MATH MATTERS Department of Mathematics • Cornell University • Ithaca NY Winter 1999 Letter From the Chair, John Smillie Bob Connelly stepped down as The Mathematics Department and research at the Pacific Northwest Chair of the Mathematics Depart- Statistics Department jointly held a National Lab. ment June 30th, after having served conference and dinner to honor as Chair for three and one-half Roger Farrell on the occasion of his I would like to mention some years. We owe him a debt of thanks retirement after 40 years of associa- department members who provided for his service to the department. tion with Cornell. The dinner was service to the Department above Bob ensured channels of communi- emceed by Gene Hwang and was and beyond the call of duty. Keith cation were open within the depart- marked by heartfelt tributes to Dennis, John Guckenheimer, Rick ment and he maintained and further Roger. There was also a demon- Durrett, Lou Billera, Mike Stillman developed our very good relations stration of excellent Scottish and and Bob Connelly were awarded a with the administration. During his English country dancing and some grant from the National Science tenure as Chair, he was integrally very lively swing dancing. Foundation to buy new state-of-art involved in the extension of small computing equipment for the lectures to all the calculus courses Moss Sweedler has let us know that Department. Also, a large group of taken by the engineering freshmen. he will be continuing in his new faculty members (18 at last count) He also oversaw the move of the position with the National Security took time out from their usual Mathematics Department to larger Agency and will not be returning to activities to help prepare the quarters. Bob is currently on Cornell. We are all sorry to see him VIGRE grant application. This is sabbatical at the University of leave after 32 years at Cornell. described more fully on page 3 of Washington taking a well-deserved this newsletter. The latest news is rest from administrative matters. A number of department members that we had a site visit from an NSF received honors and awards. Harry panel. They interviewed faculty, The Department has some new Kesten was elected as a fellow of graduate and undergraduate stu- faces this year. We are very pleased the American Academy of Arts and dents, and let us know that they are to have a new statistician, Professor Sciences. The University also very impressed with the Mathemat- Michael Nussbaum from the awarded him a Goldwin Smith ics Department. Weierstrass Institute in Berlin. Chair. Cliff Earle received an Michael has made major contribu- honorary professorship from the Lastly the whole Department owes tions to asymptotic decision theory. University of Warwick. One of our a debt of gratitude to the staff who We hired Yuri Berest as a new graduating seniors, Daniel Gardner, knocked themselves out in helping tenure-track assistant professor; he was a banner bearer for the Class of us to move to our new quarters in comes to us from the University of 1999. This honor is bestowed upon Malott. The physical move of the California at Berkeley. Yuri has the graduate with the highest grade department this past summer was a done some fascinating work on point average in the college. An- big effort and an enormous change Huygens principle. Two new H. C. other senior, Vladimir Livshitz was for all the members of the depart- Wang assistant professors join us chosen as a Merrill Presidential ment. I’m happy to report that this year. Peter Topping, working Scholar. Junior YiMin Wu was we’re settling in nicely, and look in partial differential equations and awarded the Energy Research forward to having many of you visit differential geometry and Vlada Fellowship, and will spend next in the future. Limic working in probability. semester in Washington doing

1 MALOTT HALL RELOCATION

This past year the Cornell Depart- ment of Mathematics moved from White Hall, which mathematics has called home since the 1880s, to Malott Hall. Many people were involved with the planning and preparation over the years. Professor’s Keith Dennis, Moss Sweedler and Cliff Earle worked at the job of faculty liaison. This role was eventually taken over by Professor John Smillie, who shepherded us carefully and cre- atively through the past three years of planning and renovation of the Malott Hall facilities.

We are grateful to everyone in- volved with the project. Jane Malott Hall, from Tower Road Pedersen, the Associate Dean for Administration in the College of tect in charge of the renovation creating a beautiful interior design Arts and Sciences, identified fund- project. John Barradas of Down- plan. We are thankful also to Jim ing and coordinated the many ing, Barradas and Magre Architects Holley and the construction crew institutional elements. Gary masterminded the renovations. of Welliver and McGuire, David Wilhelm was the university archi- Anne Adesso worked long hours Newman, construction supervisor for Cornell, and Henry Crans, Director of Facilities for the Arts College, for their contributions to the success of our move. Math- ematics Librarian, Steve Rockey, helped create a plan for the en- larged and improved library.

