MATH MATTERS Department of • Cornell University • Ithaca NY Winter 1998

LETTER FROM THE CHAIR, ROBERT CONNELLY

This has been an exciting year in our Greg Buzzard comes to us from join into a circle by holding ropes and department. A large number of new Indiana University after receiving a trained them to perform elementary people, with very impressive accom- Ph.D. at the University of Michigan. moves in response to audience instruc- plishments, have come to join us; we Greg’s work has centered on the tion. It was an amusing and vivid have had some exciting talks from dynamics of maps in several complex illustration of invariants of knots and visitors; and we are all anticipating our variables. Adam Epstein comes to us how certain procedures can unknot a move in May 1999 to our new home in from SUNY Stony Brook and Cal particular sort of knot. Malott Hall. My term as Chair is Tech. He received his degree under the ending in June 1999, and Professor supervision of at We are anticipating our move to Malott John Smillie has been nominated to be CUNY Graduate Center. He works in Hall with excitement. We are hoping the next Chair. I feel that John is an the field of one-dimensional to commission artwork to be created excellent choice, and I look forward to holomorphic dynamics. Vesselin especially for the Math Department the department prospering during his Gasharov comes to us from MIT, and Offices in Malott Hall. Professor Bob term as Chair. he got his degree at Brandeis under Ira Strichartz is heading a committee to Gessel. His field is symmetric func- look into the possibilities. We feel that Professor Laurent Saloff-Coste joined tions, an area that is at the interface of art and mathematics go together us this semester after a year’s leave. combinatorics and representation naturally. He came to Ithaca from Toulouse, theory. In addition to his solution to France, where he held a senior position the conjecture of Eisenbud mentioned In the past several years our team for at CNRS, the research organization at above, he also solved the conjecture of the Putnam Mathematics competition the Université Paul Sabatier. Laurent Richard Stanley that the chromatic for undergraduates has scored quite is an analyst with an interest in prob- symmetric function corresponds to a well. Assistant Professor Ravi ability and geometric group theory. character. You may find more detailed Ramakrishna has suggested that we Assistant Professor Irena Peeva comes biographical information on page 8 of use the interest on the money won by to us from MIT, where she held a this newsletter. past teams to enable Cornell to provide C.L.E. Moore Instructorship. As an prizes for our own Freshman Math undergraduate, she and Vesselin On October 22, 1998, we sponsored competition. (This is in the spirit of Gasharov solved Eisenbud’s conjecture our first Keival Lecture for under- the Hoover Calculus competition that involving the “periodicity of resolu- graduates. The lecture was given by used to be held some years ago.) We tions with bounded Betti numbers.” Professor from SUNY have decided to go ahead with this She wrote her thesis under David Stony Brook. Professor Milnor, a idea, and Ravi will direct the first Eisenbud at Brandeis University. former Fields medalist, recipient of the exam to be held this spring. Assistant Professor Ravi Ramakrishna Steele Prize, National Medal of comes to us from Yale University, Science and the Wolf Prize, spoke to a Lastly, we wish to recognize and to where he was a J. W. Gibbs Assistant packed house in the Hollis E. Cornell show our appreciation to Carly Professor. Ravi wrote his thesis under auditorium about pasting Julia sets Klivans, who has been an energetic and at Princeton. Ravi was together. We also had several interest- resourceful president of the under- also one of our “star” undergraduate ing and stimulating talks sponsored by graduate Math Club. She is graduat- Math majors some years earlier. the Oliver Club. Professor John ing at the end of the fall semester and Ravi’s field is algebraic number theory Conway of Princeton University used has received the Alice T. Schafer and Galois theory. audience participation to make his Mathematics Prize to be awarded at presentation, entitled “Tangles, the American Mathematical Society The department has three new H. C. Bangles and Knots,” one of the most meeting in San Antonio, Texas in Wang Assistant Professors this year. exciting. He had four January 1999. Congratulations Carly!

