Both Richard De Veaux and Frank Morgan were on leave this year, with Dick having spent the year at the French National Institute for Argonometric Research (I.N.R.A.) in Montpellier, France, and Frank having spent the year as the 250th Anniversary Visiting Professor for Distinguished Teaching at Princeton. Dick will be back in time for next Fall, while Frank will be taking one more years' leave, after returning to Williams for the summer to participate in the SMALL undergraduate research program. Ed Burger will be on leave next year at the University of Colorado. Deb Bergstrand will be on leave in Philadelphia, and Victor Hill will be on leave with lots of travel plans but a base in Williamstown. Both Stewart Johnson and Cesar Silva will take semester long leaves next academic year. Both of their leaves are well deserved, with Stewart having shouldered the burden of the statistics courses during Dick's leave, and Cesar having chaired our hiring committee so effectively.
With all the leaves coming up, we were pleased to appoint two visitors for next year. Steve Wang is finishing a Ph.D. in Statistics at the University of Chicago and is particularly interested in the statistics of handwriting recognition, such as might be required when the post office tries to decipher that zip code you wrote. He will teach a variety of courses for us, including a course on statistical graphics. Jorge Calvo is finishing his Ph.D. in Mathematics at the University of California-Santa Barbara. He studies questions related to knots constructed out of sticks. His courses will include Algebraic Topology and Geometry.This past year, we were lucky enough to be joined by David Morgan, who was on leave from the Bishop's School in San Diego, CA. He taught Quantitative Studies for us in the Fall and Math 103 Calculus for us in the spring. In addition, he took courses from a variety of departments on campus, including several advanced math courses. He participated in every way in the department and brought to our discussions a very thoughtful perspective that had not been represented in our department previously. We found his input extremely helpful. He will be sorely missed.
One sad note this year was the passing of Wally Jordan. A member of the Williams Mathematics Department from 1946-1977 as well as the valedictorian of Williams Class of 1937, Wally worked as an actuary before becoming a member of the Faculty. He was the author of Life Contingencies that can still be found on the bookshelves of actuaries throughout the country. Over the years, he contributed greatly to the Mathematics Department, in addition to helping innumerable students who had an interest in actuarial science.
As always, we were extremely proud of the accomplishments of our graduating seniors this year. Kariane Calta `98 was awarded a National Science Foundation Fellowship for graduate study in mathematics. She will attend the Ph.D. Program at the University of Chicago. She also received the Rosenburg prize given to the best graduating major by the mathematics department. Past major, Deborah Greilsheimer `97 received honorable mention in the NSF Graduate Fellowship competition. She will be attending the University of Pennsylvania next Fall. Andrew Raich `98, who is going to the University of Wisconsin to study math, received the Morgan Prize for teaching and/or applied math. Tristan Smith `98 received the Goldberg Prize for having given the best colloquium and the Witte Problem Solving Prize for his excellent showings on both the Green Chicken Exam and the Putnam Exam. Tristan is speaking at the Toronto SIAM meetings this summer on his joint work with Prof. Deborah Bergstrand and will be teaching mathematics in Morocco next year. Kari, Andy and Tristan were all elected to the Sigma Xi Research Society on the basis of the research they did for their theses. All three received highest honors from the department. Heath Dill `98 and Mimi Huang `98 received honors from the department, based on their accomplishments on their theses. The Benedict prize for outstanding sophomore went to Anthony Ndirango `00.
We are very grateful to the members of the Student Mathematics Advisory Board (SMAB) for their help with hiring, advice on departmental issues and organization of events. This year, the members were Patrick Anderson `00, Catherine Bagley `99, Garren Bird `99, Zack Grossman `99, Sang Pahk `99, Audrey Watkins `98 and Aaron Weinberg `99. Also, Kariane Calta `98 and Andy Raich `98 did a great job as our senior advisors.
All of the faculty had a busy and productive year. Highlights of the year's faculty activities follow:
Colin Adams became chair of the Mathematics Department in July 1997, taking over from Prof. Olga R. Beaver. In summer of 1997, he directed four students on research in alternating graphs as part of the SMALL program. The students spoke on their work at the Atlanta Mathfest in August. The paper that Adams and the students jointly produced has been submitted to a math research journal for publication.
