investigation, de- B. Krauskopf and G. Vegter, eds.), IOP Press, 2001, velopment of computer methods and studies of nonlinear pp. 261–276. sytems that arise in diverse elds of science and engi- The duck and the devil: canards on the staircase (with neering. Much of the emphasis has been upon studying Y. Ilyashenko), Moscow Math. J. 1 (2001). bifurcations. My current work focuses upon algorithm Review of Stephen Smale biography by Steve Batterson, development for problems involving periodic orbits and Am. Math. Monthly 108 (2001), 107–109. systems with multiple time scales. Current and recent Computing periodic orbits; in Fluid Mechanics and application areas include the neurosciences, animal loco- the Environment: Dynamical Approaches (J. Lumley, motion and control of nonlinear systems. ed.), 2001, pp. 107–120. Numerical analysis of dynamical systems; in Handbook Professional Activities: Chair, SIAM Activity Group of Dynamical Systems, Elsevier, 2002. on Life Sciences. Managing editor, DSWeb: a website Bifurcation and degenerate decomposition in multiple in preparation by SIAM. Theory Division Review Com- time scale dynamical systems; in Nonlinear Dynamics mittee, Los Alamos National Laboratory. AAAS Math- and Chaos: Where do we go from here?, IOP Press, ematics Section nominating committee. SIAM, Science 2002. Policy Committee. Chaos in the Hodgkin-Huxley model (with R. Oliva), SIAM J. App. Dyn. Systems (2002).
Faculty Pro les 55 Allen E. Hatcher Professor of Mathematics A common thread through much of my research is the dra, the space of all di eomorphisms of a manifold, or idea of studying the space of all topological objects of a the space of all knots. Recently I have also been writing certain kind, for example, the space of all nite polyhe- a couple of graduate-level textbooks in topology.
Timothy J. Healey Chair and Professor of Theoretical and Applied Mechanics I am interested in nonlinear elasticity and nonlin- Selected Publications: ear analysis, with applications to exible structures and Global continuation via higher-gradient regularization solids, including biological laments and martensitic and singular limits in forced one-dimensional phase phase transitions. The subject is a rich source of un- transitions (with H. Kielh ofer), SIAM J. Math. Anal. solved nonlinear problems in applied analysis and com- 31 (2000), 1307. putation. The two primary goals of the work are to un- Hidden symmetry of global solutions in twisted elastic cover new physical and/or mathematical phenomena and rings (with G. Domokos), J. Nonlinear Science 11 to develop e cient solution strategies for the analysis of (2001), 47. such problems. Material symmetry and chirality in nonlinearly elastic rods , Math. Mech. Solids, to appear. A simple approach to the 1:1 resonance bifurcation in follower-load problems (with K. MacEwen), Nonlinear Dynamics, to appear.
David W. Henderson Professor of Mathematics I would classify my work as pertaining to aspects of leges and universities. (The workshop, June 2001, was mathematics that impinge on the teaching and learning the seventh such workshop that I have led at Cornell.) of mathematics — the emphasis is on the mathematics not on education. My main theme is that we should Administrative Activities: Faculty member of the Vi- enliven our conception of what “proof” is and that proofs sual Studies Program, the South Asia Program, and the should be a central part of mathematics teaching at all graduate elds of Education and Mathematics. Mem- levels, where my de nition of “proof” is: A convincing ber of the University Faculty Committee on A rmative communication that answers — Why? Action, College Scholars Advisory Board, and Cornell In addition, I am currently involved in extensive cur- Teacher Education. riculum innovation projects in undergraduate mathe- matics. My rst book, Experiencing Geometry on Plane Invited Lectures: and Sphere, published in August 1995, has been re- Educational mathematics, invited talk to T&AM Semi- quested by faculty in 50 countries so far and has been nar, Cornell University (Nov. 2001). translated into Portugese. My second book Di erential Shape of space, Saturday workshop for teachers, Cornell Geometry: A Geometric Introduction appeared in July University (Dec. 2001). of 1997, and is now being used around the world. My Calculus concepts in secondary mathematics, Saturday third book, Experiencing Geometry in Euclidean, Spher- workshop for teachers, Cornell University (Feb. 2002). ical and Hyperbolic Spaces, appeared in summer 2000. It How can we encourage students to think like a mathe- is an extensive revision and expansion of my rst book. matician?, invited 1-hour plenary address, Canadian Other books are in process. Mathematics Society Summer Meeting, Quebec City, Canada (June 2002). Professional Activities: Served on the National Advi- Experiencing geometry, invited 2-hour workshop, Cana- sory Board for NSF’s CCLI-EMD project. Referee and dian Mathematics Society Summer Meeting, Quebec reviewer for various journals and publishers. Led an City, Canada (June 2002). NSF-sponsored week-long workshop (Teaching Under- Misconceptions about isometrically embedding the hyper- graduate Geometry) for mathematics professors at col- bolic plane in Euclidean 3-space, Janos Bolyai Con-
56 Faculty Pro les ference on Hyperbolic Geometry, Budapest, Hungary Crocheting the hyperbolic plane (with D. Taimina), (July 2002). Mathematical Intelligencer 23 no. 2 (2001), 17–28. Increasing creativity with alive mathematical reasoning, Di erential geometry; invited signed article in Ency- International Conference on the Gifted Student and clopaedia Britannica, to appear in fall 2002. Increasing Creativity in Mathematics Education, Riga, Non-Euclidean geometry (with D. Taimina); invited Latvia (July 2002). signed article in Encyclopaedia Britannica, to appear in fall 2002. Selected Publications: Geometry (with D. Taimina); invited signed article for Di erential Geometry: A Geometric Introduction, Up- The Hutchinson Encyclopedia of Mathematics, ac- per Saddle River, NJ: Prentice-Hall, 1998. cepted Dec 2001. Square roots in the Sulba Sutra; a chapter in Geometry Review of Where Does Mathematics Come From? by at Work: Papers in Applied Geometry (C. A. Gorini, Lako and Nunez, Mathematical Intelligencer 24 no. 1 ed.), MAA Notes 53, 2000, 39–45. (2002), 75–78. Experiencing Geometry in Euclidean, Spherical and Hy- Review of Geometry: Euclid and Beyond by Robin perbolic Spaces (with D. Taimina), Upper Saddle Hartshorne, Bulletin of the AMS, accepted, publica- River, NJ: Prentice-Hall, 2001. tion expected fall 2002.
John Hubbard Professor of Mathematics Di erential equations are the main way in which math- positive in uence on his education at Cornell.” ematical models of real systems are constructed, and Of the papers accepted for publication in the past year, understanding their behavior is the main contribution a two stand out. A compacti cation of H enon mappings mathematician can make to applications. I am interested in C2 as dynamical systems (with P. Papadopol and in understanding the behavior of di erential equations V. Veselov), which will appear in Acta Mathematica, and their close relatives: iterative systems. In particu- builds a bridge between dynamics and algebraic or an- lar, I try to see how such systems behave in the complex alytic geometry. The paper uses blow-ups to show that domain, largely because complex analysis brings new and there is a topology on C2 t S3 homeomorphic to a 4-ball powerful techniques to bear on the problems. such that the H enon mapping extends continuously. In The availability of powerful computers and computer doing so it proves a result suggested by Milnor, involv- graphics has changed the way this sort of research is ing embeddings of solenoids in S3 which are topologically done. In the course of investigations of even such sim- di erent from those obtained from H enon mappings. I ple iterative systems as quadratic polynomials, amazing am currently exploring the application of this method to pictures show up, rather as artifacts to be investigated other problems. than as man-made objects. I anticipate that this sort of The forced damped pendulum: chaos, complication and experimental mathematics will become a major trend. control, which will appear in the American Mathemat- Most of my research over the last ve years has been ical Monthly, shows how a computer can yield amazing devoted to dynamics in several complex variables. I have but rigorous results about di erential equations using co-authored four foundational papers in the eld. I am methods accessible to undergraduates. It explores the also writing three books on a very advanced level, one dynamics of the forced pendulum, as described by the 00 0 giving a treatment of Teichm uller space and its applica- di erential equation x + Fx + sin ωx = A cos t, for the tions in theorems of Bill Thurston, the second on dynam- parameter values F =0.1, ω = 1 and A = 1. This ics of one complex variable, and the third on di erential pendulum has an attracting periodic oscillation of pe- geometry. riod 2 , but if you color the plane of initial conditions 0 During the summer I also directed an NSF-funded x(0), x (0) according to how many times the pendulum REU program for four students (two from Harvard, one goes over the top before settling down to this oscillation, from Cornell, one from Iowa). The resulting presenta- the corresponding “basins of attraction” are extremely tion by one of these students at the MAA MathFest in wild; in fact they form “lakes of Wada”: every point in Toronto was chosen as one of the outstanding talks at the boundary of one basin is in the boundary of all the the MAA Student Paper Sessions. During the school in nitely many others. year I continued to work with undergraduates on re- I spent the spring semester on leave in Marseille, search projects. One of these students, a physics ma- France, and took advantage of it to give a number of jor, was selected as a Merrill Presidential Scholar, and lectures in Paris and other French cities, and to give in- named me as “the faculty member who has had the most vited lectures at meetings in Pisa and Crete.
Faculty Pro les 57 J. T. Gene Hwang Professor of Mathematics In recent years, I have been focusing mainly on the the- lated models (with L. Gleser), Ann. Stat. 15 (1987), ory of statistical intervals. Statistical intervals, such as 1351–1362. con dence intervals, prediction intervals and tolerance Estimation of accuracy in testing (with G. Casella, intervals, are one of the major areas in statistics. By C. Robert, M. Wells and R. Farrell), Ann. Stat. 20, providing intervals, statisticians demonstrate the possi- (1992), 490–509. ble range of the interested parameters or future observa- Is Pitman closeness a reasonable criterion? (with tions. C. Robert and W. E. Strawderman), JASA 88 (1993), Much of my research is stimulated by scienti c and 57–63. Discussed by 8 statisticians. Reply, 74–76. engineering applications. Although my primary inter- Con dence interval estimation subject to order restric- est is in theory, the solutions often can be used directly tions (with S. D. Peddada), Ann. Stat. 22 (1994), 67– in application. My recent joint work with the National 93. Institute of Standards and Technology is one example. Con dence intervals associated with tests for bio- Another recent endeavor is in genetics statistics. I equivalence (with J. Hsu, H. K. Liu and S. J. Ruberg), have published a paper on identi cation of quantitative Biometrika 81 (1994), 103–114. trait loci (QTL) and have begun working on other sta- Fieller’s problems and resampling techniques, Statistica tistics problems related to microarray analysis. Sinica 5 (1995), 161–171. Optimal con dence sets, bioequivalence and the limacon Awards and Honors: I. W. Burr Award (1979). NSF of Pascal (with L. D. Brown and G. Casella), JASA grant awards,1980–1996. IMS Fellow (1988). Elected 90 (1995), 880–890. Member of the Int’l Statistical Institute (1989). Senior Maximum likelihood estimation under order restricted Research Fellowship at NIST (Sept. 1–Nov. 30, 1993). parameters by the prior feedback method (with C. Robert), JASA 91 (1996), 167–172. Professional Activities: Referee for JASA, Ann. Stat., An unbiased test for the bioequivalence problem (with J. Multivariate Analysis, Sankhya. Member of the ASA L. D. Brown and Axel Munk), Ann. Stat. 25 (1997), and ICSA. Served as statistical consultant for the Na- 2345–2367. tional Institute of Standards and Technology (NIST). Prediction intervals in arti cial neural network (with Invited Lectures: Delivered colloq. talks at Academia A. Adam Ding), JASA 92 (1997), 748–757. Sinica, Taiwan (Aug. 2000); Dong-Hua University, Tai- Prediction intervals, factor analysis models and high- wan (Aug. 2000); and Iowa State University (Oct. 2000). dimensional empirical linear prediction (HELP) (with A. Adam Ding), JASA 94 (1999), 446–455. Selected Publications: An optimality theory for mid p-values in 2 2 con- Construction of improved estimators in multiparame- tingency tables (with M. Yang), Statistica Sinica 11 ter estimation for discrete exponential families (with (2001), 807–826. Malay Ghosh and Kam-Wah Tsui), Ann. Stat. 11, Investigating the probability of sign inconsistency in the no. 2, (1983), 351–367. Discussions by James O. regression coe cients (with D. Nettleton), Genetics Berger, H. M. Hudson and Carl Morris. Reply with 160 (2002), 1697–1705. Ghosh and Tsui, 375–376. Classi cation of pixels in a noisy grayscale image of po- The nonexistence of 100 (1 )% con dence sets of - lar ice (with S. Peddada), IEEE Transactions on Geo- nite expected diameter in errors-in-variables and re- science and Remote Sensing, to appear.
