Our department had a great year. We were joined by Visiting Professor Florian Luca (who is returning to his permanent position at the Instituto de Matem‡ticas at the Universidad Nacional Autonoma de Mexico in Morelia Mexico), Visiting Assistant Professor T.J. Hitchman (who will be an assistant professor at the University of Northern Iowa next year) and Visiting Lecturer Adam Petrie (who will be an Assistant Professor at the University of Tennessee next year). Five members of our department were on leave this past year. Ed Burger spent most of the year based in Austin at the University of Texas. Dick De Veaux spent the year at Princeton as the William R. Kenan Jr. Visiting Professor for Distinguished Teaching. Frank Morgan traveled the world but was anchored here at Williams. Allison Pacelli spent the year at Brown. We look forward to the return of all four. Kris Tapp spent the year visiting the University of Pennsylvania. Unfortunately for us, the lure of the big city was too great of a temptation for Kris, who has decided to leave us for a position at Suffolk University in Boston. We will miss him.
Back here in Williamstown, Satyan Devadoss was granted tenure and promoted to associate professor, Susan Loepp was promoted to full professor, and Bernhard Klingenberg was reappointed for another three-year term. Congratulations to all three.
We are very proud of the accomplishments of our majors. The Rosenberg Prize for outstanding senior was awarded to Ross Kravitz '07 and Brian Simanek '07. Jennifer James '07 and Alexei Zaliznyak '07 received the Goldberg Prize for the best colloquia. Diana Davis '07 and Angela Doyle '07 were awarded the Morgan Prize for Teaching and/or Applied Mathematics. Lindsey Wu received the Robert M. Kozelka Award for outstanding student of statistics. For the second year in a row, Natee Pitiwan '09 won the Witte Problem Solving Prize. Peter Nurnberg '08, Natee Pitiwan '08 and Scott Smedinghoff '08 were awarded the Benedict Prize for outstanding sophomores. Finally Colin Carroll attended the most colloquia.
The members of our student advisory board, SMASAB (Students of Mathematics and Statistics Advisory Board), were Diana Davis, Annie Ferguson, Kathryn Lindsey, Gordon Phillips, Brian Simanek and Scott Smedinghoff. They provided sage advice, in addition to organizing the department's ice creamsocials.
Back on campus in June at Reunions 2006 we held our third annual reception. Williams alums were invited to enjoy one more of our famous "Teas" with old friends and professors. The alumni link at our web page www.williams.edu/Mathematics includes more information and pictures.
All of the members of the faculty had a busy and productive year. Their individual highlights and achievements are given below.
Professor Colin Adams participated in the Park City Mathematics Institute in Park City, Utah for three weeks in summer, 2006. He was the director of the undergraduate faculty program, teaching the undergraduate faculty how to teach knot theory and how to do research with undergraduates in knot theory. He also put on several mathematical theatrical productions at the Institute.
Over 2006-2007, he worked with two thesis students. Diana Davis worked on knots made from sticks and Thomas Kindred worked on spanning surfaces of alternating knots and links.
Adams and his co-author Robert Franzosa finished work on their book "Introduction to Topology: Pure and Applied" which will be published shortly by Prentice Hall. In addition, Adams published a variety of articles and stories. He continued as the humor writer for the Mathematical Intelligencer. The DVD of "The Great Pi/e Debate," joint with Tom Garrity, was distributed by the Mathematical Association of America (MAA).
Adams served as chair of the 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.
Professor Ollie Beaver spent a portion of summer 2006 developing modules for Math 101, the quantitative studies course. Math 101 was granted funding as a CRAAS course (Critical Reasoning and Analytical Skills). She is a co-coordinator for the Quantitative Studies program. At Williams, Beaver was chair of the Winter Study Committee and a member of the Olmstead Prize Committee, which chooses high school teachers to honor at Commencement. In January she attended the Joint Mathematical Meetings in New Orleans; in February Beaver was an invited panelist on the National Science Foundation Panel for Graduate Fellowships in the Mathematical Sciences. She continues her involvement with the Mellon Mays Undergraduate Fellowship Program at Williams as well as in the teaching and coordination of the mathematics component of the Summer Science Program.
Professor Carsten Botts spent most of this academic year revising and improving the ideas and methods developed in the paper "Likelihood Approximations in Bayesian Multiple Curve Fitting." These improvements were the subject of a talk given at the Joint Statistical Meetings in August of 2006, and were also the subject of a paper entitled "A Flexible Approach to Bayesian Multiple Curve Fitting" which was submitted for publication.