1 ALICE T. SHAFER PRIZE AWARDED TO SENIOR By Nora Balfour

The Association for Women in Center for Discrete Mathematics the Budapest Semester in Math- Mathematics (AWM) awarded the and Theoretical Computer Science. ematics program for the spring ninth annual Alice T. Shafer Prize After graduating in January, she semester. She then intends to to Caroline (Carly) Klivans, a plans to travel to Hungary to attend pursue a Ph.D. in Mathematics. senior graduating in January. The $1,000 prize will be presented at MALOTT HALL MOVE UPDATE the Joint Mathematics Meetings in By John Smillie San Antonio, Texas in January 1999. The AWM is a non-profit In the last issue of Math Matters, nice department lounge. Since my organization founded in 1971 we announced that the Mathematics last report, the budget for the whose mission is to encourage Department will be moving from renovation of Malott has been women in the mathematical sci- White Hall, where we have been in approved, the Johnson School has ences. Currently, the AWM has residence for 130 years, to Malott moved out and renovation work over 4,000 members from around Hall, the former location of the has begun. Two new massive air- the world. In 1990, the AWM Johnson Graduate School of Man- handling units are being installed, Executive Committee established agement. The new building does which replace and upgrade units not have the history attached to it that were near the end of their the Alice T. Shafer Prize, named for that White Hall does but it will give useful lifetimes. Walls are being it’s founding member and former the department some much needed moved in order to create new office president. It is awarded annually to additional space. This will include and classroom space. We will have an undergraduate woman for more space for our extensive new paint and new flooring excellence in mathematics. Candi- collection of mathematics books throughout the building. In the dates are evaluated based on the and more space for library users. course of renovation it was discov- quality of performance in advanced We will have more office space for ered that the existing computer math courses and special programs, faculty, visitors and graduate network was not in good shape. a demonstration of real interest in students, an efficient suite of Fortunately, we be installing a mathematics, the ability for administrative offices and a very state-of-the-art system. independent work in math, and performance in mathematical DEPARTMENT SPONSORS FRESHMAN MATH PRIZE competitions at the local or national level. By Ravi Ramakrishna

Carly’s interests lie in discrete Fifteen years ago, the Math Depart- 1994 and 1995 respectively, earning ment sponsored the Hoover exam, a total of $11,000 for the depart- geometry and algebraic combinato- a prize exam for freshman. The ment. The high scoring team rics. She has been president of the intent was to foster an interest in members were Jeremy Bem ’97, undergraduate Math Club for two mathematics. Unfortunately the Jon Kleinberg ’93, Robert years, arranging weekly lectures by funds for this exam were depleted, Kleinberg ’97, Mark Krosky ’96, faculty and graduate students to and the prize was discontinued. Demetrio Munoz ’94, and Tong introduce undergraduates to a Zhang ’94. The income generated broad range of math topics. Last The William Lowell Putnam Exam by these funds will provide the summer she participated in the is a mathematics exam given na- prizes for the new Freshman Prize Research Experience for Under- tionally to undergraduates. From a exam. The first Freshman Math- graduates program, run by the NSF. pool of almost 300 competing ematics Prize exam will take place She researched computational colleges, Cornell teams placed 5th, in the spring of 1999. geometry at Rutgers University’s 6th, 2nd and 2nd in 1992, 1993,