Yulij Ilyashenko Professor of Mathematics My research interests are several branches of dynami- plane. For instance, in Finiteness Theorems for Limit cal systems, both in real and complex domains. They Cycles I proved that for a xed polynomial vector eld include: limit cycles in real and complex planes; an- the number of limit cycles is nite. (2) Geometric prop- alytic di erential equations, with relations to complex erties of foliations determined by analytic vector elds in analysis and algebraic geometry; local and nonlocal bi- the complex plane. (3) Bifurcations of planar polycycles furcations and so on. Some main objects to study are: (separatrix polygons). (4) New nonlocal bifurcations in (1) Limit cycles of polynomial vector elds in the real higher-dimensional spaces, and many others.
58 Faculty Pro les Professional Activities: Editor-in-Chief of the Moscow Selected Publications: Mathematical Journal (www.ams.org/distribution/mmj). Hilbert type numbers for Abel equations, growth and ze- Member of the editorial boards of Functional Analysis ros of holomorphic functions, Nonlinearity 13 (2000), and Its Applications, Dynamical and Control Systems, 1337. Ergodic Theory and Dynamical Systems, Proceedings of Some properties of skew products over a horseshoe and the Moscow Mathematical Society and Mathematical En- solenoid (with A. Gorodetski), Proceedings of the lightenment. Steklov Institute 231 (2000), 96. The duck and the devil: canards on the staircase (with Administrative Activities: Coorganizer of the Math in J. Guckenheimer), Moscow Math. J. 1 (2001), 37. Moscow program; president of the Independent Univer- Normal forms near a saddle-node and applications to sity of Moscow. nite cyclicity of graphics (with F. Dumortier and Invited Lectures: Delivered a talk at the Harvard-MIT- C. Rousseau), Ergodic Theory and Dynamical Sys- Brandeis-Northeastern Colloquium, November 2000. tems, to appear.
Peter J. Kahn Professor of Mathematics I am a di erential and algebraic topologist focusing Chern numbers and oriented homotopy type, Topology 7 currently on symplectic topology/geometry. Speci cally, (1968), 69–93. I am interested in various problems on the interface of The non- nite homotopy type of some di eomorphism this area with algebraic topology, for example, the topol- groups, (with P. Antonelli and D. Burghelea), Topol- ogy of symplectomorphism groups. ogy 11 (1972), 1–49. The Concordance-Homotopy Groups of Geometric Auto- Awards and Honors: Humboldt Senior Scientist Award, morphism Groups (with P. Antonelli and D. Burghe- 1975–76 and Summer 1981. lea), Springer Lecture Notes 215 (1972). Mixing homotopy types of manifolds, Topology 14 Professional Activities: Member of the AMS, MAA and (1975), 203–216. AAAS. Reviewer for AMS Reviews and Zentralblatt. Homotopy-dimension and simple cohomological dimen- Referee for the AMS Proceedings. sion of spaces (with K. Brown), Comment. Math. Administrative Activities: Member of the Education Helv. 52 (1977), 111–127. Policy Committee (1991–93). Chair of the Committee on Counting types of rigid frameworks, Inventiones Math. Quantitative and Formal Reasoning (1991–). Author of 55 (1979), 297–308. report on the Cornell Mathematics Major (1993). Chair Steenrod’s Problem and k-Invariants of Certain Classi- of the Department of Mathematics (1993–95). Associate fying Spaces, Springer Lecture Notes 967 (1982). Dean of the College of Arts and Sciences (1995–97, sum- Equivariant homology decompositions, AMS Trans. 298 mer and fall 1999). Chair of the Mathematics Major (1986), 245–271. Committee (2000–2001, spring 2002). Rational Moore G-spaces, AMS Trans. 298 (1986), 273– 287. Selected Publications: A paradigm for robust geometric algorithms (with Characteristic numbers and oriented homotopy type, J. Hopcroft), Algorithmica 7 (1992), 339–380. Topology 3 (1965), 81–95. Pseudohomology and homology, preprint 2001, 35pp. Self-equivalences of (n 1)-connected 2n-manifolds, Pseudohomology and Steenrod homology, in preparation. AMS Bull. 72 (1966), 562–566.
Harry Kesten Goldwin Smith Professor of Mathematics I am a probabilist. My main research interests are heard the rumor). The A-particles perform independent percolation theory and random walks, and in general I (continuous time) random walks on Zd with distribution like to dabble in models inspired by statistical mechanics. FA and similiarly the B-particles perform independent One model I have recently worked on can be viewed random walks with distribution FB. The only interac- as a model for the spread of a rumor. There are two tion between all the particles is that when a B-particle kinds of particles, A-particles (corresponding to the peo- meets an A-particle it turns into an A-particle and con- ple in the know) and B-particles (people who have not tinues forever as an A-particle. We start with indepen-
Faculty Pro les 59 dent Poisson numbers of B-particles at the sites of Zd Invited Lectures: Delivered lectures at various Swedish and a single A-particle at the origin. How fast does the universities in connection with Erlander Professorship. set of A-particles grow with time? In other words, what is the set of people who heard the rumor by time t, for Selected Publications: large t? It is expected that this set grows linearly with Once edge-reinforced random walk on a tree (with t, but so far results are known only if FA = FB,orifthe R. Durrett and V. Limic), Probab. Theory Rel. Fields B-particles do not move at all. 122 (2002). Randomly coalescing random walk in dimension 3 Awards and Honors: Awarded the 2001 Leroy P. Steele (with J. van den Berg); in In and Out of Equilibrium, Prize for Lifetime Achievement. Tage Erlander Professor Proceedings of a Conference in Mambucaba, Brazil, to in Sweden for 2002. appear. Professional Activities: Member of the editorial board Branching random walks with catalysts (with V. Sido- of the Indiana Journal of Mathematics and the New York ravicius), Probab. Theory Rel. Fields, submitted. Journal of Mathematics. Honorary board member of Journal d’Analyse Math ematique. Dexter Kozen Professor of Computer Science Joseph Newton Pew, Jr., Professor in Engineering www.cs.cornell.edu/kozen/ My research interests include the theory of computa- Club and Johnson School of Management Rugby. tional complexity, especially complexity of decision prob- lems in logic and algebra, program logic and semantics, Invited Lectures: and computational algebra. Recent work includes: new Parikh’s Theorem in commutative Kleene algebra, FLOC polynomial-time algorithms for type inference in type ’99, Trento, Italy (July 1999). systems with subtypes and recursive types; algorithms On Hoare logic and Kleene algebra with tests, FLOC ’99, solving systems of set constraints as used in program Trento, Italy (July 1999). analysis; a uni cation algorithm for set constraints and On Hoare logic, Kleene algebra and types, International a new constraint logic programming language based on Congress for Logic, Methodology and Philosophy of set constraints; development of the theory of rational Science, Kracow, Poland (Aug. 1999). spaces and their relationship to set constraints; an al- On the completeness of prepositional Hoare logic, gorithm for decomposition of algebraic functions; a new RelMiCS 5 Conference, Quebec City, Canada (Jan. polynomial-time algorithm for resolution of singularities 2000). of plane curves; e cient algorithms for optimal transmis- Language-based security, 24th Conference on Math- sion of encoded video data; optimality results for digi- ematical Foundations of Computer Science, Wro- tal interleavers; and complexity and completeness results claw, Poland (Sept. 1999); Dartmouth College (March for Kleene algebras with tests. Recently I have begun 2000). to investigate the application of Kleene algebra and the Selected Publications: modal mu-calculus to problems in software security. Parikh’s theorem in commutative Kleene algebra (with Professional Activities: Program committee of Founda- M. Hopkins), Proc. Conference Logic in Computer Sci- tions of Software Science and Computation Structure, ence (LICS ’99), IEEE (1999), 394–401. Mathematical Foundations of Computer Science. Edito- On Hoare logic, Kleene algebra and types, Cornell Uni- rial board of the Journal of Relational Methods in Com- versity, Computer Science, TR99-1760 (1999); in Proc. puter Science, the Journal of Algorithms (special issue). Conference Logic in Computer Science (LICS ’99), Supervisory Board, Centre for Basic Research in Com- IEEE (1999), 167–172. puter Science (BRICS), Aarhus University. Language-based security; in Proc. Conference of Mathe- matical Foundations of Computer Science (MFCS ’99), Awards and Honors: Class of 1960 Scholar, Williams ed. M. Kutylowski, L. Pacholski, and T. Wierbicki, College. volume 1672 of Lecture Notes in Computer Science, Springer-Verlag (1999), 284–298. Administrative Activities: College of Engineering Un- On the completeness of propositional Hoare logic (with dergraduate Admissions Committee. University Arbit- J. Tiluryn), Cornell University, Computer Science, ration Panel. Faculty advisor for Men’s Rugby, Football TR99-1766 (1999).
60 Faculty Pro les Certi cation of compiler optimizations using Kleene al- Relational Methods in Computer Science (RelMiCS gebra with tests (with M. Patron), Cornell University, 2000), ed. J. Desharnais (2000), 195–202. Computer Science, TR99-1779 (1999). Dynamic Logic (with D. Harel and J. Tiluryn), MIT On the completeness of prepositional Hoare logic (with Press, Cambridge, MA, 2000. J. Tiluryn); in Proc. of the Fifth International Seminar
Gregory F. Lawler Professor of Mathematics I study random walk and Brownian motion with an Iowa State University; Georgia Institute of Technology; emphasis on problems arising from statistical physics. IMPA, Brazil; Royal Institute of Technology (KTH), A particular interest is the self-avoiding walk and other Sweden; Uppsala University, Sweden; Got eborg Univer- models of walks with strong interactions. sity, Sweden; and University of Helsinki, Finland (2001). My recent work, done in collaboration with Oded Schramm and Wendelin Werner, concentrates on the Selected Publications: scaling limit of lattice models in two dimensions. These Values of Brownian intersection exponents I: half-plane models have been conjectured to have conformally invari- exponents (with O. Schramm and W. Werner), Acta ant scaling limits, and theoretical physicists have used Math. 187 (2001), 237–273. nonrigorous techniques to predict “critical exponents” Values of Brownian intersection exponents II: plane ex- for these models. We have established a number of these ponents (with O. Schramm and W. Werner), Acta results recently. For example, we have shown that the Math. 187 (2001), 275–308. dimension of the outer boundary of planar Brownian mo- The dimension of the Brownian frontier is 4/3 (with tion is 4/3, establishing a conjecture of Benoit Mandel- O. Schramm and W. Werner), Math. Res. Let. 8 brot. (2001), 401–411. Values of Brownian intersection exponents III: two-sided Awards and Honors: Sloan Fellow (1986). Fellow of the exponents (with O. Schramm and W. Werner), Ann. IMS (1992). Inst. Henri Poincar e 38 (2002), 109–123. Professional Activities: Chair of the AMS Editorial One arm exponent for critical 2D-percolation (with Boards Commmittee (2000). Associate editor of Combi- O. Schramm and W. Werner), Journal of Probability natorics, Probability and Computing. 7 no. 2 (2002). Sharp estimates for Brownian non-intersection probabil- Invited Lectures: Workshop on Percolation, MSRI ities (with O. Schramm and W. Werner); in In and (2001). Mathematical Physics Workshop, Mambucaba, Out of Equilibrium, Birkh auser, 2002. Brazil (2001). Conference on Random Walks and Ge- Analyticity of intersection exponents for planar Brown- ometry, Vienna, Austria (2001). Mini-course, Mittag- ian motion (with O. Schramm and W. Werner), Acta Le er Institute, Sweden (2001). Invited talks at: Math., to appear.