Botts has also spent a significant portion of the academic year consulting for the Multiple Sclerosis Center of Southern Vermont. Most of the consulting has involved sample size calculations, tests of significance, and help in writing grant proposals.
Professor Edward Burger continued his research in number theory while on sabbatical in Austin, at The University of Texas. In August 2006, he received the Lester R. Ford Award for expository excellence by the Mathematical Association of America. Burger also received the 2007 Nelson Bushnell Prize for scholarship and teaching from Williams College. His series of nearly 2000 mathematics videos, published by Holt, Rinehart and Winston in 2007, was nominated for an upcoming 2007 Distinguished Achievement Award by The Association of Educational Publishers.
In August, his text "Extending the Frontiers of Mathematics: Inquiries into Proof and Argument" was published by Key College Press in cooperation with Springer-Verlag. In October, his book "Coincidences, Chaos, And All That Math Jazz," published by W.W. Norton & Co. was released in a paperback edition. The book will be translated into Chinese, German, Japanese, Korean, and Thai. In the fall, his paper "On Diophantine Approximation Along Algebraic Curves," coauthored with his Honors Thesis student A. Pillai '05, was accepted for publication in The Proceedings of the American Mathematical Society. In the spring, 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 accepted for publication in The Journal of Number Theory.
In August 2006, Burger developed and ran the three-week summer program for high school students, "International Leadership Program on Creativity through Mathematical Thinking," at American Community Schools in Athens, Greece. Burger continued to serve as an advisor on the Paramount Pictures/CBS-TV/Texas Instruments/NCTM joint project to create mathematical modules based on the television show NUMB3RS. He served on the External Review Committees for the Fordham University Mathematics Department and the Weston Schools Mathematics Program.
Professor Burger gave over 75 invited and keynote addresses at various conferences and institutions including a special session at the MAA Mathfest, Mathematics Council of The Alberta Teachers' Association Conference, the 2006 Shenandoah Undergraduate Mathematics Conference, The University of Texas, Carleton College, Drexel University, Colorado State University, Fairfield University, Sam Houston State College, Trinity University, and Grinnell College.
Professor Satyan Devadoss continues to grow old with the passing of time, but is still having a blast. His work in both particle collisions and computational geometry has led to several papers this year, along with presenting a handful of talks. He also supervised two senior thesis students this year: Colin Carroll '07 focused his work in algebraic geometry, looking at weighted blowups of the braid arrangement of hyperplanes. Katie Baldiga '07 looked at the space of possible ways polyhedra can be sliced using moving planes, resulting in convex cross-sections.
Recently, Devadoss has developed an interest of incorporating visual mathematics with studio art, leading to offering a (fantastic) winter study on "Geometric Modeling" joint with the Art department. He was asked to be a keynote speaker at the Mishner Festival of the Arts in Pennsylvania based on his work.
Professor Richard De Veaux spent the year at Princeton University as the William R. Kenan Jr. Visiting Professor for Distinguished Teaching. The Kenan Professorship is one of Princeton's 250th anniversary endowed professorships established in 1996 to celebrate teaching. Professor Frank Morgan was one of the first two recipients in 1997-1998.
De Veaux continued his research on data mining and gave presentations throughout the U.S. He was a keynote speaker at USCOTS (U.S. Conference on Teaching Statistics) in Columbus Ohio in May. The Committee on Assessing Behavioral and Social Science Research on Aging, on which De Veaux was a member, concluded its 3-year term with the publication of their report "A Strategy for Assessing Science" published by the National Research Council. The second edition of his textbook Stats: Data and Models was published in January.
Professor Thomas Garrity has continued his research in number theory. His debate with Colin Adams, moderated by Ed Burger, on the relative merits of e and pi, has appeared on DVD, available through the Mathematical Association of America. In October he spoke at Vassar and in February he spoke to alums in Chicago. He also spoke a number of times at Williams. In winter study he organized an all-afternoon event, called the Poincarepalooza, during which many faculty members discussed the recent proof of the Poincare conjecture. He learned quite a bit from his thesis student Shea Chen. He continues being the director of WilliamsÕ 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, and the abundance of such cycles in three dimensions. Professor Johnson is continuing to explore generic forms and the types of behavior possible in degenerate cases.
Working as a statistician with Dr. Keith Edwards '69 and others, Professor Johnson has published results establishing the safety and efficacy of Galantamine as treatment for dementia with Lewy bodies. Results were published in the May issue of Dementia and Geriatric Cognitive Disorders.