In addition, we owe a special thanks to the departmental support staff, Doug Alfors, Nora Balfour, Gayle Davis, Arletta Havlik, Joy Jones, Michelle Klinger, Donna Smith, Cathy Stevens and Bob Terrell, led by Colette Walls, all of whom worked tirelessly to ensure that the move went as smoothly as possible. They had an integral part White Hall on moving day, June 1, 1999. Moving vans on the in moving 150 department Arts quad load up 130 years of Math Department. (Continued on page 9)

2 ROGER FARRELL RETIRES REINVIGORATING By Gene Hwang THE MATH On September 25, 1999, the De- school students, also gave an DEPARTMENT partments of Mathematics and outstanding demonstration. Many Statistics held the first conference of our usually shy mathematicians By Rick Durrett since the move into Malott Hall this were inspired enough to join in the The National Science Foundation’s summer. The one-day conference jitterbugging. The conference and VIGRE Program provides grants to honored Roger Farrell’s lifelong evening’s entertainment were made math departments to broaden the involvement in Mathematics. It successful and thoroughly enjoyable training of undergraduates, gradu- featured five talks delivered by by Donna Smith’s and LeMoyne ate students, and postdoctoral distinguished speakers including Farrell’s devoted efforts. fellows and to Vertically InteGrate Jim Berger (Duke University), Don their Research and Education. At Burkholder (University of Illinois), GOLDWIN SMITH the end of the last academic year, Larry Brown (University of Penn- PROFESSORSHIP John Smillie organized a depart- sylvania), Iain Johnstone (Stanford mental effort to prepare a proposal. We’re happy to announce that at University), and Jim Hobert (Uni- John and his co-principal investiga- the end of the Spring 1999 semes- versity of Florida). The majority of tors Lou Billera, Jose Escobar, and ter, Harry Kesten was elected the speakers began by commenting John Guckenheimer led the group Goldwin Smith Professor of Math- on the impact Roger Farrell has had effort to formulate our plans and ematics. The first Goldwin Smith on them both personally and profes- write the 30 pages of prose needed professorships were established in sionally. to describe them. However, they 1912 in the fields of Latin, English were aided considerably in this literature, American history, politi- The evening celebrated Roger process by Bob Strichartz, Steve cal science and English. Since that Farrell’s life outside academia. The Chase, Dan Barbasch, Tom Rishel, time they have been awarded in a festivities began with a parade led Keith Dennis, David Henderson and number of other fields, including by a Scottish bagpiper and a troupe others who provided data about mathematics. In 1989 the profes- of English and Scottish dancers, undergraduate and graduate re- sorships were expanded from 11 to including Roger dressed in full search and teaching activities, and 15. These endowed professorships Scottish regalia with kilt and helped to formulate our proposed are awarded to distinguished sporran. Roger is an avid dancer, activities in this area and outreach Cornell faculty in the College of and attendees were treated to to K-12 education. several demonstrations of Scottish Arts and Sciences. and English dances, with Roger and As proposed, our VIGRE grant Professor Kesten works in prob- his wife LeMoyne participating. (pronounced ‘vigor’) is a five year ability theory. One of his main Those unfamiliar with Roger’s multi-million dollar basket of interests is percolation, a probabi- dancing were astounded. The goodies. Specifically, if the grant is listic model that is of interest in reputation Roger acquired during funded, we will have a significant statistical physics because it is the his 40 years of service at Cornell as number of new three-year research simplest model that exhibits a phase a shy mathematician has been postdocs, several dozen years of transition. His study, Hitting broadened by this event. research support for graduate probabilities of single points for a students, as well as significant new process with independent incre- After a buffet dinner, the entertain- support for undergraduate research ments, is considered a work of ment resumed with dance demon- on pure and applied topics during seminal influence. Professor strations by several local dance the summer and in the academic Kesten was also elected a fellow of groups. The swing dancers were year. the hit of the evening. The national the American Academy of Arts and (Continued on page 9) award-winning Lindy Hop dancers, Sciences during the 1998/1999 made up of a group of Ithaca high academic year.