Vlada Limic H. C. Wang Assistant Professor of Mathematics I enjoy studying probabilistic models. My thesis random walks with reinforcement, which are a model of was on characterization of certain coalescence processes, thinking process and memory. which are a model of in nitely many dust particles merg- ing together over a long period of time and forming mete- Selected Publications: ors, planets, etc. I am also interested in problems related The entrace boundary of the multiplicative coalescent to queues and queueing systems. Stochastic queueing (with D. Aldous), EJP 3 (1998), paper 3. systems are models of a factory production cycle, or a On the behavior of LIFO preemptive resume queues in telephone exchange or the internet. These mathemati- heavy tra c, ECP 5 (2000), paper 2. cal realizations are still quite complicated to analyze di- A LIFO queue in heavy tra c, Ann. Appl. Prob., to rectly, so it is important to nd useful approximations in appear. order to answer questions about the qualitative behavior On the quantity and quality of single nucleotide poly- of the corresponding queueing system. During the past morphisms in the human genome (with Rick Durrett), year, Rick Durrett got me interested in several problems Stoch. Processes Appl. (2001). motivated by genetics, and I also became interested in
Faculty Pro les 61 G. Roger Livesay Professor Emeritus of Mathematics My major area of research is in topology, 3-dimensional manifolds with nite cyclic fundamental groups.
Anita Mareno VIGRE Assistant Professor of Mathematics My most recent work involves the use of the Leray- systems, I am currently investigating whether or not the Schauder degree to prove the existence of global solution trivial solution to these equations is unique under cer- continua to various boundary value problems in higher- tain constraints on the geometry of the domain. For this gradient 3D nonlinear elasticity. In classical nonlinear purpose, I am exploring symmetry methods and devel- elasticity the complementing condition fails for certain oping generalized Rellich-type identities. In general, I boundary value problems and due to a natural growth am also interested in overdetermined systems of fourth- condition on the material response function, the gov- order PDEs and problems pertaining to phase transitions erning equations exhibit singular behavior; the existence in elasticity. of classical smooth solutions to the equilibrium equa- tions has yet to be shown. In my work, the higher-order Selected Publications: term in the response function e ectively regularizes an Numerical simulation of blow-up of a 2D generalized ill-posed problem. Ginzburg-Landau equation (with C. Bu and R. Shull), This research has prompted my interest in various Applied Math Letters 9 no. 6 (1996), 13–17. problems in degree theory (in a more general sense) and Uniqueness of classical solutions in higher-gradient non- in particular, its applications to PDEs with nonlinear linear elasticity, Journal of Elasticity, submitted. boundary conditions. I am also interested in obtaining Some global continuation results in higher-gradient non- existence results for higher-order systems of PDEs with linear elasticity (with T. Healey), to be submitted. nonstandard boundary conditions. For these types of Russell Miller VIGRE Assistant Professor of Mathematics I study computability theory, the branch of mathemat- can use computability-theoretic approaches to consider ical logic concerned with nite algorithms and the math- randomness, the question of what we mean when we say ematical problems which such algorithms can or cannot that a particular set or real number is “random,” and I solve. By relativizing, one forms a partial order of the de- have begun examining questions in this area. grees of di culty (the Turing degrees) of such problems. Computable model theory, one of my specialties, applies Selected Publications: 0 such techniques to general mathematical structures such The 2-spectrum of a linear order, Journal of Symbolic as trees, linear orders, groups and graphs. Other in- Logic 66 (2001), 470–486. terests of mine include automorphisms of the lattice of De nable incompleteness and Friedberg splittings, Jour- computably enumerable sets (i.e., sets whose elements nal of Symbolic Logic, to appear. can be listed by an algorithm) and undecidability of the Orbits of computably enumerable sets: low sets can avoid partial order of Turing degrees of those sets. Finally, one an upper cone, Ann. Pure & Applied Logic, to appear.
Irina Mitrea H. C. Wang Assistant Professor of Mathematics My speci c interests are in the general areas of real associated with the aforementioned PDE problems in ir- and harmonic analysis and partial di erential equations. regular domains. I am particularly interested in the study of PDE prob- lems arising from mathematical physics with emphasis Awards and Honors: Alfred P. Sloan Dissertation Fel- on the study of uid dynamics, elasticity and electro- low (1999–2000). Clay Mathematics Lifto Fellowship magnetism. (2000). Eugene B. Fabes Outstanding Thesis Award, One of the main themes of my work deals with under- University of Minnesota (2000). AWM-NSF Mentor standing the nature of the boundary integral operators Travel Award (2002).
62 Faculty Pro les Invited Lectures: Delivered invited talks at the Univer- On the boundedness singular integrals (with E. Fabes and sity of Chicago, University of Rochester, University of M. Mitrea), Paci c J. Math. 189 no. 1 (1999), 21–29. Arkansas and University of Montreal (Canada). Spectral radius properties for layer potentials associated with the elastostatics and hydrostatics equations in Selected Publications: nonsmooth domains, Journal of Fourier Analysis and Monogenic Hardy spaces on Lipschitz domains and com- Applications 5 no. 4 (1999), 385–408. pensated compactness (with M. Mitrea), Complex On the spectra of elastostatics and hydrostatics layer Variables Theory Appl. 35 no. 3 (1998), 225–282. potentials on curvilinear polygons, Journal of Fourier Analysis and Applications 8 (2002), to appear.
Michael Morley Professor of Mathematics Professor Morley’s primary interest and contribution Professor Morley’s primary research interests lie in the to the department lies in his devotion to the students. areas of advanced mathematical logic and model theory. His skill, wisdom, commitment and sensitivity in ad- vising is very well-known throughout the Arts College. Awards and Honors: Robert A. and Donna B. Paul Comments about Michael Morley speak to his devotion: Award for Excellence in Advising (1996). “[Mike Morley] is exactly the sort of advisor that Cor- Professional Activities: President of the Association for nell needs...”; “...has a creative and total commitment Symbolic Logic (1986–89). to taking care of students...”; “...has been available to everyone’s advisees who wander in unhappy.” These Administrative Activities: Department advising com- comments speak eloquently of Prof. Michael D. Morley. mittee (1995–). Associate Chair and Director of Under- graduate Studies (1984–95).
Anil Nerode Goldwin Smith Professor of Mathematics Anil Nerode’s work ranges over several areas of mathe- In logic, Nerode and Khoussainov have a recent book matical logic, including computability, computable alge- on automata and their applications and a recently pub- bra and automata, and in the last ten years also over con- lished paper in the Annals of Pure and Applied Logic trol theory and hybrid systems. The variety of control on constructive concurrent dynamic logic. He contin- theory introduced by Nerode and his co-worker Kohn is ues to supervise graduate students in recursive alge- based on controls as connections in Finsler geometries bra and analysis and in hybrid systems. He has pro- and their jet space extensions. To get an idea of this duced 42 Ph.D.s as major advisor. See his web site, work, see the 2002 volume of the Houston Journal of www.math.cornell.edu/eanil/ for a biography and bibli- Mathematics dedicated to S. S. Chern. ography.
Michael Nussbaum Professor of Mathematics My research program focuses on developing a bet- Awards and Honors: Fellow of the Institute of Mathe- ter theoretical understanding of the asymptotic theory matical Statistics. of statistical experiments, in connection with statistical smoothing and curve estimation and nonparametric in- Professional Activities: Member of the editorial boards ference for stochastic processes. Current topics include of Annals of Statistics, Annales de l’Institut Henri Gaussian and Poisson approximation of nonparametric Poincar e, Probabilit es et Statistiques and of ESAIM , experiments in the Le Cam sense, constructive realiza- Probability and Statistics. tion of equivalence, asymptotic risk bounds for density estimation and nonparametric regression, nonparamet- Invited Lectures: ric models for point processes, di usion processes and Nonparametric function estimation, neural nets and risk autoregression, functional limit theorems for empirical asymptotics, summer course at Oberwolfach, Germany processes, statistical treatment of inverse and ill-posed (DMV-seminar), jointly with A. Barron, Yale and Las- problems. zlo Gyor , Budapest (June 2000).
Faculty Pro les 63 Selected Publications: The asymptotic minimax constant for sup-norm loss Asymptotic equivalence of density estimation and Gauss- in nonparametric density estimation (with A. Ko- ian white noise, Ann. Stat. 24 (1996), 2399–2430. rostelev), Bernoulli 5 no. 6 (1999), 1099–1118. Asymptotic equivalence for nonparametric generalized Minimax risk: Pinsker bound; in Encyclopedia of Statis- linear models (with I. Grama), Probability Theory and tical Sciences, Vol. 3 (S. Kotz, ed.), John Wiley, New Related Fields 111 (1998), 167–214. York (1999), 451–460. Di usion limits for nonparametric autoregression (with G. Milstein), Probability Theory and Related Fields 112 (1998), 167–214. Lawrence Payne Professor Emeritus of Mathematics My research interests lie in several areas of partial dif- Spatial decay in the pipe ow of a viscous uid inter- ferential equations: isoperimetric inequalities, ill-posed facing a porous medium (with K. A. Ames and J. C. and nonstandard problems, growth decay and/or blowup Song), Math. Models and Methods in Appl. Sciences of solutions, and applications to various problems in solid 11 (2001), 1547–1562. and uid mechanics. Recent interests include the study Eigenvalue and eigenfunction inequalities for elastically of overdetermined systems and Saint Venant type prob- supported membranes (with P. W. Schaefer), ZAMP lems for nonlinear equations. 52 (2001), 888–895. Decay results for the heat equation under radiation Invited Lectures: Delivered talks in Z urich and Basel in boundary conditions (with P. W. Schaefer), Math. Switzerland in May 2001; also a talk in Durham, Eng- Ineq. and Appl. 4 (2001), 573–584. land in May 2001. Gave a talk at the University of Ten- Continuous dependence on spatial geometry for the gen- nessee in November 2001. eralized Maxwell-Caltaneo system (with C. H. Lin), Selected Publications: Math. Methods in Appl. Sci. 24 (2001), 1113–1124. Remarks on ill-posed problems in partial di erential Growth and decay in generalized thermoelasticity (with equations, Symposium on Trends in the Application J. C. Song), Int. J. Eng. Sci. 40 (2002), 385–400. of Mathematics to Mechanics (2000), 1–9.
Irena Peeva Assistant Professor of Mathematics My research is on problems at the interface be- Topics in classical algebraic geometry, Oberwolfach, tween commutative algebra, algebraic geometry, com- Germany (June 2000). putational algebra, topological combinatorics, and non- Commutative algebra and algebraic geometry, CIRM- commutative algebra. I have worked on problems involv- Luminy, France (June 2000). ing free resolutions, toric varieties, Hilbert schemes, com- plete intersections, subspace arrangements, monomial Selected Publications: resolutions, Castelnuovo-Mumford regularity, Koszul al- Complete intersection dimension (with L. Avramov and gebras, shellings, and Grobner basis. My major research V. Gasharov), Publications Mathematiques IHES 86 interests are focussed on the properties and applications (1997), 67–114. of minimal free resolutions. Generic lattice ideals (with B. Sturmfels), J. American Mathematical Society 11 (1998), 363–373. Awards and Honors: Alfred P. Sloan Research Fellow- How to shell a monoid (with V. Reiner and B. Sturm- ship (1999–2001). C. L. E. Moore Instructorship at MIT fels), Math. Annalen 310 (1998), 379–393. (1995–1998). Alfred P. Sloan Doctoral Dissertation Fel- The lcm lattice in monomial resolutions (with V. Gasharov lowship (1994–1995). and V. Welker), Mathematical Research Letters 6 (1999), 521–532. Professional Activities: Coorganizer of a special session Deformations of codimension 2 toric varieties (with at the AMS Meeting in Montreal, May 2002. Referee for V. Gasharov), Comp. Math. 123 (2000), 225–241. various journals. Finite regularity and Koszul algebra (with L. Avramov), Amer. J. Math. 123 (2001), 275–281. Invited Lectures: Toric Hilbert schemes (with M. Stillman), Duke Math. Quadratic relations, Stockholm, Sweden (Oct. 2000). J. 111 (2002), 419–449.