Professor Johnson remains active in the college wide Quantitative Studies program which provides early identification and intervention for students with quantitative deficiencies.
Professor Bernhard Klingenberg continued his research into statistical methods for multidimensional discrete data with application to drug safety and toxicity studies. In September, his manuscript "A multivariate extension of McNemar's test" was published in Biometrics, and he has submitted a second paper to the journal dealing with the analysis of multiple, correlated ordinal data. Klingenberg recently concentrated on modeling dose-response for discrete data through either statistical modeling or stochastic order. He finished a paper proposing a unified framework for Proof of Concept and dose estimation for pharmaceutical products in phase II clinical trials that should provide more robust and powerful methods than the ones currently in use. He also developed publicly available software code (in the statistical language R) to support the analysis proposed in the paper. With his thesis student Doug Hammond, Klingenberg looked into constructing simultaneous confidence intervals for success probabilities from multiple binary data. Klingenberg gave invited talks on dose-response methodologies at the Dose Finding Conference in Philadelphia in February 2007 and at Novartis Pharmaceuticals in the US and Switzerland. He gave a contributed talk at the annual meeting of the International Biometrics Society in Atlanta in March 2007.
Professor Susan Loepp traveled to North Newton, Kansas in March, 2007 to give the Bethel College convocation and math seminar. While at Bethel, she received the 2007 "Young Alumnus" award. In January, 2007, Loepp attended the national Joint Mathematics Meetings in New Orleans. Loepp, along with her students, continued working on research in commutative algebra. The paper, "Chains of Rings with Local Formal Fibers," by Kai Chen '04, Susan Loepp, and John Provine, appeared in Communications in Algebra. During the 2006-2007 academic year Loepp advised the senior honor thesis of Myron Minn-Thu-Aye '07. In addition, she is currently serving as a mentor for Haydee Lindo '08 in the Williams College Undergraduate Research Fellowship program. They are working on a research project in commutative algebra and plan to continue their work during the summer of 2007.
Loepp and William Wootters (Physics) taught their interdisciplinary course on Protecting Information in the spring of 2007. It was the first time they used their recently published book, "Protecting Information: From Classical Error Correction to Quantum Cryptography," (Cambridge University Press, 2006) for the course.
Professor Frank Morgan spent his sabbatical year traveling the globe, consulting with other mathematicians and giving forty talks on manifolds with density, isoperimetric problems, and other related topics, at the International Congress in Madrid, across Europe, to mathematicians and business schools in Seoul Korea, in Vietnam (Hanoi and Hue), and elsewhere. He taught a short course for new PhDs in Mexico and another in Italy.
Morgan was in Hue Vietnam for Teacher's Day, a marvelous national celebration in which apparently everyone takes delight in thanking and honoring teachers past and present. On his arrival they escorted him to a student Teacher's Day musical celebration and asked him to sing for them.
In addition to the new Russian edition of his Geometric Measure Theory text, Morgan published eight articles. One, a joint paper with his thesis student Jonathan Lovett, continuing a class research project from his senior seminar on Riemannian Geometry, appeared in the American Mathematical Monthly, the flagship publication of the Mathematical Association of America. Jon is now Hillary Clinton's speechwriter. Another is a joint paper with Colin Adams. An interview with pictures of Morgan and his research students appeared in The Christian Science Journal.
Morgan's students have made valuable advances on manifolds with density and other topics. This past year five of their papers were published and two others should appear shortly. One on "Double Bubbles in S3 and H3," to appear in the excellent Journal of Geometric Analysis, is the culmination of five years of work. Conor Quinn's senior honors thesis on "Area-minimizing Partitions of the Sphere" has already been submitted for publication. Conor is now with Teach for America in Chicago. Morgan's 2007 SMALL undergraduate research Geometry Group includes Anthony Marcuccio '08 and Taryn Pritchard '08.
Professor Allison Pacelli spent her sabbatical this past year at Brown University, continuing her research in algebraic number theory. She received a Mentoring Travel Grant from the Association for Women in Mathematics to work with Michael Rosen there. Her paper "Higher Rank Subgroups in the Class Groups of Imaginary Function Fields" (with Yoonjin Lee) appeared in the Journal of Pure and Applied Algebra, and her paper "A Lower Bound on the Number of Cyclic Function Fields with Class Number Divisible by n" appeared in the Canadian Mathematical Bulletin. In addition, her paper "Parameterized Families of Quadratic Fields with 3-Rank At Least 2" (with SMALL '05 undergraduates Carl Erickson, Nathan Kaplan, Neil Mendoza '07, and Todd Shayler '06) was accepted by Acta Arithmetica. She submitted two additional papers Ð "Class Groups of Real Quadratic Fields of 3-Rank at Least 2: Effective Bounds" (with Florian Luca) and "Quadratic, Cubic, and Sextic Number Fields with Class Number Indivisible by 3", as well.