3 MATH CLUB NEWS MERRILL SCHOLAR By YiMin “Z” Wu INSPIRED BY Professor Joan Birman of Columbia Life at Cornell for the past several MATH PROFESSOR University came to Cornell to give years. the Math Club guest lecture on Physics major Mukund Thattai was November 19, 1999. Her talk was Also in Math Club news, in Sep- named a Merrill Presidential entitled “Parametrizing Knots”. tember members A. McCabe (00'), Scholar in May 1999. Merrill Professor Birman is the recipient of J. Barry (02') and Y. Wu (01') Presidential Scholars are graduating a Guggenheim Fellowship, as well attended the third annual Columbia seniors who are honored for leader- as the Chauvenet Prize given by the Practitioners Conference on the ship and scholarship. As a tribute Mathematical Association of Mathematics of Finance at Colum- to the importance of teaching in America. She is also respon bia University in New York City. shaping academic success, Merrill ible for establishing the Ruth The aim of this conference is to Scholars recognize those secondary Lyttle Satter Prize in memory o bring together academics, practitio- school teachers who provided her sister. This $4000 prize is ners and students to discuss ques- inspiration during their high school warded every two years to recog- tions of current interest, and to years. They also cite the Cornell nize an outstanding contribution to suggest open problems. Speakers faculty member who they feel has mathematics research by women. for the conference came from made the most significant contribu- finance/investment firms such as tion to their education. Thattai Birman proved to be an animated Goldman Sachs, J.P. Morgan, named John Hubbard as the faculty and amusing lecturer, filling her Merrill Lynch and Bear Stearns. member who has had the most hour-long talk with concrete results positive influence on his education from her research and challenging at Cornell. open questions at the end. Her talk CIRCUS AT was the most popular guest lecture CORNELL Over the course of a year, Thattai sponsored by the Math Club to By Lars Wahlbin helped Professor Hubbard complete date, drawing a large audience that the paper, The dynamics of the included faculty members, graduate In October 1999, the Finite Ele- forced damped pendulum, which students and undergraduates from ment Circus met at Cornell to appeared in American Mathematical various majors. Professor Graeme discuss the latest developments in Monthly in October of 1999. Bailey, a long time friend of numerical approximation of partial Hubbard had observed a particu- Birman’s, suggested the Math Club differential equations, such as those larly vexing case, where a basin invite her to Cornell. Math Club occurring in engineering practice changes from being 4-legged to president Daniel Ramras (’02) and for which the Finite Element being 3-legged, apparently without Math Club faculty advisor Profes- Method is the industry standard. passing through any intermediate sor Ravi Ramakrishna then put in a The Finite Element Circus is a states. Thattai, after working with lot of effort arranging for and semi-annual event that originated in Hubbard, discovered how a ghost organizing Professor Birman’s visit 1970. It travels from town to of a 3-legged basin can grow inside and talk. town, hence its name. It is indeed a 4-legged one like an unobserved an informal gathering of research- parasite, and suddenly kill its host After the lecture, seventy-two ers, as no advance notice is re- and take over. This turns out to be students and faculty joined Profes- quired to attend. The presentation a previously unknown example of sor Birman at the weekly Math time slots are allotted by dividing a “parabolic implosion,” a phen- “Language House” table for dinner the number of people who wish to omenon in complex dynamics in Risley Dining Hall. The Depart- speak by the amount of time avail- which has occupied the experts for ment is most grateful for this able, and the order of the speakers fifteen years. weekly gathering sponsored by the (Continued on page 11) Faculty Fellow Program of Campus