64 Faculty Pro les Richard A. Platek Associate Professor of Mathematics Professor Platek founded Odyssey Research Asso- sonnel is largely drawn from the academic community ciates (ORA), Inc., an Ithaca based private research and with a strong logic contingent. ORA tools are based on development organization, in 1982 and currently serves a variety of ideas in the forefront of applied logic. as CEO. ORA is primarily concerned with applying the Professor Platek is the senior technical advisor on all techniques of mathematical logic to software develop- projects at ORA. As such he frequently presents the re- ment in order to increase assurance that resulting sys- sults and current status of projects at numerous meet- tems are correct. These techniques include: the develop- ings, symposiums, etc. Most recently, he is an invited ment of formal speci cation languages; the development speaker at the 12th International Conference on Auto- of formal semantics for requirements, speci cations, and mated Deduction, CADE-12, in the summer of 1994. implementations of languages; the development of sound Professor Platek and ORA are recognized in technol- logics for these semantics; and the implementation of ogy policy making circles as leading advocates for in- these concepts in software tools and veri cation envi- creased rigor in software engineering with mathematical ronments. ORA is particularly concerned with hard- logic playing the primary role as the underlying scienti c ware/software system safety and security. ORA’s per- discipline.
Ravi Ramakrishna Assistant Professor of Mathematics My research is in Galois theory. This is the branch Theory, Mathematical Research Letters and Mathemati- of mathematics concerned with symmetries of solutions cal Reviews. of equations. There is an object that encodes all sym- metries of solutions to all equations, the absolute Galois Administrative Activities: Regional representative for group of the rational numbers. I study this object and the Budapest Semesters in Mathematics Program. its relations with number theory. The study of these symmetries has gained an increasingly important role in Invited Lectures: Delivered invited talks at the Uni- number theory in recent years. In particular, Galois the- versity of Michigan, September 2000; Binghamton Uni- ory played an important role in the solution of Fermat’s versity, September 2000; Boston University, December Last Theorem. 2000; The Tata Institute of Fundamental Research, Jan- uary 2001; the University of Toronto, Canada, January Professional Activities: Referee/reviewer for the Amer- 2001; and the University of Utah, March 2001. ican Journal of Mathematics, the Journal of Number
Jos e Ram rez H. C. Wang Assistant Professor of Mathematics My main focus of research is on the intersection be- Another problem of interest to me is that of study- tween analysis (PDEs) and probability. I study para- ing the asymptotics of the distribution of the lowest bolic operators. The main objective is to try to prove eigenvalue for one dimensional Schr odinger operators “Gaussian type bounds” on heat kernels, that is, tran- with random potential. I have also started to wander sition probabilities for the associated processes. The into the problem of recurrence of certain reinforced ran- premise here is that there should be some kind of (Gauss- dom walks, that is random processes that like to travel ian) universality in the behavior of such processes when through places that they already visited. time is made small. The particularities of di erent gen- erators (operators) are mainly given through a metric. Selected Publications: The need for a very general setting led me to work on Short time asymptotics in Dirichlet spaces, Comm. Pure Dirichlet spaces. Appl. Math. 54 (2001), 259–293.
Faculty Pro les 65 Richard H. Rand Professor of Theoretical and Applied Mechanics My research involves using perturbation methods and Nonlinear normal modes in a system with nonholonomic bifurcation theory to obtain approximate solutions to constraints (with D. V. Ramani), Nonlinear Dynamics di erential equations arising from applications in non- 25 (2001), 49–64. linear dynamics and biology. Nonlinear modal interactions in the oscillations of a liq- Current projects include applications to submarine dy- uid drop in a gravitational eld (with I. Rozhkov and namics, e ects of biorhythms on retinal dynamics and A. F. Vakakis), International Journal of Nonlinear Me- cardiac arrythmias. These projects are conducted jointly chanics 36 (2001), 803–812. with graduate students at Cornell and with experts in Subharmonic resonance in the nonlinear Mathieu equa- the respective application area. tion (with R. S. Zounes), International Journal of Non- linear Mechanics 37 (2002), 43–73. Selected Publications: Bifurcations in a Mathieu equation with cubic nonlin- Nonlinear Vibrations, a downloadable book located at earities (with L. Ng), Chaos, Solitons and Fractals 14 www.tam.cornell.edu/randdocs/. (2002), 173–181.
James Renegar Professor of Operations Research and Industrial Engineering I am currently devoting the majority of my research ef- I am also interested in devising algorithms for more forts to devising new algorithms for linear programming, general problems involving hyperbolic polynomials. (A i.e., for solving systems of linear inequalities. Unlike the hyperbolic polynomial p is a real multivariate polynomial situation for linear equations, surprisingly basic prob- for which there exists a vector v such that all univariate lems remain unresolved for linear inequalities. For ex- polynomials obtained by restricting p to lines in the di- ample, it is unknown whether there exists an algorithm rection v have only real roots.) These polynomials have which can solve a general system of linear inequalities us- played an especially important role in optimization in ing a number of arithmetic operations which is bounded recent years. polynomially in the number of variables and the num- ber of inequalities in the system. By contrast, elemen- Professional Activities: Associate editor for the SIAM tary Gaussian elimination (i.e., high-school mathemat- Journal on Optimization. ics) solves a system of n linear equations in n unknowns in roughly n3 operations. Invited Lectures: Semiplenary speaker at the 17th In- ternational Symposium on Mathematical Programming.
Oscar Rothaus Professor of Mathematics I spent most of the fall term on sabbatic in France, vis- Selected Publications: iting Paris, l’Institut Henri Poincar e, Toulouse, Univer- A combinatorial problem in the symmetric group (with sit e Paul Sabatier, and Strasbourg, Universit e Louis Pas- J. Thompson), Pac. Jour. Math. 18 (1966), 175–178. teur. I attended lectures and lectured myself at Toulouse On bent functions, Jour. Comb. Theory A 20 no. 3 and Strasbourg, principally on log-Sobolev inequalities (1976), 300–305. and incidentally on coding theory. On the non-triviality of some groups given by generators After several years’ research on log-Sobolev inequal- and relations, Ann. Math. 106 (1977), 599–612. ities, I am returning to an earlier interest in combina- Lower bounds for eigenvalues of regular Sturm-Liouville torics, in this instance linear coding theory. I am working operators and the logarithmic Sobolev inequality, Duke on the fundamental problem of nding the parameters Math. Jour. 45 no. 2 (1978), 351–362. for optimal linear codes and have achieved signi cant Analytic inequalities, isoperimetric inequalities and loga- progress, but I am not yet ready to publish. I have rithmic Sobolev inequalities, J. Func. Anal. 64 (1985), found peculiar connections to my earlier work on “bent” 296–313. functions. Semigroups of nite matrices, Semi-Group Forum 49 (1994), 59–65.
66 Faculty Pro les Herbst inequalities for super contractive semigroups Sharp log-Sobolev inequalities, PAMS 126 no. 10 (1998), (with L. Gross), Jour. Math. Kyoto Univ. 38 no. 2 2903–2904. (1998). Konstantin Rybnikov H. C. Wang Assistant Professor of Mathematics My research focuses on combinatorial and geometric I, with my coauthors, have been working on rigidity re- properties of graphs and polyhedra. These properties lated geometric properties of in nite random graphs. We are studied from the viewpoints of combinatorics, com- have analyzed percolation of the loss of tension for 2D putational geometry, rigidity theory, and geometry of continuous media and lattices in the plane. numbers. Lattices and quadratic forms are fundamental math- In combinatorics one of my main interests is the theory ematical objects important to number theory, the the- of k-stresses for piecewise-linear manifolds and its rela- ory of nite groups, error-correcting codes, cryptogra- tions to the combinatorics of convex polytopes. I am phy, and crystallography. One of my principal lines of especially interested in how the theory of stresses on research is the study of Delaunay polytopes and tilings polyhedra relates to the lower bound type results (e.g., of lattices and their relationship to the reduction theo- g2 > 0) and the problem of reconstruction of convex ries for quadratic forms, in particular to the theory of polytopes from partial geometric or combinatorial infor- perfect and extreme forms. mation. A major focus of this research is on relating the numbers of faces and chains of faces in polytopes to Selected Publications: rigidity properties of their skeletons. Another focus is On the density of three-dimensional compacta, Doklady on the reconstruction of polytopes or their face-lattices Mathematics 48 (1993), 110–113. from partial information such as, for instance, the poly- Generatrice: the problems of Maxwell and Voronoi (with tope graph. Algorithmic and combinatorial information S. Ryshkov), Doklady Mathematics 54 (1996), 614– sought here may be of value to various areas of applied 617. mathematics and computer science dealing with linear The theory of quality translation with applications to programming and reconstruction of polyhedral scenes. tilings (with S. Ryshkov), Europ. J. Combin. 18 no. 4 Now I am also interested in gain graphs; they are im- (1997), 431–445. portant to polyhedral geometry, in particular, to gen- Stresses and liftings of cell-complexes, Discrete and eralizations of Maxwell-Cremona correspondence that I Comput. Geom. 21 (1999), 481–517. have constructed. On traces of d-stresses in the skeletons of lower dimen- Rigidity and exibility properties of graphs are of im- sions of homology d-manifolds (with R. Erdahl and portance to many elds of engineering, physics, compu- S. Ryshkov), Europ. J. Combin. (2000), accepted. tational chemistry, molecular biology, etc. Since 1998
Laurent Salo -Coste Professor of Mathematics I am an analyst who enjoys touching on other areas of random walks to the algebraic structure of the group including probability theory and geometric group theory. and to the geometry of its Cayley graphs. I study di erent aspects of heat di usion on manifolds Random walks on nite groups are special exam- from the point of view of both partial di erential equa- ples of nite Markov chains. In the past 10 years, I tions and stochastic processes. I am mainly interested in have worked on quantitative estimates for ergodic nite those properties that relate to the large scale geometry Markov chains. Some of the most interesting examples of the underlying space. For instance, I have recently of such chains are connected to combinatorial problems been trying to understand how heat di usion is a ected that are not tractable by deterministic algorithms but by the existence of more than one end on a manifold. for which a reasonable stochastic algorithm exists. These Potential theory and functional analysis often provide stochastic algorithms often involve a nite Markov chain the framework and tools to study these properties. as one of the main building blocks. In this context, ob- I also work on random walks on groups. For in- taining quantitative estimates is essential. stance, card shu ing methods can be modelized as ran- dom walks on the symmetric group. In this example, the Professional Activities: Editor for Mathematische group is nite but, in general, it can be in nite. What Zeitschrift. Associate Editor of Stochastic Processes and interests me most in this subject is relating the behavior their Applications, the European Series of Industrial and
Faculty Pro les 67 Applied Mathematics (Probability and Statistics), and (with T. Coulhon and I. Holopainen), Geometric and Annales de la Facult e des Sciences de Toulouse. Functional Analysis 11 (2001), 1139–1191. Central Gaussian semigroups of measures with continu- Selected Publications: ous densities (with A. Bendikov), J. Functional Anal- Bounds for Kac’s master equation (with P. Diaconis), ysis 186 (2001), 206–268. Comm. Math. Physics 209 (2000), 729–755. Probability on groups: random walks and invariant dif- On the stability of the behavior of random walks on fusions, Notices of the AMS 48 (2001), 968–977. groups (with C. Pittet), J. Geometric Analysis 10 Aspects of Sobolev-Type Inequalities, London Mathemat- (2001), 713–737. ical Society Lecture Note Series 289, Cambridge Uni- On the relation between elliptic and parabolic Harnack versity Press, 2002. inequalities (with W. Hebisch), Annales de l’Institut Dirichlet heat kernel in the exterior of a compact set Fourier 51 (2001), 1437–1481. (with A. Grigor’yan), Comm. Pure Appl. Math. 55 Harnack inequality and hyperbolicity for subelliptic p- (2002), 93–133. Laplacians with applications to Picard type theorems
Alfred H. Schatz Professor of Mathematics My eld of research is numerical analysis. I have been tions than one has before. These are so called supercon- principally involved in the analysis and construction of vergent approximations and their importance resides in nite element methods for the approximate solution of the fact that the original approximations are usually dif- partial di erential equations. In particular I have been cult to obtain but usually the new approximates may investigating both the local behavior of such matters be orders of magnitude better and easily computed from and another phenomena associated with them called su- them. perconvergence. Many physical problems have solutions that are smooth in some places and are nonsmooth (hav- Selected Publications: ing singularities) in others. In the numerical solution of Superconvergence in nite element methods and meshes these problems, the singular part of the solution is not which are locally symmetric with respect to a point only di cult to approximate but often lowers the quality (with I. Sloan and L. Wahlbin), SIAM Journal of Nu- of (pollutes) the approximation even where the solution merical Analysis, to appear. is nice. I have been involved in understanding this phe- Interior maximum norm estimates for Ritz Galerkin nomena and nding a way to improve the approxima- methods part II (with L. Wahlbin), Mathematics of tions. Computation, to appear. Another facet of the research is to nd properties of Some new error estimates for Ritz Galerkin methods with the computed approximate solutions which, when taken minimal regularity assumptions (with J. Wang), Math- into account, can be used to produce better approxima- ematics of Computation, submitted.