2 OLIVER CLUB NEWS By Karen Vogtmann

This has been a banner year for the Princeton University, had Bob geometry of flag . The Mathematics Department collo- Connelly, the chairman of the math full list of distinguished speakers quium, the Oliver Club, with high department, and three others doing from outside Cornell includes quality talks and a large and appre- a square dance with ropes in the Adrian Lewis from the University ciative audience. We began the front of the room to illustrate of Waterloo, Richard Schoen of year with a beautiful lecture on arithmetic invariants of “tangles” to , Paul Sally “Exotic Hyperbolic 3-Manifolds” a packed audience. Another form from the University of Chicago, by Curt McMullen of Harvard of dancing, this time by honeybees, Richard Stanley of MIT, Phil University, who later received the was the subject of a March lecture Hanlon from the University of Fields Medal at the International by Barbara Shipman of the Univer- Michigan, Daryl Cooper of Congress of Mathematics in Berlin. sity of Rochester, who related the U.C.S.B., Benson Farb from the In October, John Conway, of honeybee’s “waggle dance” to the University of Chicago, Maxim Braverman of Ohio State Univer- GRADUATE STUDENT ATTENDS CONFERENCE IN SPAIN sity, Ricardo Perez-Marco from U.C.L.A., and F. Thomas Farrell of By Suzanne Lynch Binghamton University. Suzanne Lynch, a second year Suzanne says of the experience, The Oliver Club meets weekly in graduate student, traveled to “Yes, I learned lovely mathematics, White Hall. Speakers in the Oliver Barcelona, Spain, this past Septem- but I particularly enjoyed the Club are asked to aim their talks at ber to participate in a mini-course friendships I made with the other a general audience of mathemati- on Dynamical Systems. The trip students. We are all in dynamics, cians, including graduate students was made possible by funding from and hope to meet again at confer- and faculty in diverse fields, and in several Cornell sources as well ences and watch each others math- particular to provide history, back- from the CRM in Barcelona. The ematical careers grow. I particu- ground and motivation for the program featured lectures by larly enjoyed learning about the problems they discuss. All mem- world-class mathematicians and different cultures of my new bers of the mathematical commu- contributed talks by the students. friends, and their different math- nity are warmly encouraged to Suzanne gave her first international ematical and educational back- attend. Tea is served before the talk, entitled “The Medusa Algo- grounds.” Suzanne also enjoyed lectures in the Math lounge, and rithm in Polynomial Matings,” to an the sunshine and seafood in the there is often a dinner held after- audience of 35 students and profes- beautiful Mediterranean city, and wards in honor of the speaker. sors, representing seven countries. she hopes to return someday. The Mathematics Department is CONTRIBUTE TO MATH MATTERS! very grateful to those who have contributed to the department fund We are always looking for interesting articles for future issues. If you have any for the Oliver Club. This year, all information relevant to the mathematics community, we want to hear from you. contributors will receive a copy of one of the posters advertising a Nora Balfour Deptartment of Mathematics recent Oliver Club. The posters 129 White Hall contain mathematical graphics and Cornell University an abstract of the talk and are Ithaca, NY 14853-7901 published weekly on the Web at [email protected] http://math.cornell.edu/~oliver .

3 UNDERGRADUATES GAIN RESEARCH EXPERIENCE AT CORNELL by Robert Strichartz FIGURE 2 The Cornell Mathematics Depart- ment has a grant from the National Science Foundation to run a sum- mer program for undergraduates to participate in research projects. We are one of about 20 such Research Experiences for Undergraduates n=8 784.031 n=13 2573.49 (REU) programs. The summer of 1998 marks the fifth year of partici- pation. Our grant lasts until 2001. In addition, we received some funding from Cornell to enhance the program. We had 10 students who participated from schools n=21 5854.33 n=34 19217.3 across the country, from Harvard to the University of Northern Iowa to Sze-Man Ngai and Alexander really useful, it is necessary to be Berkeley. Karl Papadontonakis Teplyaer, a fresh Ph.D. from able to do analysis of functions represented Cornell. The research Cornell, assisted them. defined on fractals – to find the areas were Dynamical Systems, analog of the processes of calculus, supervised by Professor John Analysis on Fractals and to solve “fractal differential Hubbard of Cornell, and Analysis By now, everyone has seen pictures equations.” Kigami has been one of on Fractals supervised by Profes- of fractals and has heard that the leaders in creating such a sors Robert Strichartz from Cornell fractals are used to model many theory, and the REU students were and John Kigami from Kyoto objects in the real world, such as able to contribute to the develop- University. Graduate student ferns, snowflakes and clouds. But ment of the subject. One project Christian Henriksen and postdocs in order to make these models involved setting up the basis for a spline theory to do explicit numeri- cal analysis. Another was devoted to the properties of the Green’s function, which allows one to invert the Laplacian on fractals. Several students were involved in an ambi- tious project to try to extend the class of fractals that can be dealt with. One new fractal now included in the theory is the fractal diamond shown in Figure 1.