4 1999 SPINOZA LECTURE GIVEN BY CORNELL MATH FACULTY By Anil Nerode The European Association for problem met serious technical elaborated in the early 1930’s by Logic, Language and Information difficulties. the Brouwer-Heyting-Kolmogorov invited Sergei Artemov to give the semantics that informally specifies Spinoza Lecture of 1999. The In 1994-1998, Sergei Artemov intuitionistic logic via operations on Spinoza Lecture is an annual found a complete solution to the proofs. Despite continuous efforts special lecture given by an out- Godel provability calculus problem. of leading researchers and many standing scientist. This lecture was Artemov’s results disclosed a artificial interpretations proposed delivered in 1997 by Solomon hidden constructive content of prior to Artemov’s works, there Feferman (Stanford University) and provability. His solution is formu- were no sound semantics for in 1998 by Moshe Vardi (Rice lated in the elegant form of a propositional intuitionistic logic University). Artemov, a visiting system of proof polynomials repre- suggested which met the original professor at Cornell, devoted his senting all invariant constructive Brouwer-Heyting-Kolmogorov lecture “Understanding Construc- operations on proofs. It turned out requirements. tive Semantics” to his recent solu- that proof polynomials admit a tion of two well-known problems in concise formal description and In his paper of 1933, Godel defined mathematical logic. provide an exact realization of all the propositional intuitionistic logic invariant properties of provability. in his provability calculus. How- The first problem is the Godel ever, the ultimate goal of specifying provability calculus problem that The second problem solved by intuitionistic logic via classical had remained open since 1933. Artemov’s system of polynomials proofs had not been achieved Provability is a fundamental notion concerns the foundational question because Godel’s provability calcu- in mathematics and logic. Formal of whether intuitionism provides an lus was left without exact seman- proofs and their structure were alternative to classical mathematics tics. Artemov’s solution of the studied in details during the past or it is a definable part of the latter. Godel provability calculus problem century. On the other hand, there Brouwer developed intuitionistic provides a solution to the Brouwer- was no satisfactory theory of the mathematics in the beginning of this Heyting-Kolmogorov problem as provability operator known. Such a century. A major component of well. From those results, it follows theory is necessary for expressing intuitionism has been Brouwer’s that intuitionistic propositional provability of sentences that them- thesis that a statement is true if we logic is indeed a definable fragment selves involve the notion of prov- have a proof of it, and false if we of classical mathematics that studies ability. In 1933, Godel introduced can show the assumption that there the provable properties of math- a logical calculus axiomatizing the is a proof for the statement which ematical objects. basic laws of provability operator leads to a contradiction. For and used it to build a constructive example, the logical principle of Artemov’s work opens up new semantics for intuitionistic logic. excluded middle “P or not P” is not areas of research in proof theory, This calculus is now widely used in valid intuitionistically, since it is not constructive and modal logics, logic and applications. Godel the case that for any proposition P lambda-calculus, automated deduc- noticed that the straightforward there is either a proof of P or a tion and formal verification, knowl- interpretation of this calculus was proof of “not P”. This intended edge representation etc. incompatible with his Second meaning of intuitionistic logic was Incompleteness theorem. Since VISIT THE MATH DEPARTMENT WEB SITE: then, finding the mathematical http://math.cornell.edu/ model for the Godel provability calculus became one of the fore- Our home page offers links to the Annual Report, faculty and graduate most open problems in logic. student home pages, information on the grad and undergrad programs, seminars and courses. New links are added all the time. Numerous attempts to tackle this

5 RESEARCH EXPERIENCE FOR UNDERGRADUATES The summer of 1999 marked the 6th student Suzanne Lynch. addresses. To begin the process year of the math department’s 3) Discrete Geometry, directed by we have been concentrating on Research Experience for Under- Karoly Bezdek, a visitor from certain very symmetric examples, graduates Program. REU is an Eötrös University in Budapest. such as the Sierpinski gasket. Two intensive 8-week program in which complementary goals are to extend 10 of the brightest undergraduate The students working on analysis our understanding as deeply as math majors from around the on fractals were continuing work possible for these special examples, country come to Cornell to work that has engaged many REU stu- and to broaden the class of fractals on research projects under the dents since 1996. The goal is to as much as possible. Both goals direction of Cornell faculty and create a kind of calculus for func- were advanced during this visitors. The program is funded tions whose domain is a fractal summer’s work. A notable by the National Science Founda- rather than a smooth space, to achievement was the completion tion, and the current grant contin- create a framework in which impor- of a working finite element method ues through 2001. If the VIGRE tant scientific problems may be to approximate solutions of fractal proposal is funded, it will enable us to upgrade the REU Program. SMORGASBORD SEMINAR A new component of the program 1999 Cornell REU Program this summer was the inclusion of three high school teachers (funded The Smorgasbord Seminar is part of the REU program which is open to by the Research Experience for the public. It is billed as ‘a little taste of a lot of mathematics’ and gives Teachers program, a new NSF the REU participants a high level of exposure to math topics they may initiative.) not yet have encountered in their education. The talks were given twice a week, and the speakers and topics follow: This is the first year the program was held in Malott Hall, and the Irena Peeva (Algebra) Counting in Algebra students were enthusiastic about our new headquarters. Instead Richard Shore (Logic) Computable structures and their presentations of complaints about the lack of air conditioning in White Hall, we Ravi Ramakrishna (Number Theory) Fermat’s last theorem were treated to complaints about too much air conditioning – you Robert Strichartz (Analysis) Hölder-Zygmund smoothness classes can’t win them all! This year, all the students in the program were Lars Wahlbin (Numerical Analysis) Some questions and answers in housed together in the Cayuga numerical analysis for differential equations Lodge Cooperative. The students found this arrangement conducive Peter Kahn (Topology) What is symplectic topology? to forming lasting friendships. Lou Billera (Combinatorics) Combinatorics, Topology, and The areas of research for 1999 Evolutionary Biology were: 1) Analysis on Fractals, directed John Hubbard (Dynamical Systems) The KAM Theorem by Robert Strichartz, with the assistance of Alexander Teplyaev, Rick Durrett (Probability) Scaling limits of particle systems a recent Cornell Ph.D. 2) Complex dynamics, directed by Karoly Bezdek (Geometry) Sphere Packings Adam Epstein and John Hubbard, with the assistance of graduate Jose Escobar (Partial Differential Equations) The Maximum Principle