Jason Schweinsberg H. C. Wang Assistant Professor of Mathematics I work in probability theory. Much of my research has is merging at rate one. I have studied primarily alterna- focused on stochastic processes involving coalescence. tive models of coalescence called “coalescents with mul- One can think of coalescent processes as modeling a sys- tiple collisions” in which many particles can merge to- tem of particles in which the particles start out separated gether at once. These coalescent processes can be used and then merge into clusters as time goes forward. The to model populations which have a few very large fami- probabilistic behavior of a coalescent process is deter- lies. They can also be used to model “selective sweeps,” mined by the rates at which clusters merge. in which a selectively favorable mutation sweeps through Coalescent processes can be used to model the ances- the entire population within a short time. In my thesis, tral structure of a population. In this application, the I studied “coalescents with simultaneous multiple colli- “particles” represent individuals in the current genera- sions,” in which many particles can merge together at tion, and the merging of particles corresponds to the one time and many such mergers can occur simultane- merging of ancestral lines going backward in time. The ously. ancestral structure of many populations can be described I have recently worked on some problems involving by Kingman’s coalescent, in which each pair of particles fragmentation processes, which can be viewed as coales-
68 Faculty Pro les cent processes run in reverse. I have also done some re- Coalescents with simultaneous multiple collisions, Elec- search related to reversible Markov chains. Some of this tron. J. Probab. 5 (2000), 1–50. work has focused on the link between the recurrence and Applications of the continuous-time ballot theorem to transience of reversible Markov chains and the notion of Brownian motion and related processes, Stochastic P -admissibility in statistical decision theory. Process. Appl. 95 (2001), 151–176. An O(n2) bound for the relaxation time of a Markov Awards and Honors: NSF Postdoctoral Fellowship chain on cladograms, Random Struct. Alg. 20 (2002), (2001–2004). 59–70. Selected Publications: Conditions for recurrence and transience of a Markov A necessary and su cient condition for the Lambda- chain on Z+ and estimation of a geometric success coalescent to come down from in nity, Electron. probability (with J. Hobert), Ann. Statist., to appear. Comm. Probab. 5 (2000), 1–11. Shankar Sen Professor of Mathematics Most of my research concerns invariants associated and at the Durham conference on Group Theory and with representations of Galois groups of p-adic elds Number Theory (3 lectures, 1997). and algebraic number elds. These invariants, though Selected Publications: of an arithmetic nature, are related to classical invari- Lie algebras of Galois groups arising from Hodge-Tate ants arising in complex algebraic geometry; their study modules, Annals of Math. (1973). should shed light on geometric aspects of equations over On explicit reciprocity laws, J. Reine Angew Math. (1980 number elds or p-adic elds. Recently, I have studied & 1981). families of Galois representations depending analytically Continuous cohomology and p-adic Galois representa- on p-adic parameters, and how the invariants for such tions, Inventiones Math. (1980). families change with the parameters. Techniques from Integral representations associated with p-adic eld ex- p-adic analytic function theory and functional analysis tensions, Inventiones Math. (1988). have proved useful in this connection. The analytic variation of p-adic Hodge structure, Annals of Math. (1988). Invited Lectures: Delivered a talk at the Nottingham An in nite-dimensional Hodge-Tate theory, Bulletin conference on Number Theory (1996); at Cambridge Math. Soc. France (1992). University, England (1996); at a Conference on Arith- Galois cohomology and Galois representations, Inven- metic, Algebra and Geometry, Braga, Portugal (1997); tiones Math. (1993). Richard A. Shore Professor of Mathematics My major research interests have centered around an- plexity and ones based on the di culty of de ning func- alyzing the structures of relative complexity of computa- tions in arithmetic. Restricting the computational re- tion of functions on the natural numbers. The primary sources more directly in terms of time or space leads out measure of such complexity is given by Turing reducibil- of recursion theory and into complexity theory. Relaxing ity: f is easier to compute than g, if there is a (Turing) the restrictions by allowing various in nitary procedures machine which can compute f if it is given access to leads instead into generalized recursion theory or set the- the values of g. I have also worked with various other ory. interesting measures of complexity that are de ned by The methods developed in these investigations are also restricting the resources available primarily in terms of useful in determining the e ective content of standard access to g. The general thrust of my work has been mathematical theorems (when can existence proofs be to show that these structures are as complicated as pos- made e ective) and the inherent di culty of combinato- sible both algebraically and logically (in terms of the rial theorems in proof theoretic terms. Recently, I have complexity of the decision problems for their theories). also been working on issues in e ective model theory and These results also allow one to di erentiate among dif- algebra connected with the problem of how the compu- ferent notions of relative complexity in terms of the or- tational properties of algebraic structures can vary with derings they de ne. di erent (but always computable) presentations of the Another major theme in my work has been the rela- models. tionship between these notions of computational com-
Faculty Pro les 69 Professional Activities: Editor of the North-Holland On the strength of K onig’s theorem for in nite bipartite book series Studies in Logic and the Foundations of graphs (with R. Aharoni and M. Magidor), J. Comb. Mathematics. President of the Association for Symbolic Theory (B) 54, (1992), 257–290. Logic. The p-T -degrees of the recursive sets: lattice embeddings, extension of embeddings and the two quanti er theory Invited Lectures: Spoke at a special session on reverse (with T. Slaman), Theoretical Computer Science 92 mathematics, ASL, Philadelphia, PA, March 2001. (1992), 263–284. Logic for Applications (with A. Nerode), Texts and Selected Publications: Monographs in Computer Science, Springer-Verlag, -recursion theory; in Handbook of Mathematical Logic New York, 1993; second edition, Graduate Texts in (J. Barwise, ed.), North-Holland, 1977, pp. 653–680. Computer Science, Springer-Verlag, New York, 1997. The homogeneity conjecture, Proceedings of the National De nability in the recursively enumerable degrees (with Academy of Sciences 76 (1979), 4218–4219. A. Nies and T. Slaman), Bull. Symb. Logic 2 (1996), De nable degrees and automorphisms of D (with L. Har- 392–404. rington), Bull. Amer. Math. Soc. (NS) 4 (1981), 97– De ning the Turing jump (with T. Slaman), Math. Re- 100. search Letters 6 (1999), 711–722. The degrees of unsolvability: the ordering of functions On the solution of the Goncharov-Ash problem and the by relative computability; in Proc. Inter. Congress of spectrum problem in the theory of computable models Mathematicians (Warsaw) (1983) PWN-Polish Scien- (with B. Khoussainov), Dokl. Akad. Nauk 371 (2000), ti c Publishers, Warsaw 1984, Vol. 1: 337–346. 30–31 (Russian); English version: Doklady Mathemat- The structure of the degrees of unsolvability; in Recur- ics 61 (2000), 178–179. sion Theory (A. Nerode and R. A. Shore, eds.), Pro- The prospects for mathematical logic in the twenty- rst ceedings of The Symposia in Pure Mathematics 42, century (with S. Buss, A. Kechris and A. Pillay), Bul- AMS, Providence, R. I. (1985), 33–51. letin of Symbolic Logic 7 (2001), 169–196. Recursive limits on the Hahn-Banach theorem (with A. Nerode and G. Metakides), Contemporary Math- ematics 39 (1985), 85–91.
Reyer Sjamaar Associate Professor of Mathematics I study actions of Lie groups on symplectic manifolds. Selected Publications: This is an area of di erential geometry related to al- Moment maps and Riemannian symmetric pairs (with gebraic geometry and mathematical physics. Some of L. O’Shea), Math. Ann. 317 no. 3 (2000), 415–457. my recent work concerns moment polytopes and leads Coadjoint orbits, moment polytopes and the Hilbert- to improved versions of certain eigenvalue inequalities in Mumford criterion (with A. Berenstein), J. Amer. matrix analysis. Math. Soc. 13 no. 2 (2000), 433–466.
John Smillie Professor of Mathematics My area of interest is dynamical systems. I have done Polynomial di eomorphisms of C2 VII: hyperbolicity and work on polygonal billiards and dynamics of ows on external rays (with E. Bedford), Ann. Scient. Ec. Teichm uller space; analysis of algorithms; and di eomor- Norm. Sup. 4 (32) (1999), 455–497. phisms of surfaces. I am currently working on complex Billiards on rational-angled triangles (with R. Kenyon), dynamics in two dimensions. Comment. Math. Helv. 75 (2000), 65–108. The dynamics of billiard ows in rational polygons; Professional Activities: Served on the NSF Panel on in Encyclopedia of Mathematical Sciences, vol. 100 Dynamical Systems and Ergodic Theory. (edited by Yu. Sinai), Springer-Verlag, 1999. Polynomial di eomorphisms of C2 VIII: quasi-expansion Selected Publications: (with E. Bedford), Amer. J. Mathematics 124 (2002), Polynomial di eomorphisms of C2 VI: connectivity of J 221–271. (with E. Bedford), Annals of Mathematics 148 (1998), Real polynomial di eomorphisms with maximal entropy 695–735. I: tangencies, preprint.
70 Faculty Pro les Lawren Smithline VIGRE Assistant Professor of Mathematics I study p-adic modular forms. This area of number modular forms. As described in recent seminars and a theory generalizes classical modular forms, which have forthcoming paper, the U operator is an example of a starred in the resolution of long-standing problems such compact operator with rational generating function. as Fermat’s Last Theorem. The methods of p-adic anal- Administrative Activities: Selection committee for the ysis bridge algebraic geometry and classical analysis. Ithaca High School senior math prize. Co-organizer of a The combinatorial properties of the Atkin U operator special seminar for very able high schoolers next year. have held special interest for me. Their structure makes computer experiments easy. The data suggest properties Invited Lectures: Gave a talk at the Quebec-Vermont of the operator which result from the mode of generation, number theory seminar (Apr. 2002) and at the Canadian rather than the particular parameters derived from the Number Theory Association (May 2002).
