Our department had a great year. Edward Burger has been selected to be the next Williams Gaudino Scholar. Satyan Devadoss won the Henry L. Alder Award for Distinguished Teaching. This national award of the Mathematical Association of America is to honor a beginning college or university mathematics faculty member whose teaching has been extraordinarily successful and whose effectiveness in teaching undergraduate mathematics is shown to have influence beyond their own classrooms. Cesar Silva has been appointed the Hagey Family Professor of Mathematics.
We were joined by Visiting Assistant Professor Shawn Rafalski, who next year will be starting at Fairfield University. We will miss him. We look forward to the return of Susan Loepp, who has been on leave all year, and Ollie Beaver, on leave this spring. Carsten Botts and Mihai Stoiciu were both reappointed.
We have some new people coming this next year. Steven Miller has been hired as an assistant professor. Steve is an analytic number theorist who has most recently been at Brown. Daniel Look will be joining us as a visiting assistant professor. Daniel works in dynamical systems and is visiting from Indiana University of Pennsylvania. In the fall, Lori Pedersen will be a visiting lecturer.
Over 100 attended our first Math/Stats/Computer Science Mini-Conference/Reunion June 8, on the occasion of the 20th anniversary of our SMALL undergraduate research project, the largest and most prolific such program in the country. Bethany McLean '92 of Fortune Magazine, who exposed Enron, gave the opening talk, "How Math Makes Me a Better Journalist." Another 25 alums spoke, including Professor Michael Hutchings SMALL '92 of UC Berkeley on "How the Double Bubble Conjecture was Proved." The day ended with dinner at the Water Street Grill. For more information and photos, see our alum webpage at www.williams.edu/Mathematics/alumni. Sponsored by the National Science Foundation, the Research Corporation, and Williams College. Thanks to Frank Morgan for organizing such a wonderful event.
We are very proud of the accomplishments of our majors. The Rosenberg Prize for outstanding senior was awarded to Michael Daub'08. Son Ho '08 and David Rogawski '08 received the Goldberg Prize for the best colloquia. Anna Ferguson '08 was awarded the Morgan Prize for Teaching and/or Applied Mathematics. Zhichun Ying 08 received the Robert M. Kozelka Award for outstanding student of statistics. Edward Newkirk '09 won the Witte Problem Solving Prize. Ralph Morrison '10 was awarded the Benedict Prize for outstanding sophomore. Finally Wasin Vipismakul '08 attended the most colloquia.
The members of our student advisory board, SMASAB (Students of Mathematics and Statistics Advisory Board), were Ali Barrett, Michael Daub, Anna Ferguson, Joanna Hoffman, Marius Iordan, Haydee Lindo, Natee Pitiwan, and Rahul Shah. They provided sage advice, in addition to organizing the department's ice cream socials.
During summer, 2007, Professor Colin Adams worked with six students as part of the SMALL Undergraduate Research Project at Williams College on stick numbers for knots. He also published "Introduction to Topology: Pure and Applied" co-authored with Robert Franzosa. This is a textbook that takes an applied approach to topology. In addition, Adams published a variety of articles and stories. His paper, "The Projection Stick Index of Knots", co-authored with Todd Shayler '06, was accepted for publication in the Journal of Knot Theory and its Ramifications. He continued as the humor writer for the Mathematical Intelligencer.
In the Fall, he did a review of the mathematics department at Oberlin College. At the Joint Mathematics Meetings in January, he gave several talks on various aspects of knot theory and he also produced and performed in a series of humorous math theatrical productions, with help from a variety of colleagues.
In Spring, 2008, he taught "Applied Topology", providing the first opportunity to use his new textbook for the course. Adams served as chair of the Mathematical Association of America (MAA) Haimo Teaching Awards Committee, and as a member of the MAA Coordinating Council on Meetings. He was a member of the American Mathematical Society Eastern Section Meetings Invited Address Selection Committee, and a member of the MAA Carriage House Advisory Board. He served as a co-principal investigator on an NSF Grant to support undergraduate mathematics conferences, administered by the MAA. At Williams, he served as chair of the Committee on Priorities and Resources.