6 differential equations on the unexpected approximate periodic- know what the minimum diameter Sierpinski gasket, which may be ity. Since all of the projects were is for a convex polytope in d-space found on the Web at: http:// related, participants working on with vertices with edge lengths of mathlab.cit.cornell.edu/~gibbons. different problems often helped one at least 1? No one knows exactly, An article describing the whole field another out. This created a collabo- but it is now known to be at most 3 was published in the November rative atmosphere that played a provided n > d + > 4. While such 1999 issue of the Notices of the large part in the results of each results are easy to state, they AMS. participant. required considerable ingenuity to discover! One of the students also The students working on complex The students working on discrete discovered an error in a much dynamics met together for the first geometry were able to solve several quoted paper of Bieberbach. It few weeks to familiarize and offer problems involving bodies of seems that Bieberbach merely a general understanding of the constant width and sphere stated that a proof he had given in subject to the participants. Having packings. For example, did you the case of plane geometry also established a foundation upon know that every convex body of works in spherical geometry. Not which to start their research, the constant width in 3-space may be so, it turns out, but Greg participants broke off into groups illuminated by 6 directional Blekherman, NYU, came up with to explore different problems. sources? (Hint: illumination means a correct proof. Two of the stu- Scott Wilson made an extensive that the light ray must hit the dents in this group have been investigation of the family M3 surface and enter the body, not just invited to a conference in Budapest where one critical point is periodic glance a corner point.) Do you to discuss their work. of period 3. Ben Wittner and Mary Rees have studied this family, but much of the structure is still myste- DURRETT RECEIVES FUNDING FOR DNA rious. Scott located in particular RESEARCH a whole new family of “exotic hyperbolic components.” Vicki For most of this decade, Rick Jefferson fathered slave’s last Kowalski and Scott Corry started Durrett’s research has been fo- child,” and the verification that writing a program called Medusa, cussed on the application of sto- Dolly the sheep was indeed a clone. which computes parameter values chastic spatial models to problems Less famous, but perhaps more for a class of rational functions that arise from problems in Ecol- important, are their use as markers called captures. This should be- ogy. Much of this work has been for locating genes, and for dating come a major exploration tool for done with Simon Levin, who left events associated with the move- the entire field. Alex Raichev Cornell for Princeton in 1992, and ment of humans out of Africa and investigated “long ray connec- Rick Harrison, head of the Ecology subsequent colonization of Europe tions.” The question of whether and Evolutionary Biology Depart- and the Americas. there are arbitrary long ray connec- ment. Three years ago, during the For the purposes just mentioned, tions has implications for the supervision of a Ph.D. thesis writ- one needs a model of how DNA limiting behavior of matings, and ten by Semyon Kruglyak, Durrett repeat sequences evolve in time. In locating such things is a delicate met Chip Aquadro and became 1998 Kruglyak, Durrett, Aquadro, problem in combinatorics. Melkana interested in his work on and postdoc Malcolm Schug Brakalova and Keith Hilles-Pilant “microsatellites.” These DNA introduced a new model that investigated the family M4. This is repeat sequences have higher avoided some of the problems with largely unexplored territory, and mutation rates than the rest of our the then standard “stepwise muta- even the algebraic problems are DNA and are thus useful as genetic tion model.” It provided a good fit interesting. They discovered many markers. Examples that have been new phenomena, including an in the headlines are “Thomas (Continued on page 9)