Avery Solomon Senior Lecturer of Mathematics My position involves me in mathematics, math edu- Our program in the classrooms focuses on a few exem- cation and outreach programs in several area schools. I plary teachers, supporting their e orts to develop mod- teach courses in mathematics at Cornell and teach a va- ules and activities in the classroom, and share these riety of sections of the special course Math 508 — Math- with other teachers through visits, workshops, and ac- ematics for Secondary Teachers — both at Cornell and tual classroom intervention. One of our middle school at local sites within a 50 mile radius of Ithaca. My po- teachers taught a model two-week unit at two di er- sition in the Cornell Teacher Education program in the ent middle schools while the 7th and 8th grade teachers Department of Education has involved me in supervis- watched, and then they taught the lessons to their other ing student teachers and co-teaching the math/science sections. Math lab activities and structure developed methods course Educ 602. with high school teachers is being used in classrooms in In addition to these courses, I am the director of several districts. the Cornell/Schools Mathematics Resource Program My current interests include developing exploratory (CSMRP). Through this program I organize and co- units for high school mathematics, the use of Sketchpad teach Saturday workshops and summer programs, con- as an environment for learning geometry, and integrat- sult with school districts, work with teachers directly ing mathematics and philosophy in a humanist context. to develop curriculum and programs, visit classrooms A long range plan is to produce materials for a man- and occasionally teach classes in middle schools or high ual for 6-12 mathematics teachers which would provide schools, teach workshops in schools and at BOCES. essential insights into selected topics, interrelations and For the past eight years the CSMRP has held teacher meanings. This text would also serve pre-service teach- workshops meeting four Saturdays a year. These work- ers of mathematics, helping them to look back at their shops focus on both content and pedagogy, giving teach- own pre-college experiences from a more mature stand- ers a chance to immerse themselves for a time in math- point. I am interested in studying the role of intuition in ematical problems, share ideas, and get inspiration for mathematical exploration, and in continuing to pursue their classes. We often examine basic mathematics con- the relation of philosophy and mathematics as a route cepts from a more mature standpoint, and also present to self-knowledge. interesting and relevant topics to get teachers interested in their own mathematical explorations, as well as pre- Grants: Twelve DDE Title IIA grants awarded by the senting new curricula and introducing software environ- New York State Department of Education to support in- ments as teaching tools. We now have a core group of service programs for teachers, 1986–present. Participant about 25 teachers, and a larger group of about 50 others in UFE grant through NSF for enhancement of college who are part of our e-mail list and occasionally attend. teaching, with David Henderson, 1995–present. Our week long summer institute for mathematics teachers, given for the past eleven years, has recently Articles/Videos: focused on teaching geometry, especially exploring ge- A manual of mathematics labs to accompany Course ometry on spheres and other surfaces, and Geometer’s I mathematics (with Amy Davis of Moravia High Sketchpad software. School), self published.
Faculty Pro les 71 Puppies Pen, a video of a pilot intervention program for Proportions and levels of meaning in mathematics;in Middle School Mathematics. For the Learning of Mathematics, 1991. Levels of knowledge submitted for publication in What is a line?; in For the Learning of Mathematics, Parabola, 1997. 1991. A constructivist dilemma: an episode from middle school A fractal outline of a fractal course, AMTYS journal, mathematics. 1989. Geometric patterns in nature, being prepared for publi- cation. Birgit Speh Professor of Mathematics Director of Undergraduate Studies I am interested in representation theory of semisim- Invited Lectures: Delivered a lecture at Analytic and ple Lie groups as well as in arithmetic groups and ana- Geometric Aspects of the Langlands Program, Tel Aviv lytic number theory. In the last few years most of my University, March 2001 and at the Max Plank Institut work concerned the cohomology of arithmetic groups, fuer Mathematik, June 2001. the Arthur Selberg trace formula and its application to problems in automorphic forms and number theory. Selected Publications: Absolute convergence of the spectral side of the Arthur Professional Activities: Editor of the Journal of Rep- Selberg trace formula for GL(n) (with W. Mueller), resentation Theory and the New York Journal of Math- preprint. ematics. Served on the AMS Committee on Academic Pseudo Eisenstein series and the cohomology of arith- Freedom, Tenure and Employment Security. metic groups II (with J. Rohlfs), preprint.
Michael Stillman Professor of Mathematics My main areas of interest are computational algebra erations in algebraic geometry (written with D. Eisen- and algebraic geometry, commutative algebra, and alge- bud). braic geometry. My original interest in computational methods was their application to problems in algebraic Selected Publications: geometry. Since then, my work has proceeded in several A criterion for detecting m-regularity (with D. Bayer), related directions. I have studied the complexity of the Invent. Math. 87 (1987), 1–11. algorithms (mainly Gr obner bases). I have been devel- A theorem on re ning division orders by the reverse lex- oping algorithms for computing in commutative algebra icographic order (with D. Bayer), Duke Math. J. 55 and algebraic geometry. For example, I have developed (1987), 321–328. algorithms for manipulating line bundles in algebraic ge- Determinantal equations for algebraic curves of high de- ometry (with M. Brundu), computing Hilbert functions gree (with D. Eisenbud and J. Koh), Amer. J. Math. (with D. Bayer), and nding integral closures of polyno- 110 (1988), 135–147. mial rings. On the complexity of computing syzygies (with D. Bay- My original interest in these methods was to actually er), J. Symbolic Comp. 6 (1988), 135–147. use them in my research in algebraic geometry. D. Bayer Computing the equations of a variety (with M. Brundu), (of Columbia) and I have designed and implemented Trans. AMS (1991), to appear. a specialized computer algebra system, which we call Some matrices related to Green’s conjecture (with “Macaulay,” which includes many of these algorithms. D. Bayer), Sundance Conference Proceedings on Free Hundreds of researchers use this system. The latest ver- Resolutions (1991), to appear. sion includes algorithms for a large number of useful op-
Robert S. Strichartz Professor of Mathematics Mathematics is an adventure. As a research mathe- knowing exactly where I might be heading next. I have matician, I have wandered along many paths, always en- certainly not been following a geodesic! Perhaps its has joying the discoveries that have come my way and never been just a random walk. Yet sometimes I think there
72 Faculty Pro les has been some purpose behind it, to bring me to the Recently, I have been working on analysis on fractals. work I am doing today. So here is a synopsis of where I The idea is to develop the analog of calculus for functions have been and what it might add up to. de ned on fractals and to study the resulting fractal dif- In my thesis I studied Sobolev spaces, an important ferential equations that might be used to model physical class of function spaces useful in the theory of partial processes taking place in fractal objects. Through the di erential equations, and gave an important characteri- work of Jun Kigami, it is possible to de ne the analog zation of Sobolev spaces with smoothness coe cient not of a Laplacian on some fractals as a limit of di erence equal to an integer. In my early work I studied applica- quotients. This Laplacian has some strange properties, tions of harmonic analysis to wave equations and made such as: 1) there exist localized eigenfunctions; 2) there contributions to the theory of pseudo-di erential oper- exist harmonic functions locally constant, but not glob- ators and harmonic analysis on semi-simple symmetric ally constant; 3) if the Laplacian of u is de ned, then spaces. the Laplacian of u2 is not de ned (unless u is constant); Beginning in the 1980s, my work became more geomet- 4) the associated wave equation does not have a nite ric. I applied harmonic analysis to integral geometry, in propogation speed. I have been working on learning which the central problem is to reconstruct a function more about this Laplacian, and I have developed tools from its integrals over geometrically simple sets such as of numerical analysis to approximate solutions to various straight lines or planes. I used Riemannian geometry fractal di erential equations. The graph of the ground as a kind of metaphoric prism to understand the signif- state eigenfunction on the Sierpinski gasket is shown be- icance and relationships among the basic concepts and low. constructions of harmonic analysis. I also studied a gen- 1.4 eralization of Riemannian geometry which I am trying to call “Sub-Riemannian” (as opposed to the unwieldy 1.2 name “Carnot-Caratheodory”). This geometry is related to sub-elliptic di erential equations, and arises naturally 1.0 in the theory of nilpotent Lie groups. In the 1990s I began working on fractal geometry and 0.8 the theory of wavelets. The underlying theme in both 0.6 these areas is the idea of self-similarity, in which the whole is written as a sum of parts, each of which is sim- 0.4 ilar to the whole. I have developed the idea of a Fractal Plancherel Theorem, both in the general case and for 0.2 self-similar measures, in which I showed how the frac- 0 tal properties of a measure show up in the asymptotic 0 0.2 0.4 0.6 0.8 1.0 1.2 behavior of its Fourier transform. In connection with this work I have become involved In addition to my research, I have maintained an inter- with what might be called “experimental mathemat- est in mathematical exposition. I received a Lester Ford ics.” The idea is to use computer experiments to ex- Award from the Mathematical Association of America in plore mathematical problems, with the goal of generat- 1983 for expository writing, and in 1982 I won the rst ing interesting conjectures that can then be proven using prize in the French Museum Competition sponsored by conventional mathematical reasoning. My experimental the Mathematical Intelligencer. I have published two research has been done in collaboration with undergrad- textbooks, A Guide to Distribution Theory and Fourier uate students, with the support of the REU (Research Transforms and The Way of Analysis, based on course Experiences for Undergraduates) Program sponsored by notes that have been used at Cornell for many years in the NSF. Starting in the summer of 1994, I have directed Math 413, 414, 422 and 615. an REU site program at Cornell. Edward Swartz VIGRE Assistant Professor of Mathematics My research centers on the interplay between ma- ity theory. My interest in matroids originally started troids, geometry/topology and algebra. Matroids are with the discovery of a close connection between ma- combinatorial abstractions of linear independence. Their troids and quotients of spheres by elementary abelian enumerative properties have applications in a variety of p-groups. More recently, I have used face rings to es- elds, including graph coloring and ows, linear coding, tablish a matroid analog of the g-theorem for simplicial arrangements of hyperplanes, and problems in reliabil- polytopes.
Faculty Pro les 73 Selected Publications: g-elements of matroid complexes, submitted. Matroids and quotients of spheres, Mathematische h-vectors of k CM, broken circuit and independence Zeitschrift (2002). complexes, preprint.
Moss Sweedler Professor Emeritus of Mathematics First I worked in the area of Hopf algebras and wrote phenomena, simple algebras and generalizations of the Hopf Algebras, which came to be the standard refer- Brauer group, and di erential algebra. Since the mid ence book on the subject. H. Allen and I used Hopf eighties I have primarily worked in the area of computer algebras to prove a 25 year old conjecture of Jacobson. algebra, especially computational commutative algebra. Over the ensuing years until about the mid eighties, I This has produced both theoretical and applied results worked and published in the areas of commutative al- with applications beyond mathematics, such as to error gebra and algebraic geometry, real-algebraic geometry, control codes and resulted in my position as Director of homological algebra, algebraic groups, purely insepara- the Army Center of Excellence for computer algebra. ble eld extensions and general positive characteristic
Maria S. Terrell Senior Lecturer of Mathematics Director of Teaching Assistant Programs As the director of teaching assistant programs, I am in- to create materials for calculus instruction to enhance terested in providing opportunities for our graduates stu- classroom discussion of concepts. dents to explore and develop their ideas about learning My research area is the geometry of rigid structures. and teaching mathematics. I have organized workshops I am interested in some questions about the rigidity of for teaching assistants at Cornell, and at regional and symmetric tensegrities. national meetings. I am currently working on a project
Robert E. Terrell Adjunct Associate Professor of Mathematics www.math.cornell.edu/ebterrell Bob Terrell enjoys teaching mathematics and has writ- He was once an engineer, and might be the only member ten software for teaching partial di erential equations. of the department with patents on machinery.
Harrison Tsai H. C. Wang Assistant Professor of Mathematics I am interested in the application of algebraic algo- Selected Publications: rithms in mathematics and science. In the past, my re- Polynomial and rational solutions of holonomic systems search has been in the development of algorithms for (with T. Oaku and N. Takayama), Journal of Pure and nding algebraic solutions to systems of linear partial Applied Algebra, to appear. di erential equations. Currently, I am becoming inter- Computing homomorphisms between holonomic D-modules ested in the optimization of polynomials. For polynomi- (with U. Walther), Journal of Symbolic Computation, als with many variables, heuristic methods are necessary to appear. for practical purposes and the behavior of algorithms can D-modules on smooth toric varieties (with M. Mustata, be unpredictable. However, for certain special classes of G. Smith and U. Walther), Journal of Algebra, to ap- polynomials, algorithms can be robust. I am interested pear. in identifying such situations and investigating their rel- Algorithms for associated primes, Weyl closure and local evant mathematical properties. cohomology of D-modules, Proceedings of Guanajuato conference on local cohomology, to appear. Awards and Honors: NSF Postdoctoral Fellowship (2000–2003). Japan Society for the Promotion of Sci- ence (JSPS) Fellowship (spring 2001, Kobe University).