Not all fractal analysis involves fractal sets. One project dealt with an analog Fourier series for the ordinary unit interval, but based on FIGURE 1 a fractal measure. The analog of the usual sines and cosines are oscillating functions that have one

4 FIGURE 3

derivative (but not two,) but do not For the second project, Cornell’s by Strichartz, Complex Dynamics appear to follow a predictable Karl Papadantonakis wrote pro- directed by Adam Epstein, and a pattern. However, a remarkable grams to investigate the parameter project on the Kepler Conjecture fact uncovered in this research is space for Henon mappings; this has directed by Karoly Bezdek of the that if we index the functions fn in a been a challenge in dynamical Eötvös University, Hungary. The natural way (fn has exactly n zeroes) systems for many years. He tried a Kepler Conjecture concerns the then the ones associated with 3-pronged attack with all three optimal packing of spheres of n=1,2,3,5,8,13… (the Fibonnaci prongs inspired by a result of radius one in 3-space. Recently, sequence) do exhibit a regular Bedford and Smillie. One of these Thomas Hales of the University of pattern. You can see this in approaches requires solving poly- Michigan has announced an affir- Figure 2. nomials of degree 2k for values like mative solution. The project will be k=12, and finding all the roots. The devoted to checking out the proof, Dynamical Systems: third project resulted in a program to see if it is correct, to see if it can One project dealt with matings of to find homoclinic bifurcations of be improved or simplified, and to polynomials, resulting in a program maps f : R2 → R2 . This again is a see if the ideas of the proof can be called Medusa, which finds rational long-standing challenge, which was used to tackle other questions. functions with special combinatorial addressed by using carefully properties. The underlying math- adapted splined to approximate A new feature of the REU program ematical result is a theorem of stable and unstable manifolds. for 1999 will be the inclusion of Thurston’s, but implementing this high school teachers, who will be theorem was a major challenge. An The REU program will continue in working alongside the undergradu- example of a mating is shown in the summer of 1999. There will be ates on the research projects. Figure 3. more Analysis on Fractals directed

5 RECENTLY PUBLISHED BOOKS

Yulij Ilyashenko and Weiu Li, beginning. A discussion of the their ideas, publishing articles in Nonlocal Bifurcations, AMS, Provi- fractal dimension of attractors journals and attending invited talks. dence, RI, 1998. including some recent achievments Tom’s ideas about writing assign- is presented as a preliminary mate- ments in the teaching of math were Nonlocal bifurcations describe rial. The book is addressed to included in a book about writing sudden changes in global topologi- students, graduate students and across the disciplines. Mary Ann cal properties of parameter depend- scholars in pure and applied math- Malinchak Rishel, an Associate ing dynamical systems that occur ematics, computer sciences and Professor of writing at Ithaca when the parameter passes through engineering. College, became involved, and so called critical value. The book together with Tom and John began studies the bifurcations that occur teaching workshops. Tom and John John Meier and Thomas Rishel, on the boundary of the set of presented their ideas at the national Writing in the Teaching and Learning Morse-Smale systems. For these Math Association meeting in bifurcations the precritical values of of Mathematics, MAA Math Notes Cincinnati, and began this text over the parameter correspond to rather #48, 1998. coffee afterwards. The book was simple dynamical systems. The written in two years, but it took an solutions of these systems tend Tom Rishel began teaching courses additional two years for the publi- either to equilibrium points or to that required writing assignments cation process to work itself out. periodic orbits. The number of over a decade ago. He was inter- There are a handful of other profes- equilibrium points and periodic ested in involving his students in the sors at Cornell who also integrate orbits is finite. The postcritical narrative history of mathematics, writing assignments into their values correspond, in general, to and emphasizing active learning. teaching of math, with generally much more complicated systems. He experimented with assignments, positive reactions from the stu- The latter may have countable and honed the phrasing and content dents. Students are forced to think number of periodic orbits, hyper- until he was successfully engaging about math differently than they bolic and partially hyperbolic the students in what was for many a traditionally have, and it puts the invariant sets or even strange new way of learning math. impetus on the student to learn. attractors. The limit behavior of solutons to such systems is chaotic. John Meier, while a graduate The response to the book has been Different scenarios of this kind are student at Cornell, experimented strong. Meier and Rishel will be described in the book. Most part of with writing assignments in his giving another workshop at the them is discovered by Shilnikov and calculus classes. He came to Tom MAA winter meetings in San his students; Newhouse, Palis, for advice, and the two began Antonio. It is selling well, and Takens; some results are new. The comparing notes and ideas. As they information requests are coming in study is proceeded from the unifom developed their writing assign- from around the country. point of view. It is based on the ments, they also found a market for theory of normal forms for local families of vector fields and diffeomorphisms, as it was accom- VISIT THE MATH DEPARTMENT WEB SITE: plished by Ilyashenko and http://math.cornell.edu/ Yakovenko in early 90s. The other Our home page offers links to the Annual Report, faculty and ingredient is the theory of hyper- graduate student home pages, information on the graduate and bolic dynamical systems. Necessary undergraduate programs, seminars and courses. facts from both theories are New links are added all the time. presented in the book from the very