7 CORNELL STORMS POPULAR PRESS

Cornell Math Department members known card-shuffling schemes. American Math. Monthly, October, are constantly publishing technical This and other applications are 1999. The forced pendulum has articles in the leading mathematics discussed in some detail. The tremendously complicated dynam- research journals, intended for article can be found in American ics, as this paper illustrates. It specialists. In recent months, they Mathematical Monthly, Volume explores the motions of a forced have also been publishing articles 106, no. 6, June-July 1999. pendulum, illustrating the amazing meant for a wider audience in the complication. It shows that you American Mathematical Monthly During the 1997-98 academic year, can choose an initial condition so and the Notices of the AMS, two of John Guckenheimer served as that the pendulum will go through the most widely distributed math- President of the Society for Indus- any prescribed sequence of gyra- ematics periodicals. trial and Applied Mathematics, the tions. It also that the basins of primary professional organization attraction for attracting periodic Robert S. Strichartz, Analysis on for applied mathematics. One of his motions can have the Wada prop- Fractals, Notices AMS, November obligations as SIAM President was erty: any point in the boundary of 1999, 1199-1208. This article to give an address at the annual one basin is in the boundary of all describes the construction and meeting following his term of the others. So letting the pendulum analysis of the analog of differential office. A written version of this loose near such a point is a gigantic equations for functions defined on address was published in the Octo- roulette game, with all of infinitely fractals. This is a new area of ber, 1999 SIAM News, “Computer many outcomes possible with mathematics that is intended to simulation and beyond—for the arbitrarily small perturbations of the create a framework for serious 21st century”, Notices AMS Oct initial state. Hubbard has also scientific applications, but it also 1998 (Vol 45 # 9) 1120 - 1123. In collaborated with his wife, Barbara fits in with the purely mathematical the address, he tried to weave Burke Hubbard, on a calculus text. goal of extending the theory of together comments about scientific Vector Calculus, Linear Algebra, analysis on manifolds to objects policy with reflections on problems and Differential Forms: A Unified that are very rough. Much of the that were particularly intriguing Approach (Prentice Hall) has work described in this article was throughout his own career. SIAM earned praise for its original presen- carried out in collaboration with volunteered to help the National tation of material usually taught in undergraduates participating in our Science Foundation investigate the separate courses. The couple are in REU program. (See related article topic of “uncertainty” related to the process of completing a sequel. on page 6.) simulations with a view towards future research programs or initia- Tom Rishel has published his Lou Billera, Ken Brown and tives. As part of this effort, John second book, A Handbook for Persi Diaconis have a recent paper, Guckenheimer wrote a paper about Mathematics Teaching Assistants, “Random walks and plane arrange- the challenges that he sees in (MAA). The book is a natural ments in three dimensions”, in the enhancing the use of simulation as a extension of the extensive notes American Mathematical Monthly, tool in science and engineering. The that Tom gave to participants in his June-July 1999 issue. They de- paper was published in the Notices national teaching assistant work- scribe recent work by Brown, of the American Mathematical shop at last summer’s MAA Diaconis and others on random Society as a “Forum” column. The Mathfest in Providence, RI. Rishel, walks in hyperplane arrangements outcome of SIAM’s efforts to help who has been training TA’s in the and show, in the case of dimension the NSF plan future programs Cornell Mathematics department 3, that these walks have a surpris- remains uncertain. for twenty years, will also conduct ingly simple form for their limiting a workshop for TA trainers at the distribution. Such walks are of John Hubbard, The dynamics of joint AMS – MAA meetings in interest since they generalize well- the forced damped pendulum, Washington, DC, this January.

