MATHEMATICS DEPARTMENT

It has been a great year in the Department of Mathematics at Williams. We were happy to have Frank Morgan, Ed Burger and Victor Hill back from full year leaves and Stewart Johnson and Cesar Silva back from half-year leaves. This fall, Mikhail Chkhenkeli was at Harvard for his junior leave. Susan Loepp spent the entire year at Michigan State. This spring, we hired a new member of the department, Janine Wittwer, from the University of Chicago. She studies wavelets and will be joining us in the fall.

An article about the successes of the Williams Mathematics Department appeared in Newsweek magazine in the June 5, 2000 issue (p.61). It focused on the increase in the number of majors (42 graduating this year, an all-time high) and on how the Department makes math fun, without watering it down.

Over the last year, Colin Adams served his third and final year as chair of the Department of Mathematics. In summer of 1999, Colin Adams worked with three students as part of the SMALL summer program on alternating knots, extending previously known results. One of the students, Tom Fleming, went on to do a thesis with Adams, extending the results still further.

Professor Adams finished his term as one of the two Polya lecturers for the Mathematical Association of America, giving a variety of expository talks around the country. He began his term as a Sigma Xi Distinguished Lecturer, one of two in mathematics. For the opening banquet of Mathfest, the national summer math meetings in Providence in 1999, Adams and 18 performers from the faculty and students of SMALL put on “The Newest Inductee in the Number Hall of Fame”. Written by Adams, it presents the awards ceremony for the Number Hall of Fame, where the Geiseking Constant (played by Susan Loepp) is inducted, with explanation as to why. At the opening banquet of the winter mathematics meeting in Washington D.C. in January 2000, Adams, five members of the faculty and a student presented Vital Sines, a short play about a mathematics emergency room.

Melkana Brakalova, a high school teacher from the Hotchkiss School receives an award at MathBlast! 2000.
Organizers of the event, Mikhail Chkhenkeli, Edward Burger and Olga R. Beaver, appear behind her.

Professor Adams also began his career as a mathematics humor columnist in the Mathematical Intelligencer, an expository mathematics magazine. So far, two of his stories have appeared. He also published three research papers, one of which was co-authored with four students.

Professor Adams created a new course called “Applied Topology” in spring, 2000. He is co-authoring a textbook for the course. This next year, he will be on leave but at Williams, working on a variety of projects, including an on-line calculus course, several research papers on knots and on hyperbolic 3-manifolds, additional books in the How to Ace Calculus series, and a book with attached toy called “Why Knot?” His research will be supported by a continuing grant from the National Science Foundation. This spring, Adams was named the Francis Christopher Oakley Third Century Professor of Mathematics.

This year, in addition to serving on several college committees, Professor Ollie Beaver coordinated the high school outreach program MathBlast! 2000. MathBlast! is a daylong program of mathematically oriented contests, games and workshops, designed to excite high school students about mathematics. Nearly 100 students and teachers came from as far as Connecticut to participate in the first annual happening. In January, Beaver attended the annual meeting of the American Mathematics Society in Washington D.C. At Williams, Beaver gave a fall Faculty Seminar. She has also continued her long association with the Summer Science Program for minority students, again teaching in the mathematics component.

Professor Edward Burger spent part of the summer of 1999 as a Visiting Fellow at the Centre for Number Theory Research at Macquarie University in Sydney, Australia. In the fall, he offered a new senior seminar, discovery approach, tutorial in number theory. The course led to the upcoming text, Exploring the Number Jungle: A Journey into Diophantine Analysis to be published this summer by the American Mathematical Society. Burger was awarded the 2000 Northeastern Section Mathematical Association of America Award for Distinguished Teaching at a College or University.

Professor Burger’s first book, The Heart of Mathematics: An Invitation to Effective Thinking (co-authored with Michael Starbird from The University of Texas at Austin) was published in November by Key College Press in cooperation with Springer-Verlag. This year Burger published three research papers, and one opinion piece. In the fall, Burger was a contributing writer for National Public Radio’s ECO-Essays Series. In the spring, he served as an external reviewer for the science curriculum at the Massachusetts College of Liberal Arts. He was also a reviewer for Mathematical Reviews, Addison Wesley Longman Publishers and Oxford University Press. Burger refereed papers for the Journal of Number Theory, the Transactions of the American Mathematical Society, and the MAA’s Mathematics Magazine.