6 UNDERGRADUATE FACULTY ENHANCEMENT WORKSHOPS “TEACHING UNDERGRADUATE GEOMETRY” By David Henderson

The fourth in a series of Under- curricular materials into their own techniques and materials to faculty graduate Faculty Enhancement courses, learn about national in their home institution, share their (UFE) workshops at Cornell was guidelines and standards put forth own classroom experiences and held in the summer of 1998. These by Mathematical Sciences Educa- materials with the workshop staff weeklong workshops are supported tion Board, National Council of and other participants via e-mail, by grants from the National Science Teachers of Mathematics, and the and use the workshop staff as a Foundation. Each year we have Mathematical Association of resource to assist in the implemen- had many more applicants than we America, participate after the tation and evaluation of the new can accept, and preference is given workshop in several of the follow- materials and techniques. to those who will be teaching ing follow-up activities: use materi- geometry to future schoolteachers. als and techniques from the work- The fifth UFE workshop is sched- This year’s participants included shop in their own teaching, give a uled for June, 1999. thirty mathematics professors from presentation/workshop on the new around the U.S. and one from England. Cornell Professor David Henderson led the workshop with DEPARTMENT CREATES MALOTT ART FUND help from Kelly Gaddis, a recent Ph.D. from Cornell and currently an By Bob Strichartz Assistant Professor at Buffalo State, Jane-Jane Lo, a Visiting With the the Math Department’s ematics related directly to Cornell. Scholar in our department and move to Malott on the horizon, we A sculpture realizing one of the currently teaching at Ithaca Col- are making plans to commemorate Douady-Hubbard matings (the lege, and Avery Solomon, Senior our updated presence on campus. subject of Milnor’s Kieval lecture Lecturer at Cornell. Our goal is to acquire artworks for this fall) is a possibility. Other Malott that are both decorative and possible artists are Kenneth Follow-up surveys indicate that the have a mathematical theme. We Snelson, who does tensegrity workshops succeed in providing would like to commission artwork sculptures, and George Roads, who opportunities for university math- that embodies our view of math- creates kinetic interactive ball ematics faculty to: experience new ematics as a profoundly human sculptures. teaching strategies and techniques, activity with deep connections to experience and/or see examples of other human activities and nature. A committee to discuss artwork for non-test based assessment schemes, One possibility we are considering Malott has been formed, chaired by learn about and observe techniques is a sculpture by Helaman Bob Strichartz and including Bob that have been successful in encour- Ferguson, who is both a mathemati- Connelly, John Hubbard, Peter aging women and underrepresented cian and a sculptor. He has a Kahn, Anil Nerode, Beverly West minorities to excel in mathematics, catalog of works based on geomet- and Keith Dennis. Contributions learn new subject matter and ric and topological themes. Many for the Malott Art Fund would be experience new instructional mate- of his works are exhibited in math- very welcome, and there are dona- rials, have the opportunity to ematics departments and centers tion instructions on the last page of interact and share with colleagues around the world, including MSRI. the newsletter. and experts incorporate both He would consider doing a com- teaching techniques and new missioned work based on math-