8 (...Durrett Receives Funding, (...Malott Hall Relocation, continued from p. 7) continued from p. 2) to data from genetic databases on members and their belongings from The moving of the department’s the abundance of microsatellites White Hall into Malott Hall. They computer room machines and and to experimental work on their provided much needed help and network and their reinstallation mutation rates. The math involved direction, coordinating the move Malott were coordinated and in the model is very simple. In for faculty members. Donna Smith, implemented by our computer principle, an undergraduate with the graduate field coordinator, support staff, Doug Alfors and knowledge of stochastic processes helped the graduate students. Robert Terrell. Their considerable could have developed it. However, Duties for the staff included provid- efforts and dedication to excellence the model is useful because it ing packing materials, disseminating resulted in a nearly flawless net- provides more accurate predictions information, coordinating details of work conversion with minimal of properties of microsatellites. the move, and directing the place- “down” time. ment of furniture and boxes into the In order to follow up on this work, new offices. Graduate student Durrett and Aquadro submitted a representatives Leah Gold and (Reinvigorating the Math proposal for a supplement to Matthew Horak, with the assistance Dept, continued from p. 3) Aquadro’s NIH grant under a of Walker White, admirably man- program to foster the development aged the concerns and needs of At this point the proposal has of cross-disciplinary collaborations their fellow grad students. Admin- passed the first hurdle: a three- for the “study of complex biological istrative manager Colette Walls person team came to Cornell on systems.” The grant was funded in coordinated the move, overseeing November 2 for a one-day site visit. the spring of 1999 and will provide the staff effort and serving as liaison In the morning of that day, the eight teaching relief for Durrett during between the college, movers, writers of the grant mentioned the next three years so that he can interior designer, contractor and above and newly appointed VIGRE develop the background necessary construction crews. coordinator, Rick Durrett, de- to do research in this area. scribed the proposal and answered a number of questions sent to us by FRESHMEN WRITE PROGRAM TO NSF. In the afternoon, the panel DISPLAY SURFACE DEFINED BY held closed-door meetings with current postdocs, graduates, and EQUATION undergraduates to find out what Adam Barth, a freshman enrolled in Math 223, with help from classmate they really thought about life at Joseph Palin, has been writing a program to display surfaces given by an Cornell. equation f(x,y,z)=0. This requires a discretization of the surface, which might be done using a cubical decomposition of space. They built a Based on the exit interview with the model to illustrate this out of site panel we are cautiously opti- pumpkin-shaped gumdrops and mistic that in late December we will toothpicks, shown below. get some good news from the The model shows the failure of a National Science Foundation. If “tetrahedral” decomposition of not, then we will be looking at our space. reviews and regrouping for the next If you try to add more gumdrops, round of competition in July 2000. you discover that the toothpicks are We do not want the math depart- too long or too short. This illus- ment to miss out on this golden trates the fact that you cannot pave opportunity. space with regular tetrahedra.

9 COMINGS AND GOINGS...

Alexander Bendikov is a Visiting from Ithaca College. His areas of Math from Cornell University in Professor from Mathematisches interest include Logic, Computa- August 1999; his thesis advisor was Institut, Universitaet Erlangen- tional Complexity, Asymptotic Richard Rand. Stephen’s research Nuernberg. He will be with us at Methods in Combinatorics, among interests are dynamical systems and Cornell for the academic year 1999- others. John’s area of current mathematical biology. He co- 00. His areas of interest are Poten- research involves finding finite directed the summer 1999 MTBI, tial Theory and Probability mea- dimensional Steinitz Exchange Mathematical and Theoretical sures on algebraic structures. Prof. Systems whose lattices of closed Biology Institute at Cornell Univer- Bendikov graduated from Gorky subsets code various sity, for talented undergraduate University (Kharkov, Ukrain Re- noncomputable sets of integers. minority students. Stephen is public), and has held the position of Also, asymptotic results on com- married to the former Erika professor at both Rostov University plexity of algorithms for Exact Camacho, a graduate student in and Erlangen-Nuernberg University. Satisfiability. He is also working Cornell’s Applied Math program. with Diane Schwartz (Ithaca Visiting Professor Bill Dunbar is College) on an Applied Calculus Sumio Yamada is a Visiting on sabbatical this year from text. John lives in Ithaca with his Professor for 1999-2000. Origi- Simon’s Rock College of Bard. He wife, and has two grown sons and nally from Japan, Sumio has been in wrote his Ph.D. thesis on Euclidean one grandchild. the U.S. for 13 impressionable 3-dimensional orbifolds in 1981, years, although this is the first year under Bill Thurston, and his inter- Ed Swartz is a Visiting Professor at Cornell. Sumio received a Ph.D. ests remain centered in low-dimen- for the academic year. He received from Stanford in 1996, and has sional geometry and topology his Ph.D. from the University of interests in geometric analysis, in (broadly defined to include differen- Maryland, College Park in spring of particular harmonic maps and tial geometry, crystallography, 1998. As a long time resident of Teichmueller space. geometric group theory, knot Connecticut and Rochester, spend- theory, and the geometry of defor- ing the last 5 years in College Park, Andrzej Zuk is a Visiting Profes- mation spaces). He is a devoted fan alias “the land that snow forgot,” sor for fall semester, 1999. His of Brazilian music, and still pines has left him eagerly anticipating permanent residence is in Lyon, for the fresh-squeezed passion-fruit winter in Ithaca. Ed’s main fields France, where he works at the drinks that he drank at the street of interest are geometry, topology Ecôle Normale Superieure, and stands in Rio 15 years ago, during 8 and combinatorics. His current holds a research CNRS position. months spent in Brazil as a visiting research centers on a connection He did his graduate studies in researcher. He still speaks Portu- between matoids and quotients of France in both Paris (Orsay) and in guese tolerably well, though it spheres. When not at work, Ed can Toulouse. Andrzej’s mathematical would be difficult to get him to occasionally be found at the bridge interests are geometric group admit as much. table or walking his pet ferret theory, Kazhdan’s property (T), throughout campus. harmonic analysis and random Maria Fung is a Visiting Professor walks on groups. During his for 1999-00. She completed her Stephen Wirkus is a Visiting semester at Cornell, he is teaching a Ph.D. at Cornell in August, under Professor in Spring, 2000. He was graduate course and presenting Dr. Birgit Speh. She is happy to born and raised in Kansas City, several talks at seminars related to remain at Cornell for one more MO, and received bachelor degrees his research. He is finding Cornell year. in Math and Physics from the University an excellent place to do University of Missouri-Kansas City. research and has begun some new John Rosenthal is a Visiting He received his Ph.D. in Applied research projects while here. Professor. He is on sabbatical leave