Professor Burger gave numerous lectures throughout the country including one of the keynote addresses at the AMS, MAA, SIAM Meetings in Washington, DC. (See the list of talks at the end of this section.) Besides the talks he gave in the Mathematics Department, he also gave an address at the Phi Beta Kappa Induction in the fall; and gave lectures in the Williams Today Program; Gaudino Forum; Faculty Lecture Series; Williams College Faculty Club; HMB Premedical Society; and the Oakley Center. Finally, with Ollie Beaver he co-hosted the game show “Math Rocks” at MathBlast 2000.

Professor Mikhail Chkhenkeli continued his research in Four Dimensional Topology and Gauge Theory. In particular, he investigated the problem of determining quadratic forms that occur as intersection forms of smooth 4-manifolds. In the fall, he visited Harvard University and participated in several research seminars there. He gave two talks on his research at Tbilisi State University. At Williams, he gave a Faculty Seminar in March.

Professor Chkhenkeli was one of the organizers of MathBlast! 2000 - a Math event for High school students. In the summer of 2000, he was invited by the Institute for the Academic Advancement of Youth (The Johns Hopkins University) to teach courses in Mathematical Reasoning and Game Theory.

Professor Richard De Veaux continued his research in data mining and computational statistics. He gave several invited talks and short courses this year on Data Mining, both in this country and abroad. He was the Dresden lecturer at Swarthmore College and was the speaker of the year at the Southern California American Statistical Association chapter in Long Beach, California. Professor De Veaux continued his work as Associate Editor of Technometrics, and Environmetrics and started his work as Program Chair for the Joint Statistical Meetings in Atlanta in 2001.

Professor Thomas Garrity has continued his research in higher codimensional CR structures, classical algebraic invariant theory and number theory. His paper “Global Structures on CR Manifolds via Nash Blow-ups” has been accepted by the Michigan Journal of Mathematics. His book All the Math that You Missed: Preparing for Graduate School in Mathematics has been accepted by Cambridge University Press. His SMALL group for 1999 developed a web page (http://www.williams.edu/Mathematics/tgarrity/triangle.html) on their work in number theory. He had two senior thesis students this year: Tegan Cheslack-Postava and Adam Schuyler. He spoke a number of times at Williams this year, including in the faculty seminar, the math colloquium, the Gaudino forum and the Williams College Debate Union and gave a talk at Skidmore in the fall. In the spring, Tom was promoted to full professor. He will be spending next year visiting the University of Michigan at Ann Arbor.

Victor E. Hill IV, Thomas T. Read Professor of Mathematics, returned from his year’s sabbatical during which he worked on the mathematical theory of change-ringing, the history of the teaching of mathematics at Williams, and materials for his regular Winter Study “Fantasy Novels of C. S. Lewis and Charles Williams.” In the fall, he taught a new junior/senior course on Mathematics of Investment, prepared during his leave.

He continued his work as a freelance harpsichordist and organist, which included four solo recitals as the 32^nd season of his Griffin Hall Concerts at Williams. The January program took place in the Mathematics Library at Bronfman, the first time that space has been used for a musical event. Professor Hill remains on the Board of the Association of Anglican Musicians, which he also serves on the Editorial Board and as CD reviewer.

Professor Stewart Johnson continued work in modeling, control and optimization. Recent work involves an analysis of continuous verses periodic dosing for cancer chemotherapy, modeling of hematopoietic stability under stressed conditions, and measuring performance of cyclic controls. A paper on optimal periodic chemotherapy has been submitted for publication, and a second paper on controls with lower bounds for vulnerable subsystems is in preparation. Over the summer, Professor Johnson will attend the annual meeting for the Society for Mathematical Biology, with a particular interest in the symposium on cancer dynamics.

Professor Johnson has developed phase portrait software for his differential equations course, restructured his senior seminar in dynamic modeling (which was well received by this year's seniors), and will again run the quantitative studies test and learning program this coming year.

Professor Susan Loepp continued her research in Commutative Algebra. During the summer of 1999, she advised a group of four undergraduates in the mathematics department’s SMALL research program. They were successful in proving two original results in Commutative Algebra. One result appeared in an electronic undergraduate research journal while the other has been accepted for publication in the Proceedings of the American Mathematical Society.

Professor Loepp spent the 1999-2000 year on leave at Michigan State University working with Christel Rotthaus, a well-known expert on excellent rings. Her leave was supported by Williams College and a POWRE grant from the National Science Foundation. Loepp and Rotthaus successfully proved several results, including some related to the theory of Tight Closure.