In summer 2007, Professor Ollie Beaver led a small group in research in Williams REU, SMALL. Additionally, she taught in and coordinated the mathematics component of the Summer Science Program. During the academic year, Beaver continued her involvement in the Quantitative Studies program and was again chair of the Winter Study Committee. In January she attended the Joint Mathematical Meeting in San Diego. In February Beaver was an invited panelist on the National Science Foundation Panel for Graduate Fellowships in the Mathematical Sciences. Beaver was on sabbatical in the spring and worked on a number of mathematical projects.
Professor Carsten Botts, in the academic year of 2007-2008, his paper "A Flexible Approach to Bayesian Multiple Curve Fitting" was accepted for publication in the journal Computational Statistics and Data Analysis. This paper explores how to use Monte Carlo methods when fitting curves to functional data observed from multiple subjects. This is joint work with Professor Michael Daniels from the University of Florida, and was the subject of my talk given at the hedge fund, SAC Capital, in July of 2007. This academic year he also spent time developing a new algorithm which samples from a truncated multivariate normal distribution. This new algorithm was the subject of his faculty seminar given in the math department in the fall of 2007.
Professor Edward Burger, upon his return from his sabbatical, continued his research in number theory while developing a new course offered in the fall entitled "The Art of Creating Mathematics." In 2007 Burger received an Award of Excellence by Technology & Learning magazine for educational mathematics videos that break new ground, acknowledging his mathematics videos published by Holt, Rinehart and Winston. In 2008, the College named Burger the next Gaudino Scholar. He will follow in the footsteps of the first mathematics professor to receive this honor nearly 20 years ago: Professor Olga R. Beaver. In this role, Burger will offer a new interdisciplinary course this fall entitled EXPR 309 "Exploring Creativity."
In 2008, Burger published two papers coauthored with his students. His paper "On Diophantine approximation along algebraic curves", coauthored with his Honors Thesis student A. Pillai '05, was published in The Proceedings of the American Mathematical Society (136 (2008) 11-19), and his paper "Shrinking the period lengths of continued fractions while still capturing convergents", coauthored with four undergraduates including Nicholas Yates '06 and Ross Kravitz '07, was published in The Journal of Number Theory (128 (2008) 144-153). Also in 2007 his book "Coincidences, Chaos, And All That Math Jazz", coauthored with Michael Starbird, was published in Chinese and German editions. This year Burger produced two 24-part video lecture series with The Teaching Company. His first course is entitled "Zero to Infinity: A History of Numbers" and his second is "An Introduction to Number Theory."
This year Burger was the Honors Thesis advisor for Wasin Vipismakul '08, who wrote a thesis entitled, "The number of summands in Ostrowski's numeration." They are currently planning on submitting a paper based on this work to a journal for publication.
Professor Burger gave over 40 invited and keynote addresses at various conferences and institutions including lectures at Boston University, the Smithsonian Institute, an invited special session at the 1039th AMS Conference, and keynote addresses at The Arizona Undergraduate Conference, The Northwest Ohio Center of Excellence in Mathematics Education Conference at Bowling Green State University, Detroit Area Council of Teachers of Mathematics Annual Conference, NCTM Regional Meeting in Kansas City, NCSM National Meeting in Sacramento, Associated Teachers of Mathematics in Connecticut Annual Conference, and the Joint Meeting of the San Antonio Mathematics Collaborative. In the Summer of 2007, he gave a Short Course at MathCamp at Colby College, and in the fall delivered the 2007 Sigma Xi Lectures at Williams College as well as several Williams College Alumni events around the country.