10 (...Circus at Cornell, continued from p. 4) NEW MATH is determined by a lottery (formerly About forty people attended the FACULTY FELLOWS by drawing from a hat, now by Circus at Cornell, and sixteen Professors Buzzard and computer). The Circus does have people spoke. These days, travel- Ramakrishna were appointed this an interesting rule which is en- ling to a two-day conference is a bit year to the Faculty Fellow Program forced: participants come to listen of an expensive hassle and to at Cornell, and join current Fellows as well as to talk. You are not combat this the Circus has spawned Professors Speh and Bailey. This allowed to talk unless you stay for an offspring, the Texas Finite program is sponsored by Campus the whole conference. While the Element Rodeo. Periodically, this Life, and is designed to bridge the Circus has visited Cornell many meets in spite of distance; the gap between faculty and students times, this was the first time it was Spring 2000 meeting will be a joint by supporting interactions outside held in the Math department’s new Circus-Rodeo down in Austin. the classroom, often through shared quarters. The organizers proudly meals and events. Each Fellow is showed off Malott Hall to their For more about the Circus, see ‘attached’ to a dormitory and have colleagues, and many envious http://www.math.psu.edu/dna/ enthusiastic followings of students comments were overheard, in fecircus from all fields. More information at particular about our Math Library. www.campuslife.cornell.edu

YES, I WOULD LIKE TO HELP SUPPORT THE MATHEMATICS DEPARTMENT

ENDOWMENTS WITH MY DONATION OF $______FOR:

The Malott Art Fund. Established to enable the Math The Logic Endowment. Recently established by a Department to purchase commissioned artwork for the donation from a former Cornell undergraduate. Seeks new offices in Malott Hall. to actively support promising logic students in the areas of institutional memberships and travel expenses, for As- The Mathematics Faculty Book Fund. Provides the sociation for Symbolic Logic meetings and events, and Cornell Community with immediate access to one of the other activities in the field of logic. world’s finest assortments of mathematics books and pub- lications by enriching the collection of the Mathematics Make checks payable to Cornell University. 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 310 Malott Hall teach extra courses and donate their earnings to the fund. Cornell University Ithaca, NY 14853-4201 The Eleanor Norton York Award in Astronomy and Mathematics. Established in honor of Eleanor Norton Name: ______York, a valued Astronomy Department employee who worked closely with graduate students. Recognizes out- Address:______standing graduate students in Astronomy and Mathemat- ______ics with an annual prize. ______ The Israel Berstein Memorial Fund. Honors the memory of a former Mathematics Department professor 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 1990-00 Annual the fields of topology and/or geometry. Report when it becomes available.

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

Graeme Bailey David Brown Rick Durrett John Hubbard Gene Hwang Mikki Klinger Anil Nerode John Smillie Donna Smith Bob Strichartz Lars Wahlbin Colette Walls Scott Wilson YiMin Wu Joy Jones

Nora Balfour Editor

Department of Mathematics 310 Malott Hall Cornell University Ithaca, NY 14850

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