In January 1998, Adams was awarded the Deborah and Franklin Tepper Haimo Distinguished Teaching Award, given annually to three recipients nationwide. He is the second winner in the department. Frank Morgan won it in 1993, the first year that it was awarded. Only one other department in the country has as many recipients of this award as we do, and that is the Purdue Math department (which incidentally has three times the number of faculty).
Adams also became a Polya Lecturer for the Mathematical Association of America, making him one of two nationally and the seventh appointed so far. He gave over 20 talks around the country, including a second production of the mathematical play, co-authored and performed jointly with Edward Burger, entitled Casting About: About Casting at the National Mathematics Meetings in Atlanta, GA, Aug. 4, 1997. He wrote several papers and had several others accepted for publication. He edited a special issue of the Journal of Chaos, Solitons and Fractals devoted to "Knot Theory and Its Applications." His new book How to Ace Calculus: the Streetwise Guide, co-authored with Joel Hass and Abigail Thompson, will appear in July 1998. His National Science Foundation research grant has been renewed for the next three years. As of July 1998, he becomes the Mark Hopkins Professor of Mathematics at Williams College.
Professor Ollie Beaver was on sabbatical leave in the fall. In November, she gave a Bronfman Bag Lunch talk on Williams' Summer Science Program. Also in November, Beaver was an invited speaker at the 1997 Fall Conference of the Northeastern Section of the Mathematical Association of America, presenting a lecture, "The Williams Summer Science Program - Not With a Whisper But a Bang." In the spring she was a panelist in the Connecticut Association of Independent Schools Math Forum Calculus Panel Discussion, held at The Hotchkiss School in Lakeville, Connecticut. She has continued her long association with the Summer Science Program, again teaching in the mathematics component.
Deb Bergstrand continued her work in graph theory. She spoke on "Graceful Graphs" at the Williams Faculty Seminar. She served as the Director of the 1997 SMALL Project. She was also Chair of the Faculty Steering Committee until January when she took a leave of absence to care for a newly adopted daughter, Julia Michelle Stanley, born February 11, 1998. Mom, dad, and daughter are enjoying life in Philadelphia.
Professor Edward Burger spent the summer of 1997 as a Visiting Scholar at the University of Texas at Austin. This past academic year he advised three honor's thesis students: Kariane Calta `98, Heath Dill `98, and Mimi Huang `98, on various number theory research projects. Next year Professor Burger will be on sabbatical at the University of Colorado at Boulder where he was named the Ulam Visiting Research Professor of Mathematics.
Burger published "Mathematics Beyond the Ivy-Covered Hall" in The Mathematical Intelligencer (vol. 20, 1998), and completed his text, The Heart of Mathematics: An Invitation to Effective Thinking, co-authored with Michael Starbird, to be published by Springer-Verlag in 1999. He is also completing the first-ever virtual interactive video WEB calculus textbook. It may be found at http://www.thinkwell.com/.
Burger was the Chair of the Program Committee for the Fall 1997 Northeastern Mathematical Association of America Meeting, held on November 21 and 22 at Western New England College in Springfield. He reviewed numerous articles for Mathematical Reviews, and served as referee for the Journal fur die Reine und Angewandte, the Fibonacci Quarterly, Columbia University Press, and W.H. Freeman Press. He also was a reviewer for the National Science Foundation.
Professor Burger gave numerous invited lectures throughout the country. (See the list of talks at the end of this section.) Here at Williams, Professor Burger lectured on mathematics during the Summer Open House in August, at the Williams College Faculty Club and in the Mathematics Faculty Seminar in September, at a Mathematics Colloquium in October, and again in the Mathematics Faculty Seminar in April. Also in April, Burger delivered a lecture in the Williams Writers on Writing Lecture Series.
Professor Mikhail Chkhenkeli continued his research in Four Dimensional Topology and Gauge Theory. In particular he investigated the problem of determining the genera of homology classes of 4-manifolds and representing them by smoothly embedded 2-spheres. Chkhenkeli wrote two papers: "Homology Classes of K3" and "Homology Classes of 4-Manifolds."
At Williams, he gave Mathematics Faculty Seminars in November and May. In the Fall of 1997 he taught a new senior seminar,Differential Topology MATH 427. He organized the First Annual Purple Cow High School Math Contest, the Twentieth Annual Green Chicken Math Contest, and monthly mathematics conundrums. He was the coach of the Williams College team in the national Putnam mathematical competition.