7 GRADUATE STUDENT OUTREACH PROGRAM by David Brown, [email protected]

Each spring, the Public Service was not to present results, but Gaskets and testing whether they Center at Cornell coordinates the rather guide the students to a result. could work in groups to build one Graduate Student Outreach Pro- For example, after having students giant Sierpinski Gasket from their gram, which seeks to match gradu- verify that they could tile a checker- little ones, thus reinforcing the idea ate students with classes in local board with 32 dominoes, I had of repeated patterns. school districts. The goal of the them conjecture and test to see if program is to share the knowledge they could tile the checkerboard, While the program requires a great of graduate students with elemen- minus two opposite corners, with deal of time and thought, I have tary and secondary students, enrich- 31 dominoes. The answer is no, found the Graduate Student Out- ing both the children’s education but I was a bit surprised that a few reach Program to be a rewarding and the graduate student’s teaching students had the correct reason why experience and a pleasant diversion skills. It also establishes a wonder- this is impossible. This first course from university life. Students have ful collaboration with local teachers convinced me that the program been responsive and I have enjoyed and provides a glimpse into the life benefits all the participants and left exchanging knowledge with the of teaching elementary and second- me looking forward for the next teachers. I recommend the ary students. The graduate student time. program to anyone who seeks an prepares his or her own eight alternative to teaching undergradu- session mini-course on a topic of This past spring, I changed my ate courses. his or her choice. The Public program to deal with two topics in Service Center then solicits interest much more detail, met twice a from local teachers, and once a week for four weeks and titled it, CORNELL PH.D. WINS mini-course is accepted, the gradu- “Geometry in Nature and Sci- ate student and the teacher schedule ence—An Introduction to PRIZE eight meetings with the class. Fractals.” I chose to work with By Cliff Earle two schools, a sixth grade math Spring 1999 will mark my third class in the Newfield School Dis- On September 27, 1998 it was year of participation in the Pro- trict and another seventh grade announced that Subhashis Nag had gram, and it has been one of the math class of Harry Myers. The won the 1998 Shanti Swarup most rewarding experiences of my first part of the course dealt with Bhatnager Prize in Mathematics. graduate education. The first year I investigating geometry in nature, These prizes are the Indian participated I taught a program such as growth patterns of plants government’s highest awards in entitled, “A Journey through and patterns in shells of certain science and mathematics. Nag, who Mathematics,” consisting of eight animals. The messiest and most received his Ph.D. from Cornell in distinct mathematical topics. I popular portion of these first four 1980, is also a Fellow of the Indian taught weekly in Harry Myers’s sessions was investigating soap Academy of Science. Since his time seventh grade math class in the bubbles and soap films, looking at as a graduate student in mathemat- Candor School district. Among the such ideas as how to create minimal ics at Cornell, Nag has twice topics were figurative numbers, networks. The second part of the returned to the department as a topology, cryptology, polyominoes, course focused on fractals and how visiting faculty member. He was a and even proofs of the Pythagorean to create them, emphasizing Visiting Assistant Professor in theorem. The challenge of such a repeated patterns on ever diminish- 1987-88 and a Visiting Professor in program is balancing lecture with ing scales. The culmination of the the Fall 1997 semester. We con- hands-on experience for the stu- course involved students making gratulate him on this new award. dents. The first lesson I learned many small colorful Sierpinski