Professor Satyan Devadoss continues to fight the good fight here at Williams. His research in the areas of discrete geometry and topology led to presenting a handful of talks, the most notable being a plenary speaker at the A.M.S. meeting at Rutgers University. He had papers appear in the journals of "Discrete Mathematics" and "GeoInformatica" (on geographic information systems). He also led a group of students under the SMALL REU program over summer 2007 on "Particle Collisions".
Professor Devadoss recently won the Alder national award from the MAA in summer 2007 for distinguished teaching by a junior faculty. He also has enjoyed giving various talks at Williams, especially giving a faculty lecture on da Vinci and Art.
Professor Richard De Veaux returned to Williams this year after spending the 2006-2007 academic year as the William R. Kenan Jr. Invited Professor for Distinguished Teaching at Princeton University. Dick continued his work in data mining and gave a variety of invited talks and keynote addresses on teaching and data mining. The third edition of his book Intro Stats, an introductory statistics co-authored with David Bock and Paul Velleman, was published in December by Pearson.
In December, Dick was elected as the Mosteller Statistician of the Year by the Boston Chapter of the American Statistical Association for the year 2008.
Professor Thomas Garrity has continued his research in number theory. He was a keynote speaker at a conference on "The Art of Teaching Mathematics" held at Harvey Mudd from June 10 to June 12, 2007, gave the Christie Lecture at the fall meeting of the northeast section of the Mathematical Association of America held at Framingham State University on November 16, 2007, was the speaker the MAA's northeast section dinner at Norwich on April 15, gave a colloquium at Norwich University on April 15, was a keynote speaker at the CURM conference in March at Brigham Young, was the speaker the MAA's Intermountain section meeting at Brigham Young and gave a colloquium at Middlebury in April. He also spoke a number of times at Williams. In July at Williams and in February at Foxboro, he spoke to alums, as part of the Williams Roadscholars program. In winter study he organized an all-afternoon event, called the Stochastic Fantastic Day, during which many faculty members discussed the nature of stochasticity and randomness. He learned quite a bit from his thesis students Son Ho, Haydee Lindo, Amy Steele and Paul Woodard. He continues being the director of Williams' Project for Effective Teaching (Project PET).
Professor Stewart Johnson continues his research in dynamical systems, modeling, and optimal control with a focus on systems that exhibit continuous and discrete behavior. He is interested in small rapidly switching cycles that approximate probabilistic behaviors. Professor Johnson has demonstrated the generic existence of such cycles in high dimensions with multiple flows. Results have been submitted for publication in a joint paper with Jordan Rodu, '05.
Professor Johnson remains active in the college wide Quantitative Studies program which provides early identification and intervention for students with quantitative deficiencies, and is currently working on converting Math 101: Mathematical analysis and Descriptive Statistics to tutorial format.
Professor Bernhard Klingenberg spent his sabbatical year in Padua, Italy and as a visiting professor at the Institute of Statistics at the TU-Graz, Austria. There, he gave a short course on categorical data analysis which he developed at Williams and presented a lecture on an Introduction to Statistics at a meeting of undergraduate engineering students from Europe and Asia. He also gave a 5 day course (jointly with A. Agresti from the niversity of Florida) on the analysis of repeated categorical data at the University of Oslo, Norway. Klingenberg's research focused on new methods in biostatistics, such as developing tests for detecting toxicity in chemical compounds, establishing efficacy and modeling a dose-response relationship for drugs in phase II clinical trials or comparing several success rates across many groups. He gave invited talks on these and related topics in Padua and Venice, Italy and at several universities across Austria.
Professor Susan Loepp was on leave during the 2007-2008 academic year and focused on her research. In January, she attended a special session on commutative algebra at the national Joint Mathematics meetings in San Diego. In February, she traveled to Austin Texas to meet with commutative algebraists and present a lecture on her research. While there, she met with seven Williams alums who are currently working on research in mathematics at the University of Texas at Austin. In April, Loepp traveled to Portland, Oregon where she gave a talk on her research at Reed College.