In the summer of 1997 he taught an accelerated course, Mathematical Logic and Reasoning at the summer program organized by the Institute for the Academic Advancement of Youth (The Johns Hopkins University). In the summer of 1998 he is an invited by the IAAY to teach a course in Mathematical Reasoning and Probability Theory.
Professor Richard D. De Veaux spent the year as a visiting scientist at the French National Institute for Argonometric Research (I.N.R.A.) in Montpellier, France. He gave a variety of talks in the United States and France. He will give the J.S. Hunter Lecture in Australia at the International Environmetrics Meeting this July on "Hybrid Neural Networks for Environmental Process Control."
Dick continued as Associate Editor for Technometrics, Environmetrics and Journal of Environmental Statistics. He will serve as General Methodology Chair for the ASA 1998-99 and was elected Program Chair Elect for the Section on Statistics in Sports. His paper "Prediction Intervals for Neural Networks via Nonlinear Regression" will appear in Technometrics in November. This paper, with co-authors Jason Schweinsberg `97 and Jennifer Schumi `97, is based, in part, on research performed by Jason and Jenny when they were undergraduates. They are both currently enrolled in Ph.D. programs in Statistics (at Berkeley and Iowa State respectively).
Professor Thomas Garrity has continued his research in higher codimensional CR structures and classical algebraic invariant theory. His paper "Vector-valued Forms and CR Geometry" written with R. Mizner, has appeared in a collection CR Geometry and Overdetermined Systems, Advanced Studies in Pure Mathematics, published by the Mathematical Society of Japan. He has spoken a number of times at Williams and at the Hudson River Undergraduate Mathematics Conference.
Victor E. Hill IV, Thomas T. Read Professor of Mathematics, developed a new senior seminar on Axiomatic Set Theory, offered in the fall. He continued as a History of Mathematics reviewer of books for Scott Foresman and of articles for Mathematics Magazine. He also participated in the spring meeting of the Northeastern Section of the Mathematical Association of America, held in Keene, N.H.
Professor Hill continued his work as a free-lance professional harpsichordist and organist. The 30th anniversary season of his Griffin Hall Concerts at Williams College featured the inaugural in January and a varied program in May using his new double-manual Franco-Flemish harpsichord, completed by Richard Kingston (Asheville, N.C.) in October; additional programs on the series were an all-Bach organ recital and a harp/organ concert with Teresa Mango. Professor Hill completed his 16th year on the Board of the Association of Anglican Musicians; he also serves on the Editorial Board of this Association, on the Board of Trustees of the Berkshire Unit of Recording for the Blind & Dyslexic, and on the Executive Board of the Berkshire Chapter of the American Guild of Organists.
Professor Stewart Johnson continued his research in dynamical systems and control theory, focusing on the dynamics and optimality of controls that have continuous and discrete components. His research is in the new area of "passive controls." These controls have no feedback loops and are not self-monitoring, but maintain stability by a dynamic design that is inherently self-correcting. This work was the subject of his Faculty Lecture Series talk given in March titled "Dynamics, Noise and Chaos." Professor Johnson taught his senior seminar on math modeling to a large group of 25 students, in addition to teaching the two core statistics courses while Professor De Veaux was on leave and a tutorial on Numerical Methods.
Professor Susan Loepp continued her research in commutative algebra. Her paper "Excellent Rings with Local Generic Formal Fibers" appeared in the Journal of Algebra. During the year, she attended several conferences including the annual Joint Mathematics Meetings, the Mathematics and Statistics Centennial Celebration of the University of Nebraska, the fall Mathematical Association of America conference, and the Hudson River Undergraduate Mathematics Conference. She gave talks at three of these conferences. Loepp gave several other talks during the year including colloquia at Smith College, Colgate University and Williams College.
Loepp served on the steering committee for the 1998 Hudson River Undergraduate Mathematics Conference, held at Union College. Eleven Williams students and three faculty participated in the conference.
Professor Frank Morgan has spent the year as Princeton University's new 250th anniversary Visiting Professor for Distinguished Teaching. Over 100 graduate students, faculty, and undergraduates, from Mathematics and other departments (notably Molecular Biology), participated in his innovative teaching seminar, videotaped model teachers and each other, and discussed strengths and weaknesses. Professors Colin Adams and Edward Burger of Williams College, the sensations of recent national mathematics meetings, came to Princeton to produce their imaginative mathematical play and conduct teaching workshops.