8 COMINGS AND GOINGS...

NEW FACULTY dynamics in this broader picture. research interests are in analytic By Nora Balfour His efforts to understand the overall number theory, more specifically context have kindled interests in the study of various zeta and L- Greg Buzzard, a new H.C. Wang mathematical logic and algebraic functions to derive number-theo- Professor, received his Ph.D. from number theory. retic information. This often the University of Michigan in 1995, involves techniques drawn from and held a three-year appointment Vesselin Gasharov obtained his complex and p-adic analysis and in the Department of Mathematics undergraduate degree from Sofia from the infinite-dimensional at Indiana University. During his University, specializing in algebra. representation theory of algebraic time at Indiana, he took a couple of In his undergraduate thesis, among groups. Anthony was married on semesters off to do research at other results, he and Irena Peeva July 7th of this year to Dr. Belinda MSRI. His research centered on resolved Eisenbud’s Conjecture on Burner, who teaches English at the dynamics of maps in several the periodicity of resolutions with Ithaca College. complex variables. He has worked bounded Betti numbers. In 1990, mostly on questions of stability: i.e. Vesselin became a graduate student Irena Peeva obtained her first when does a small change in a under Ira Gessel at Brandeis Uni- research results as an undergradu- system lead to a correspondingly versity. His thesis was on symmetric ate student, when she and V. small change in the behavior of that functions, an area that is at the Gasharov resolved Eisenbud’s system? In other areas of several interface of combinatorics and Conjecture on the periodicity of complex variables, he has been representation theory. One of the resolutions with bounded Betti interested in the construction of results in the thesis was a proof of a numbers. They published a paper in various maps with prescribed conjecture by Richard Stanley that the journal “Transactions of the properties. He enjoys playing the the chromatic symmetric function American Mathematical Society.” violin and is a member of the corresponds to a character. After This paper won first prize in the Cayuga Chamber Orchestra. He obtaining a Ph.D. in 1994, he held Bulgarian Mathematical Competi- also enjoys hanging out at the Math an Assistant Professor position at tion for Best Undergraduate Re- Table on Friday evenings. the University of Michigan from search Work. She started graduate 1994-97, and a visiting position at study in mathematics at Brandeis Adam Epstein received his Ph.D. MIT during 1997-98. He has University in 1990. In 1994, Irena in 1993 from the CUNY Graduate written 20 research papers, 7 of was awarded a Sloan Dissertation Center under the direction of them with co-authors. He became Fellowship; during the 1994-95 Dennis Sullivan. He has previously an H.C. Wang Assistant Professor academic year she visited the held appointments at SUNY Stony at Cornell in July 1998, with re- University of Michigan. She re- Brook and Caltech. His work is in search interests in combinatorics ceived her Ph.D. in July 1995. Irena the field of one-dimensional and commutative algebra, especially held an Instructor position at MIT holomorphic dynamics, a subject in the beautiful and fruitful inter- from 1995-98, and a Postdoc at that he views as the latest chapter in play of ideas from these two areas. U.C. Berkeley in 1995-96. Irena a tradition encompassing the study became an Assistant Professor at of compact Riemann surfaces and Anthony Kable arrived in the Cornell in July 1998. Her work is in their Teichmüller spaces, as well as department this year as an H.C. the field of Commutative Algebra, the classical value-distribution Wang Professor after a year as a and she has co-organized four theory of entire and meromorphic Visiting Assistant Professor at conferences on the subject. Her functions. He is currently working Oklahoma State University. He interests lie in applying methods to finish a foundational paper that completed his degree at OSU the and ideas from other branches of clarifies the position of the central previous year under the direction of mathematics in order to obtain finiteness theorems of holomorphic Professor James Cogdell. His results in Commutative Algebra.

9 COMINGS AND GOINGS...

Irena has co-authored 20 research STAFF CHANGES papers, obtaining algebraic results FACULTY ON LEAVE 98/99 by innovative applications of By Colette Walls foremost results in the fields of Acad. Year: Persi Diaconis combinatorics, integer program- Mark Gross Bob Terrell was hired as a part- ming, subspace arrangements, Moss Sweedler time computer consultant/advisor in computer algebra, algebraic geom- December 1997. He fills half of the etry, and algebraic topology. Fall: Allen Hatcher position vacated by Rachel Engler at the end of last year. His primary Ravi Ramakrishna received his Spring: Ken Brown responsibility is to maintain the math computer network. Bob is Ph.D. in 1992 from Princeton Rick Durrett also an adjunct professor in the University. He held positions at the John Hubbard department. The other half of our University of Chicago and Yale computer support budget line was before coming to Cornell as an filled in late May ‘98 by Doug Assistant Professor. His area of VISITING PROGRAM 98/99 Alfors, who also works in the interest is algebraic number theory. department as the director of the In particular, he is interested in Acad. Year: Samer Habre Mathematics Support Center. Galois Theory, the branch of James Hall Doug provides primary computer mathematics that has to do with the Rachel Hastings support to the departmental admin- symmetries of solutions to equa- Kevin MacEwen istrative staff. Both Bob and Doug tions, and how this subject relates provide support to faculty and Fall: Karl David to classical questions such as graduate students. solutions to Diophantine equations. Ravi’s wife Janet teaches math- In April 1998, our long term ac- ematics at Ithaca High School. TEACHING VISITORS 98/99 counts coordinator, Terri Denman, left to take the administrative Laurent Saloff-Coste grew up in Acad. Year: Sergei Artemov manager position in the Department France, and received his Ph.D. in Thomas Deck of Rural Sociology at Cornell. 1983 with N. Varopoulos in Paris at Hongyu He Terri was first hired in the Math Paris VI. He held a junior position Daina Taimina Department in September 1985. In at CNRS from 1985 to 1992, at Vladimir Veselov June 1989, she was promoted into Paris VI. During these years he the accountant position to replace visited MIT several times, and met Fall: Karoly Bezdek Tony Augustine. Terri will be his wife, Cathy, while there in 1989. Boris Okun missed for her dry wit and exem- In 1990 they returned to Paris for plary skills. We thank her for her two years. They then moved to many years of good service to the VISITING SCHOLARS 98/99 Toulouse where he held a more department, and we wish her the senior position at Université Paul best of luck in her career at Cornell. Sabatier. He began at Cornell in Acad. Year: Jane-Jane Lo June of 1998, and finds the Math Gayle Davis accepted the position Fall: Christopher Atkin department both friendly and very of accounts coordinator effective David Finston stimulating. They have a son, April 13, 1998. She has worked at Zhonggen Su Sam, born in 1996 in France, and a Cornell for over 20 years. Starting daughter Claire, born in Ithaca last in 1991, she worked for the College October. of Industrial and Labor Relations in