In late 2007 a paper co-authored by Loepp and four of her undergraduate students appeared in the Rocky Mountain Journal of Mathematics. During the summer of 2007, she advised five undergraduates as part of the Williams College SMALL program. They proved several original results, which will be submitted for consideration for publication in refereed mathematics research journals.
Professor Frank Morgan taught a Winter Study course on Tournament Bridge. His students participated in local tournaments and in regional events in Boston and New York. One student, Edward Newkirk '09, wrote up a bridge hand and found it published in Phillip Alder's column in The New York Times, January 26, 2008. William Jannen '09 and Bryant Renaud '11 had a write-up published in the Bulletin of the American Contract Bridge League.
In the fall Morgan taught a new senior seminar on "The Big Questions", including Fermat's Last Theorem, the Riemann Hypothesis, and Perelman's recent proof of the Poincare Conjecture. Class discussions inspired a new theorem a proof of the existence of least-perimeter partitions of space to appear in Philosophical Magazine with an acknowledgement of the class's contribution. In the spring Morgan taught for the second time his course on Investment Mathematics, including a proof of the Nobel Prize winning Black-Scholes formula for pricing stock options.
Morgan has continued his work on isoperimetric problems and manifolds with density. He published five papers and has six others in the works. One publication is a joint paper in The American Mathematical Monthly with thesis student Jonathan Lovett '04, now Senator Clinton's speech writer. Another is a joint note with Cesar Silva on the SMALL Undergraduate Research Project. A new fourth edition of his Geometric Measure Theory book is appearing later in 2008.
Morgan gave over thirty talks at venues ranging from high schools to mathematics colloquia. For an undergraduate student workshop at Millersville University, Morgan had asked the students to try to reproduce computer-predicted minimal surfaces with soap films in a plexiglass box. Their resulting article and photographs appear in the April 2008 issue of Math Horizons.
Morgan's own students have made valuable advances on partitioning problems and other topics. One new publication in the excellent Journal of Geometric Analysis on "Double Bubbles in S3 and H3" is the culmination of five years of work. The thesis of Conor Quinn '07 on "Area-Minimizing Partitions of the Sphere" appeared in the Rose-Hulman Undergraduate Mathematics Journal. Conor is now with Teach for America in Chicago. His paper with Colin Carroll '07 and the rest of the 2006 undergraduate research Geometry Group on "The Isoperimetric Problem on Planes with Density" has been accepted by the Bulletin of the Australian Mathematical Society. A paper of the 2007 Geometry Group, including Anthony Marcuccio '08 and Taryn Pritchard '08, on "Area-Minimizing Partitions of the Sphere" has been accepted by the Canadian Mathematical Bulletin. They are now preparing a second paper for publication. Matthew Simonson '08 has submitted his thesis on "The Isoperimetric Problem on Euclidean, Spherical, and Hyperbolic Surfaces" for publication. The new 2008 Geometry Group includes Jonathan Dahlberg '09 and Edward Newkirk '09. Richard McDowell '09 will be doing a thesis with Morgan this coming year.
Professor Allison Pacelli taught a three-week course in Algebraic Number Theory at the Summer Program for Women in Mathematics at George Washington University during the summer of 2007. She also taught a new senior seminar in Algebraic Number Theory at Williams during the spring of 2008, and participated in the Faculty Roundtable program at Williams in the fall of 2007.