74 Faculty Pro les Warwick Tucker H. C. Wang Assistant Professor of Mathematics Mainly, I have been studying auto-validating algo- Professional Activities: Reviewer for Mathematical Re- rithms for ordinary di erential equations. In particular, views. Referee for Foundations of Computational Math- I have focused on Taylor methods using automatic dif- ematics. Supervised Ben Szekely, a Math 420 student, ferentiation tools combined with interval arithmetic. In on a project aimed at visualizing ODEs using Java. a second project, I have been collaborating with Mike Coleman of Cornell’s Human Power and Robotics Lab Invited Lectures: Delivered invited talks at the Univer- on a project on passive dynamic walking. In a third sity of Maryland, Penn State University, Queen Mary’s project, I have been working with the Cornell Big Red College (UK) and at Cornell’s CAM Colloquium. Invited Arti cial Intelligence Navigator team. The goal of this lecturer at the conference “Recent Trends in Dynamics,” project is to “advance the state-of-the-art Autonomous University of Porto, Portugal, 2001. Underwater Vehicles (AUVs) by challenging a new gen- eration of engineers to perform realistic missions in the Selected Publications: underwater environment.” The competition is to be held Computational algorithms for ordinary di erential equa- July 11–15, 2001, and takes place at the United States tions, EQUADIFF 99, World Scienti c, Singapore, Naval Academy in Annapolis, Maryland. 2000. A rigorous ODE solver and Smale’s 14th problem, Foun- Awards and Honors: The Swedish Mathematical Soci- dations of Computational Mathematics, to appear. ety’s Wallenberg Prize.
Alexander Vladimirsky H. C. Wang Assistant Professor of Mathematics My research is mostly focused on design of Ordered putational interest include rst-arrival times (e.g., when Upwind Methods (OUMs). Numerical schemes for non- will a spreading re reach a certain location?), multiple linear static PDEs often require solving coupled systems arrivals (e.g., aftershocks of earthquakes), and asymp- of non-linear discretized equations. OUMs use partial totic behavior (e.g., what will be the ultimate shape of knowledge of the direction of information ow to de- a growing crystal?). couple those systems: solving the discretized equations one at a time is much more e cient. My thesis was Awards and Honors: NSF Postdoctoral Research Fel- devoted to construction of OUMs for the PDEs arising lowship, 2001–2004. Bernard Friedman Memorial Prize in the anisotropic exit-time optimal trajectory problems. in Applied Mathematics, University of California at These methods were later extended to a wider class of Berkeley, 2001. problems in anisotropic control theory and front propa- gation. I am currently collaborating with John Gucken- Selected Publications: heimer to build OUMs for the computationally intensive Fast methods for the Eikonal and related Hamilton- problems in dynamical systems (e.g., grid representation Jacobi equations on unstructured meshes (with J. A. of invariant manifolds for systems with multiple time Sethian), Proc. Nat’l Acad. Sci. USA 97 no. 11 (2000), scales). 5699. I am also fascinated by the phenomenon of “anisotropy” Ordered upwind methods for static Hamilton-Jacobi and its di erent manifestations in wave physics, crys- equations (with J. A. Sethian), Proc. Nat’l Acad. Sci. tallography, and optimal control. A na ve statement USA 98 no. 20 (2001), 11069. of Huygens’ principle can be extended to construct the Ordered upwind methods for hybrid control (with J. A. wave fronts expanding in inhomogeneous anisotropic me- Sethian), Proceedings of the 5th International Work- dia; however, its e cient usage for computational pur- shop on Hybrid Systems: Computation and Control, poses can be problematic. The questions of direct com- Stanford, CA, USA, March 25–27, 2002 (LNCS 2289).
Faculty Pro les 75 Karen Vogtmann Professor of Mathematics A fundamental technique for studying a group G is to Committee on Meetings and Conferences of the AMS. view G as a group of automorphisms of geometric object Research board of the American Institute of Mathemat- C. Geometric and topological properties of C can then ics. be used to study algebraic properties of G. Beautiful classical examples of this are the theory of arithmetic Selected Publications: and S-arithmetic groups acting on homogeneous spaces Spherical posets and homology stability for On,n, Topol- and buildings, including work of Borel and Serre on co- ogy 20 (1981), 119–132. homological properties of these classes of groups, and Moduli of graphs and automorphisms of free groups (with the theory of groups of surface homeomorphisms acting M. Culler), Inventiones 84 (1986), 91–119. on the Teichm uller space of the surface. My main area Equivariant outer space and automorphisms of free-by- of research interest is in developing geometric theories nite groups (with S. Krstic), Comment. Math. Hel- for other classes of groups. In particular, I have worked vetici 68 (1993), 216–262. with orthogonal and symplectic groups, SL2 of rings of A group-theoretic criterion for property FA (with imaginary quadratic integers, groups of automorphisms M. Culler), Proc. AMS 124 no. 3 (1996), 677–683. of free groups, and mapping class groups of surfaces. Cerf theory for graphs (with A. Hatcher), Jour. London Math. Soc. 58 part 3 (1998), 633–655. Awards and Honors: NSF Visiting Professorships for Whitehead’s algorithm for surface groups (with G. Levitt), Women, Cornell University (1984–85). Invited hour ad- Topology 39 no. 6 (2000), 1239–1251. dress, AMS Summer Meeting, Provo, Utah (1986). NSF The symmetries of Outer space (with M. Bridson), Duke Career Advancement Award, MSRI (1989). Research Mathematical Journal 106 no. 2 (2001), 391–409. Professorship, MSRI (1995). Geometry of the space of phylogenetic trees (with Professional Activities: Executive committee of the L. Billera and S. Holmes), Advances in Applied Math AMS. Referee for professional journals. Chair of the 27 (2001), 733–767.
Lars B. Wahlbin Professor of Mathematics At present one can compute “solutions” to very tough the precise and detailed behavior of the nite-element nonlinear, singular problems on, say, a supercomputer. methods in a variety of problems; the most interesting Most often, numerical analysis does not furnish theo- ones contain singularities of various degrees of nastiness. rems that cover a practical situation, but it provides in- Professional Activities: Editor for Mathematics of Com- sight into the behavior of the relevant numerical method putation. on carefully chosen model problems with, at best, some of the most pertinent di culties of the real problem Selected Publications: present. Local behavior in nite element methods; in Handbook My work in numerical analysis is aimed at gaining a of Numerical Analysis (P. G. Ciarlet and J. L. Lions, fundamental understanding of numerical methods. Such eds.), Vol. II (Part 1), North Holland (1991), 353–522. insight is also necessary for constructing better algo- Superconvergence in Galerkin Finite Element Meth- rithms. My particular interest is in methods for partial ods , Springer Lecture Notes in Mathematics 1605, di erential equations, and lately I have been studying Springer-Verlag New York, 1995.
Beverly H. West Senior Lecturer of Mathematics My chief interest is in mathematics teaching, partic- Awards and Honors: Invited address, Computer graph- ularly of di erential equations, multivariable/vector cal- ics in mathematics education, at the Grand Opening culus and dynamical systems (both real and complex). of Fields Institute, Waterloo, Ontario (1992). Plenary I use interactive computer graphics, writing, student in- address, Computer graphics in di erential equations,at teraction, and many choices within assignments to reach Seventh International Congress on Mathematical Educa- and empower a diverse student audience. tion (ICME7), Quebec (1992). Guest Editor of The Col-
76 Faculty Pro les lege Mathematics Journal for Nov. 1994 issue devoted to Selected Publications: innovations in the teaching of di erential equations. Analyzer (with D. Alfors), an exhaustive software package for studying functions of a single variable Professional Activities: Member of the MAA, SIAM, (1990 EDUCOM/NCRIPTAL Distinguished Mathe- AWM, NYAS, NCTM, and CODEE (NSF Di eren- matics Software Award), Addison Wesley, 1992. tial Equations Consortium with Harvey Mudd College, MacMath (with J. Hubbard), 12 interactive graphics Rensselaer Polytechnic Institute, St. Olaf College, Wash- programs for the Macintosh, to accompany the Dif- ington State University and West Valley Community ferential Equations texts, second edition, Springer- College to promote computer graphics experimentation Verlag, 1994; new expanded version in progress. in di erential equations courses and provide workshops). A new look at the Airy equation with fences and fun- National Advisory Board for Silvia Heubach’s Cal- nels (with J. Hubbard, J. McDill and A. Noonburg), ifornia State University at Los Angeles NSF project College Math. J. (1994); Proc. Organic Mathematics on An Innovative Modeling Approach at the Fresh- Project (1996); CECM, Simon Fraser Univ. (1997). man/Sophomore Level (1997–99) and for J. McDill’s Cal Di erential Equations: A Dynamical Systems Approach Poly San Luis Obispo NSF project on interactive busi- (with J. Hubbard), Springer-Verlag; Part I: One- ness calculus. Dimensional Equations, 1991, 1997; Part II: Higher- Two intensive consulting trips to Olin College of En- Dimensional Equations, 1995. gineering about inventing the appropriate mathematics Interactive Di erential Equations (with S. Strogatz, curriculum for their innovative college — dynamical sys- J. M. McDill, J. Cantwell and H. Hohn), a CD-ROM tems with technology and qualitative analysis were the with laboratory workbook, Addison Wesley Interac- focus of their request for expertise. tive, 1996, 1.1 for Mac and 2.0 for Windows, 1997. ODE Architect (with C ODE E, NSF Consortium for Invited Lectures: ODE Experiments), John Wiley and Sons, 1998. An MAA Short Course on Teaching Di erential Equations interactive teaching, learning and research environ- (with Paul Blanchard et. al.; July 1999). ment on CD Rom with Companion Book of 269 pages. Successful take-home examinations: multivariable cal- This package won an Invision ’98 award as one of “The culus and di erential equations, International Con- 9 Best CD-Roms on the Planet” (against all sorts of ference on Technology in Collegiate Mathematics nonmathematics competitors)! (ICTCM), San Francisco (Nov. 1999). Technology in di erential equations courses: my experi- Real time dynamics: why it makes a di erence (with ences, student reactions, a chapter for an MAA volume J. McDill), International Conference on Technology in on teaching di erential equations “in the new mille- Mathematics Teaching (ICTMT), Plymouth, England nium” (M. Kallaher, ed.). (Aug. 1999) and MAA Winter Meetings (Jan. 2000); Di erential Equations and Linear Algebra (a combined Women in Science Delegation to Egypt. text with J. Farlow, J. Hall and J. McDill), Prentice Hall, 2002.
James West Professor of Mathematics My research has focused on the topology and symme- classical matrix algebra to describe equivariant homeo- tries of manifolds of nite and in nite dimensions, and on morphisms and homotopy types of manifolds with locally the related topics of polyhedra, absolute neighborhood linearizable transformation groups, which in turn has led retracts, function spaces and spaces of sets. to new results on the topological classi cation of linear An example of the interplay between these theories is representations of nite groups. I have been involved in that manifolds modeled on the Hilbert cube appear nat- these studies. urally in several ways as limits of stabilization processes for nite-dimensional objects, and, unlike standard func- Professional Activities: Member of the editorial board tion space stabilization, retain more of their important of Fundamenta Mathematicae. properties, e.g., simple homotopy type. Study of the Administrative Activities: Faculty reader of Arts Col- Hilbert cube manifolds has produced several of the ini- lege freshman admissions applications. tial breakthroughs in introducing control into the home- omorphism theory of nite-dimensional manifolds. This Invited Lectures: Delivered an invited talk at the Uni- in turn, has been useful in analyzing the failure of the versidad Nacional Aut onoma de M exico.