10 COMINGS AND GOINGS...

budget, fiscal management, and in graduate studies at Wells Col- agreed to become the Undergradu- general operations. Prior to work- lege. This fall, she’s completing ate Coordinator effective 10/1/98. ing for ILR, she held accounting her student teaching at the Alterna- Nora has spent the past year and a positions at the Biotechnology tive Community School in Ithaca. half as the receptionist and adminis- Program, the Department of Bio- Upon completing her teaching trative assistant for the Dean’s chemistry, and Statutory Finance certification, Cheri plans to teach Office in the College of Arts and and Business Services. Gayle has American History at the junior or Sciences. Nora’s thoughtful comfortably and confidently settled senior high school level. Cheri analysis of business operations has in, and we consider ourselves was a personable and gracious already proved helpful. In the short fortunate to have her with us. receptionist, and we were sorry to time she’s been here, she has see her go. endeared herself to all. We look Cheri Farnsworth resigned as forward to getting to know her Undergraduate Coordinator this Although we all miss Cheri, I’m better. past September when she enrolled happy to report that Nora Balfour

YES, I WOULD LIKE TO HELP SUPPORT THE MATHEMATICS DEPARTMENT ENDOWMENTS WITH MY DONATION OF $______FOR:

The Malott Art Fund. Established to enable the The Logic Endowment. Recently established by a Math Department to purchase commissioned artwork donation from a former Cornell undergraduate. Seeks for the new offices in Malott Hall. to actively support promising logic students in the areas of institutional memberships and travel expenses, for The Mathematics Faculty Book Fund. Provides Association for Symbolic Logic meetings and events, the Cornell Community with immediate access to one and other activities in the field of logic. of the world’s finest assortments of mathematics books and publications by enriching the collection of the Math- Make checks payable to Cornell University. ematics Library. Please send to: The Mathematics Colloquium Endowment Fund. Instituted to invite distinguished scientists to speak at The Mathematics Department Endowments Cornell. Major contributions come from faculty who 135 White Hall teach extra courses and donate their earnings to the fund. Cornell University Ithaca, NY 14853-7901. The Eleanor Norton York Award in Astronomy and Mathematics. Established in honor of Eleanor Name: ______Norton York, a valued Astronomy Department employee who worked closely with graduate students. Recog- Address:______nizes outstanding graduate students in Astronomy and ______Mathematics with an annual prize. ______ The Israel Berstein Memorial Fund. Honors the memory of a former Mathematics Department profes- sor with an initial donation from his sister, Gita Fonarov. Please send me a receipt for tax purposes. Funds annual awards for deserving graduate students in Please send me a copy of the 1998-99 Annual the fields of topology and/or geometry. Report when it becomes available.

11 FROM THE EDITOR...

Math Matters is published through a joint effort by members of the Mathematics Department. Thanks to:

David Brown Ravi Ramakrishna Robert Connelly Steve Rockey Cliff Earle John Smillie David Henderson Robert Strichartz Yulij Ilyashenko Karen Vogtmann Suzanne Lynch Colette Walls

and special thanks to Mikki Klinger.

Nora L. Balfour Editor

Department of Mathematics 129 White Hall Cornell University Ithaca, NY 14853-7901