She continued her research in both algebraic number theory and fair division, and completed her book, Mathematics and Politics: Strategy, Voting, Power, and Proof (with Alan Taylor), second edition. It will appear in the fall. Her paper Parameterized Families of Quadratic Fields with 3-Rank At Least 2 (with undergraduates Carl Erickson, Nathan Kaplan, Neil Mendoza '07, and Todd Shayler '06) was published by Acta Arithmetica. Her paper Class groups of real quadratic fields of 3-rank at least 2: Effective bounds (with Florian Luca) was published by the Journal of Number Theory. She also submitted two additional papers in algebraic number theory, and one paper (with Noam Yuchtman '05) on using the Adjusted Winner procedure to study the Israeli-Palestine conflict. She is currently working (with David Craft) on extending the procedure to the case of three or more parties, and was invited to the Fair Division Workshop at Dagstuhl during the summer of 2007 to discuss this work. Pacelli also gave talks at the Maine-Quebec Number Theory Conference, the department's faculty seminar, and the Williams College Science Lunch. She received a Hellman Fellow Grant to continue her research. She also supervised the senior honors thesis of Michael Daub '08 on Subfields of Hilbert Class Fields with Class Number One.
Visiting Assistant Professor Shawn Rafalski taught the second semester Single-Variable Calculus course and Differential Geometry during the fall semester, and Multivariable Calculus in the spring. He facilitated "Conundrums", the mathematical monthly contest in which students attempt to solve challenging mathematical questions for prizes, and served as one of the judges for the annual Middlebury-Williams' "Green Chicken" mathematics competition. In the summer 2008, he will lead a research group in" Hyperbolic Geometry" for the Williams Mathematics SMALL undergraduate research program.
Professor Rafalski gave several talks both at Williams and at other institutions. He gave two talks for the Williams faculty this year: one for the Mathematics and Statistics faculty seminar, and one to the Division III sciences as a "Bronfman Science Lunch" lecture. Outside of Williams, he gave research talks about his work on "hyperbolic turnovers" at the University of Massachusetts-Amherst, Tufts University, the City University of New York Graduate Center (Hunter College), Boston College, and the 2008 Georgia Topology Conference (University of Georgia-Athens). He also spoke on hyperbolic geometry for the Advanced Placement Calculus class at Pittsfield High School in nearby Pittsfield, Massachusetts.
Professor Cesar Silva taught calculus, chaos and fractals, and linear algebra. He continued his research in ergodic theory and published a book that he used in his ergodic theory tutorial. In summer 2007 he supervised four students on research in ergodic theory, and was director of the SMALL summer research program.
A paper based on his research with his SMALL group was accepted for publication in the Transactions of the American Mathematical Society. He completed an invited review paper with his colleague A. Danilenko to appear in Springer's Encyclopedia of Complexity.
Professor Mihai Stoiciu taught Multivariable Calculus in the fall semester and Probability in the spring. During the year, he worked with two thesis students: Sunmi Yang '08 and Irina Zhecheva '08. Sunmi studied the spectrum of the Almost Mathieu operator using methods from numerical analysis and statistics and Irina investigated the connections between ergodic theory and random Schrodinger operators. Stoiciu also supervised the SMALL 2007 Mathematical Physics Group, which studied the distribution of eigenvalues for certain classes of unitary matrices.
Stoiciu continued his research in Mathematical Physics and submitted one paper for publication. He was invited to give talks at Tokyo Institute of Technology, Tokyo, Japan, Keio University, Yokohama, Japan, University of Connecticut, Brown University, and University of Kentucky. Stoiciu also gave a talk on his recent research in the AMS Session on Probability, Statistics, and Applications at the Joint Mathematics Meetings, San Diego. His paper "On the Irrationality of a Certain Factorial Series" was published in the journal Integers.
At Williams College, Stoiciu gave a faculty seminar talk in November 2007 and delivered the Spring Family Days Faculty Lecture in April 2008. He also gave a presentation titled "Random Matrices - An Introduction" at the Stochastic Fantastic Seminar organized by the Mathematics and Statistics Department.
During the year, Stoiciu organized and ran the weekly problem-solving club "Math Puzzle Night", preparing and training the Williams College students for various math competitions.
This year, the Williams College Mathematics Team won, for the fifth consecutive time, the traditional Green Chicken Mathematics Contest. The team also had a good performance in the Putnam Competition.