Faculty Pro les 77 Milen Yakimov H. C. Wang Assistant Professor of Mathematics The main area of my research is representation theory Professional Activities: Referee for several journals. and its applications. More concretely I study quantized universal enveloping algebras and a ne Kac-Moody al- Invited Lectures: Oliver Club, Cornell University gebras. I am interested in the interplay between their Mathematics Department (Oct. 2001). AMS meeting, categories of representations (extending the work of Williamstown (Oct. 2001). Conference on representa- D. Kazhdan and G. Lusztig) as well as developing the- tions of loop groups, IPAM, UCLA (Nov. 2001). Yale ory of Harish-Chandra modules for those. Primarily cat- University Geometry, Symmetries and Physics seminar egories O in the sense of J. Bernstein, I. Gelfand, and (Nov. 2001). S. Gelfand for those were studied so far. From another side I work on the approach to representations of Hopf Selected Publications: algebras through the geometry of the related quasiclassi- Symplectic leaves of complex reductive Poisson-Lie cal structures Poisson-Lie groups (“Kirillov-Kostant or- groups, Duke Math. J. 112 (2002), 453–509. bit method”). The latter turns out to be much richer Discrete Darboux transformations from Jacobi polyno- than the geometry of the coadjoint orbits in Lie alge- mials (with F. A. Gr unbaum), Paci c J. Math. 204 bras and is very interesting by itself. I am also working (2002), 395–431. on applications of Hopf algebras and Poisson-Lie groups Quantum invariant measures (with N. Reshetikhin), to quantum and classical completely integrable systems. Comm. Math. Phys. 224 (2001), 399-426. Large part of my research dealt with applications of tech- The double and dual of a quasitriangular Lie bialgebra niques of completely integrable systems (e.g., B acklund- (with T. Hodges), Math. Res. Lett. 8 (2001), 91–105. Darboux transformations, W -symmetries) and represen- Deformation quantization of Lagrangian ber bundles tation theory (W1+∞ and Weyl algebras) to the so-called (with N. Reshetikhin); in Conf erence Mosh e Flato “bispectral problem.” I am also interested in applica- 1999, vol. 2, Kluwer Acad. Publ., 2000, 269–288. tions of representations of Hopf algebras to topology and Highest weight modules over the W1+∞ algebra and the mathematical physics. In the eld of deformation quan- bispectral problem (with B. Bakalov and E. Horozov), tization I studied in detail the question of quantization Duke Math. J. 93 no. 1 (1998), 41–72. of classical completely integrable systems via Fedosov Bispectral algebras of commuting ordinary di erential quantization. operators (with B. Bakalov and E. Horozov), Comm. Math. Phys. 190 no. 2 (1997), 331–373. Awards and Honors: Clay Foundation Lifto Mathe- matician, Summer 2001.
78 Faculty Pro les Visiting Faculty Program Participants
B ela Bajnok Gettysburg College I spent the fall of 2001 and the spring and summer of o er. I am grateful for the opportunity to interact with 2002 at the Cornell Mathematics Department as a visit- a wonderful faculty and to use Cornell’s unsurpassed ing associate professor. I am fortunate to have been able Mathematics Library. Teaching such responsive, moti- to take part in this wonderful opportunity. The Visiting vated, and interesting students was a delight; I especially Faculty Program is a unique adventure for mathemati- enjoyed and learned from my many discussions on teach- cians on sabbatical or other leave from their home insti- ing and curriculum with Maria Terrell. I also extend tution to advance their teaching and research activities my thanks to the sta members of the department; this at a leading university. cheerful and professional group helped to make my visit I enjoyed the amazing array of seminars, lectures, and enjoyable and successful. other academic and cultural events that Cornell had to
Carolyn DeSilva Gettysburg College As my two years at Cornell as a visiting associate pro- Even though I’ve been teaching for a long, long time fessor come to an end, it’s pleasant to re ect on my expe- (as they say, since before dirt), I recognize and appreciate riences here as a teacher and mathematician, colleague what I’ve learned here in working with Cornell faculty, (and temporary resident of a singularly quirky town). other visiting faculty, graduate students and undergrad- Good times, for the most part, with a few truly memo- uates. Being part of a large community of mathemati- rable moments and maybe a couple best forgotten. cians has been intellectually stimulating and challenging. The good times (and some of the great) include teach- I return to my home institution energized and renewed in ing Cornell students. I’ve particularly relished the cul- my dedication to the profession. (I give it three months.) tural diversity among the student population and the I cherish the friendships begun here. (These will last.) intellectual climate on campus. It goes without saying The support sta in the Mathematics Department are that the majority of students are extremely bright, hard- rst-rate (and all deserve massive raises). I’m grateful working, respectful and attentive. Beyond those quali- for their help, their patience and good humor. ties, I discovered them to be warm, funny, modest, in- Goodbye and good luck to all. tensely concerned about the world we all live in, and possessed with social consciences. Maybe they’ll clean up after us.
Visiting Faculty Program Participants 79 Sta Pro les
and screens inquiries pertaining to course o erings. She Administration also acts as back-up technical typist, processing origi- Linda Clasby, Assistant to the Chair (2001): Linda pro- nal entry and editing of highly technical mathematical vides administrative support to the chair of the Mathe- manuscripts. Mikki is the editor of the annual report, matics Department. She maintains the chair’s calendar, and she generates department database directories and screens calls and schedules appointments. She works reports. Mikki is our web administrator and designer, with the chair to compile committee assignments, co- and she updates and maintains many of our department ordinates faculty searches, maintains sabbatical records, web pages. processes academic personnel forms and maintains aca- demic personnel les. She assists foreign nationals in ob- Gayle Lippincott, Accounts Coordinator (1998): Gayle taining proper visa status, arranges lectures and accom- provides administrative, nancial and non-academic per- modations for prospective faculty/visitors and schedules sonnel support for the department. In accordance with bene ts counseling for new academic employees. university and agency regulations, she develops research budgets and oversees proposal submissions to the Of- Arletta Havlik, Department Registrar (1968): Arletta ce of Sponsored Programs. She monitors account provides secretarial and administrative support for the transactions, approves expenditures, and maintains ac- instructional and research programs of the Mathematics count information and records. She also processes non- Department faculty. Her responsibilities include coordi- academic appointments, maintains non-academic per- nating the paperwork, course enrollments and inquiries sonnel records, oversees time collection, processes payroll pertaining to enrollment in math courses, and she over- vouchers and distributes paychecks. Gayle assists the sees the department’s presence at the central course ex- administrative manager in the day-to-day operations of change each semester. In her role as department regis- the department and serves as acting manager when the trar, she coordinates course enrollments, evaluations and administrative manager is unavailable. She is the func- grade submissions. She is the primary technical typist tional supervisor for the administrative sta . for the department and prepares complex documents in- volving sophisticated typesetting software (TEX), which Brenda Smith, Undergraduate Coordinator (2001): involves designing, editing and formatting. Arletta also Brenda is the primary resource person for the undergrad- provides back-up receptionist support. uate program, which includes approximately 140 majors. The undergraduate coordinator acts as liaison between Joy Jones, Building Coordinator (1980): Joy is the build- faculty and their advisees, both majors and over 200 ing coordinator and copyroom specialist for the depart- freshmen and sophomores with undeclared majors. She ment. She coordinates the day-to-day service operations coordinates the application process for the summer Re- provided to faculty, visitors, sta and students. She or- search Experience for Undergraduates (REU) program ders supplies, processes purchase orders, and performs and maintains various department web pages. She coor- records and facilities maintenance, information gather- dinates the annual capital equipment inventory. She is ing and data input. Joy assists the accounts coordina- also the department receptionist, conducts the annual tor with travel reimbursements, cash deposits, records faculty recruitment e ort and provides administrative management and accounts payable. She oversees the support both for the undergraduate program and the mailroom operations, maintains repair and renovation administrative manager. records and secures the building at night. Joy is the person you would call to report any building issues (e.g., Donna Smith, Graduate Field Coordinator (1997): repairs, heating and cooling). In addition, she coordi- Donna is responsible for the administration of the de- nates the refreshments for the weekly seminar series. partment’s graduate program, beginning with the admis- sions process and continuing through graduation. She Michelle Klinger, Web and Database Administrator provides primary support to the director of graduate (1993): Mikki assists the director of undergraduate studies, maintains matriculated student records, pro- studies and the director of teaching assistant programs cesses appointments and generally oversees the admin- with various parts of our teaching e ort. She works di- istrative functions of the graduate program, consisting rectly with the teaching assistant coordinator to gen- of approximately 63 graduate students. She works with erate the department course schedules. Mikki oversees the administrative manager and the director of teach- room assignments and changes, course le management, ing assistant programs to monitor the annual teaching
80 Sta Pro les assistant budget. In addition, she coordinates, sched- Robert Terrell, Network Administrator (1997): As net- ules, plans and oversees all department social functions. work administrator, Bob is responsible for the depart- Donna provides backup support to the accounts repre- ment computer servers, including networking, backup, sentative for the department’s time collection and payroll software and hardware installation, operations and secu- e ort, and serves as the department’s telephone coordi- rity. He maintains some of the department’s web pages, nator. provides maintenance for the department computer sys- tems — including UNIX, SUN, Macintosh and PC op- Catherine Stevens, Teaching Program Coordinator (1969): erating systems — and provides computer consulting, Cathy performs a variety of administrative functions in diagnostic and troubleshooting support for department support of our teaching program. She assigns o ce space members. and works with the chair and the director of undergrad- uate studies to compile teaching assignments. She over- Mathematics Support Center sees textbook ordering, issues keys and maintains the department’s access device log for keyholders. Cathy Douglas Alfors, Director (1983): Doug directs and co- plays a key administrative role in overseeing the summer ordinates MSC academic support for mathematics, prin- session course o erings, including budget development, cipally for introductory courses. Such support includes teaching assistant assignments and grader support. In the interviewing, hiring and supervision of student tu- addition, she is the editor of the department newsletter, tors; the day-to-day running of the MSC o ce; prepa- Math Matters. ration and distribution of written support capsules; and planning and conducting various workshops on topics of Colette Walls, Administrative Manager (1996): Colette common interest (e.g., graphing, in nite series, integra- directs the nancial, personnel, facilities, communica- tion, etc.). He also oversees the use of the computers in tions and funds procurement operations. Her responsi- the MSC. bilities include planning, managing and evaluating the administrative operations. She assists the chair (and Richard Furnas, Teaching Associate (1981): Richard others) in administering selected academic activities in- has been a mainstay of the Mathematics Support Cen- cluding the course count, budget process, leave replace- ter since its inception in the early 1980s. He serves as a ment funding and TA budget. She maintains, monitors tutor, review session leader and general Macintosh guru. and reconciles departmental appropriated, gift and en- Graduate students from other departments often bene t dowment accounts, and acts as liaison with central col- from his counsel on the use of a variety of mathematical lege and university o ces. She oversees and participates techniques in their eld of research. Dick also assisted in the publication of newsletters, the annual report and this year in the instruction of MATH 105 (Finite Mathe- various external surveys, and generates a variety of de- matics for the Life and Social Sciences) and MATH 171 partment, college and university reports. Colette super- (Statistical Theory and Application in the Real World). vises the administrative support sta . She is responsi- ble for maintaining the department’s web-based Survival Mathematics Instructional Computer Lab Manual for Faculty and Teaching Assistants. Allen Back, Director (1993): Allen is responsible for the primary computer instruction laboratory for the Computer Support teaching of mathematics. The lab is a teaching arm Douglas Alfors, Computer Consultant and Advisor (1998): of the Mathematics Department, and the director ad- Doug provides organizational and administrative com- dresses pedagogic issues in appropriate instructional uses puter support for the Department of Mathematics. He of computers, acting as a resource person in all related has primary responsibility for the administrative com- areas. He is responsible for the installation and upkeep puter server, including backup, software and hardware of hardware and software, as well as addressing all per- installation, operations, inventory and security. He sonnel issues of the lab including selection, training and provides computer consulting, including diagnostic and supervision. Allen also contributes to the development of troubleshooting support for department members. Doug sample materials, assignments, and help documentation assists the network administrator in maintaining the de- and software of interest to faculty and sta . He gives partment’s computer network. demonstrations, helps with software use, serves as an advisor on technical issues and assists in relevant grant proposals.
Sta Pro les 81 Mathematics Library Steven Rockey, Mathematics Librarian (1972): Steve is in charge of the library and makes all policy, manage- ment and budget decisions. He is the contact for ques- tions about book, journal or other format purchases for the library. Drawing on many years of experience in the library, he can often nd an answer or solution for most any question or problem.
Natalie Sheridan, Access Services Supervisor (2001): Natalie oversees the operation of the Math Library’s cir- culation and reserve services. She is also responsible for the hiring, training and supervision of student employ- ees. Natalie can help you with reference questions and is in charge of the library when Steve is not available.
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