Morgan took his call-in Math Chat TV show to Princeton, where it was broadcast before a live audience off a dining hall. The volunteer staff of graduate and undergraduate students directed the show, operated the camera and control booth, screened the calls, and took turns as co-host. Special guests included John Conway, Freeman Dyson, and the young winners of Morgan's Soap Bubble Geometry Contest at Riverside Elementary School. (Check out the March 9 show on the web via Morgan's homepage at http://www.williams.edu/Mathematics/fmorgan, where you can also find his Math Chat newspaper column from The Christian Science Monitor.) An interview of Morgan was featured as the cover story of the September 1997 issue of Math Horizons.
Morgan studies the geometry of soap bubble clusters and other structures in nature and in materials. He is currently writing two papers with two former undergraduate research students, Hugh Howards `92 and Michael Hutchings, on the most efficient enclosures of prescribed area ("soap bubbles") in curvy surfaces. This summer his SMALL undergraduate research Geometry Group will study efficient enclosures on the surface of the cube and other surfaces.
During the year Morgan published three papers and has five others in press. He has given some forty talks, ranging from mathematics seminars to his popular Soap Bubble Geometry Contest. A write-up of the contest, written jointly with undergraduate research students Ted Melnick and Ramona Nicholson, was published in The Mathematics Teacher (December 1997). A second edition of Morgan's Riemannian Geometry appeared this spring.
Morgan is planning a number of visits for his upcoming sabbatical, including three months in Spain at the University of Granada.
Professor Cesar Silva taught a course on chaotic dynamics and fractals along with his other courses, and continued his research in ergodic theory (measurable dynamical systems). He supervised a group in the SMALL summer `97 research program. His group completed research in ergodic theory and a manuscript was submitted for publication "Power Weakly Mixing Infinite Transformations," with S.L. Day, B.R. Grivna, and E.P. McCartney `99. (See their site at http://front.math.ucdavis.edu/math.DS/9803105 .) He also supervised Andy Raich `98 who wrote a thesis in ergodic theory. Andy presented his work http://front.math.ucdavis.edu/math.DS/9803105 at the Hudson River Undergraduate Mathematics Conference, in April 1998. Andy's thesis together with the work of previous research students are part of a paper that has been submitted for publication "Infinite Ergodic Index Zd Actions in Infinite Measure", with E. Muehlegger `97, B. Narasimhan `97, A. Raich `98, M. Touloumtzis `96, and W. Zhao). Silva also submitted two other papers and published three papers, one of them based on research from SMALL `96.
In January, Silva attended the annual meeting of the American Mathematical Society in Baltimore. He delivered a Faculty Lecture titled "Determinism and Randomness in Kneading Dough" and "Fractals and Dynamics," Bronfman Science Summer Lunch, Williams College. He also was a reviewer for Mathematical Reviews. During September, Silva hosted Professor Philippe Thieullen from the University of Paris at Orsay; they continued their long term collaboration on entropy characterization of distal dynamical systems.
In summer `98, he will be preparing a course on fractals to be taught in the fall. This work is being supported by a college Mellon grant, which is also supporting a student, Jonathan Kallay `00, who will write some programs for the course.
Victor E. Hill IV
Nancy Ann Neudauer
Wolfgang M. Schmidt
SMALL Geometry Group
SMALL Graph Theory Group
SMALL Dynamical Systems Group
SMALL Higher Co-dimensional Geometry Group
SMALL Knot Theory Group
Amrita Ahuja `98
Daniel Anello `98
Kariane Calta `98
Heath Dill `98
Clay Elliott `98
Steven Ellis `98
Victoria Fang `98
Katherine Hedden `98
Mimi Huang `97
Edward Johnson `98
Paul Kari `98
Jeremy Kay `98
Adrian Ludwig `98
Linden Minnick `98
Jonathan Novita `98
Andrew Raich `98
Catherine Riihimaki `98
Derek Sasaki-Scanlon `98
Tristan Smith `98
Adam Sterns `98
Surach Tanboon `98
Audrey Watkins `98
Olga R. Beaver
Deborah J. Bergstrand
Edward B. Burger
Richard De Veaux
"Re'seaux de Neurones De'mele's"(Neural Networks Untangled)
French National Institute for Argonometric Research, Montpellier, France
"Neural Networks Untangled"
American Statistical Association Joint Meetings, Anaheim, California
Victor E. Hill IV