Pacelli also began research in a new field, fair division, a subfield of mathematics and politics. She is currently working with David Craft (visitor at Williams in 2005-06) on an extension of the Adjusted Winner Procedure to three or more parties and was invited to attend the Fair Division Workshop at Dagstuhl this summer. She is also co-authoring the second edition of Mathematics and Politics: Strategy, Voting, Power, and Proof with Alan Taylor (Union College).
This year, Pacelli was invited to speak at the George Washington University Summer Program for Women in Mathematics, the Fields Institute Workshop on Computational Challenges in Algorithmic Number Theory and Cryptography, the Brown University Graduate Student Seminar, the University of Wisconsin Graduate Student and Number Theory Seminars, and the Five College Number Theory Seminar. She also spoke at the Canadian Number Theory Association Meeting IX, and organized (with Michael Rosen) a Special Session on the Arithmetic of Function Fields at the Joint Mathematics Meetings in January 2007 and organized (with Florian Luca) a Special Session in Number Theory at the AMS Eastern Section Meeting in April 2007. Pacelli was a co-instructor of the Professional Development Seminar for Advanced Graduate Students at the Sheridan Center for Teaching and Learning in Higher Education at Brown University this past year, and will be teaching a three-week course in Algebraic Number Theory at the George Washington University Summer Program for Women in Mathematics during July of 2007.
In fall 2006 Professor Cesar Silva taught a tutorial on ergodic theory, his area of research, and a course on second semester calculus. In the spring he taught linear algebra. He continued his research in ergodic theory and writing a book that he used in his ergodic theory tutorial. In summer 2006 he supervised four students on research in ergodic theory. A paper based on this research has been accepted for publication in the Proceedings of the American Mathematical Society. He had two students who wrote year-long theses in various aspects of dynamics. He will be director of the SMALL program in summer 2007. He submitted several papers for publication and was a referee for several journals. He was also a member of the committee that visited the Pomona College math department in fall 2005. He published a paper with his colleague A. Danilenko.
Professor Mihai Stoiciu taught Calculus, Applied Real Analysis, Complex Analysis and a new 300-level tutorial (cross-listed between Mathematics and Computer Science) on "Numerical Problem Solving." He also taught the Winter Study course "Godel, Escher, Bach," using as a textbook the Pulitzer Prize winning book of Douglas Hofstadter. Also, Stoiciu supervised a thesis by Brian Simanek '07 titled "Spectral Properties of Random Unitary Band Matrices." In his thesis, Brian investigated the spectrum of random CMV and Joye matrices, two important classes of random unitary matrices.
Stoiciu continued his research in mathematical physics and submitted two papers for publication. He was invited to give talks at Ruhr University, Bochum, Germany and at the Pan-American Advanced Studies Institute, Santiago de Chile, Chile. His paper "Poisson Statistics for Eigenvalues: From Random Schrodinger Operators to Random CMV Matrices" will appear in CRM Proceedings and Lecture Notes.
At Williams College, Stoiciu gave a faculty seminar on his recent research in December 2006 and a math colloquium in June 2007. He also gave a presentation on the local existence of the Ricci Flow at the Poincarepalooza Seminar organized by the Mathematics and Statistics Department.
During the year, Stoiciu organized and ran (together with Professor Florian Luca) the weekly problem-solving club "Math Puzzle Night", where Williams College students prepared and trained for various math competitions. This year, the Williams College Mathematics Team won again (for the fourth consecutive time) the traditional Green Chicken Mathematics Contest and had a good performance in the Putnam Competition. Also, Jerry He '08, a member of the Williams College Math Team, won the First Prize in the Problem Solving Competition, a national math competition held at MathFest in Knoxville, Tennessee.
Professor Kristopher Tapp led a team of five undergraduates researching invariant metrics on Lie Groups during the summer. He spent his sabbatical year visiting the University of Pennsylvania, where he focused his research on symmetry and positive curvature. He traveled to several conferences, and pursued collaborations with colleagues from Dartmouth, SUNY Oneonta, and Germany.