In January, Professor Loepp attended the annual Joint Mathematics Meetings in Washington DC and in April the Centennial Celebration of Commutative Algebra in Lincoln, Nebraska, where she gave a talk on her current research. Loepp gave several other talks during the year including colloquia at Hope College, Bethel College, and Williams College. She also gave two seminars at Michigan State University about her current research.

Professor Frank Morgan and his collaborators this March announced a proof of the Double Bubble Conjecture (see Science magazine, March 18, 2000 or Morgan’s Math Chat column report at http://www.maa.org/data/features/mathchat/mathchat_3_18_00.html. Their result says that the familiar double soap bubble indeed has the perfect shape: the least-area configuration to enclose and separate the two given volumes of air. The first collaborator, Michael Hutchings, a 1992 SMALL undergraduate research student, is now Szego Assistant Professor of Mathematics at Stanford University. The other two collaborators, Ritoré and Ros of the University of Granada, Spain, hosted Morgan’s sabbatical visit last spring. This May, Professor Morgan revisited southeastern Spain, giving popular talks on “The Geometry of Soap Bubbles 2000,” at Alicante, Murcia, Valencia, and Cartagena, as well as a short course for experts. The leading newspaper, El Pais, wrote: “I want to know, for example, how much Morgan’s visit is costing us. ... Unless this gentleman can explain to me how the soap bubbles of 2000 are markedly different from those of 1999, I do not understand why an academic institution would spend money for something like this.” Of course, the point is that geometry is advancing rapidly, and that what we learn about the simple geometry of soap bubbles helps us understand the more complicated geometry of the universe. There were a number of excellent responses in newspapers and on TV.

In an amazing postscript, the 1999 “SMALL” Geometry Group extended the proof of the Double Bubble Conjecture to bubbles in four-dimensional space. Incidentally, two previous Geometry Groups have current publications on crystals and immiscible fluids in Acta Crystallographica and the Pacific Journal of Mathematics.

Professor Morgan’s Math Chat Book, a popular collection of math puzzlers for folks who know nothing about math, based on Morgan's TV show and regular column at www.maa.org, appeared in January. A third edition of his Geometric Measure Theory book appeared in July, providing the first published accounts of the proof of the Double Bubble Conjecture and other new results, lavishly illustrated. He has nine other articles and appearances in print or on radio, and another ten articles in the pipeline. On the controversial question of whether the new millennium begins in 2000 or 2001, an AP release quoted him as saying that, “The inexorable mathematical logic which cannot be refuted is that the year 2000 is the last year of this millennium and 2001 is the first of the next millennium.” He has given over thirty talks.

In January 2000, Professor Morgan taught a Winter Study on Teaching School, in which Williams students worked with fourth and fifth graders and publicized the ideas the young students came up with. One group, led by Math major Brendan Kinnell ’00, followed the famous Escher in creating their own tessellations on paper and in a computer video. They appeared on Math Chat TV and wrote a press release, which resulted in a reporter’s visit and an article in the Berkshire Eagle.

This spring Morgan’s differential geometry class found themselves using Einstein’s theory of general relativity to predict minor discrepancies in the orbit of Mercury.

Professor Morgan awarded the new $1000 High School Calculus Student Award from ecalculus.org, based at Williams and UC Davis, to Beeneet Kothari at Half Hollow Hills High School West, Long Island. Beeneet has used calculus to model HIV and recommend new treatments.

Morgan has been elected as second vice-president of the Mathematical Association of America and chair of the Nominating Committee of the American Mathematical Society.

Professor Jerome Reiter enjoyed his first year at Williams College. In research, he had an article published in the American Mathematical Monthly about how causal inferences can be made using statistical methods. He also submitted an article to the Journal of Official Statistics describing methods he developed for combining information across groups to improve estimation. He talked about this research at the conference “Interface 2000” in New Orleans and at the 2000 meetings of the International Society for Bayesian Analysis in Crete. In teaching, Jerry developed lab modules for use in the department's introductory statistics courses and taught a new senior seminar on survey design and analysis. He also advised Cory Heilmann’s senior thesis on hierarchical Bayesian modeling. In service, Jerry is a General Methodology chair for the Joint Statistical Meetings of 2001. He also is a statistical advisor to North Star, a local non-profit organization seeking to measure and improve the health status of children in Berkshire County.

Professor Cesar Silva taught a new course on ergodic theory in the spring. This was a senior seminar that covered graduate-level material. He wrote the lecture notes for the course and is currently preparing them for publication.

Professor Silva continued his research in ergodic theory and had two articles published. One of the articles contains part of the theses of M. Touloumtzis ’96, E. Muehlegger ’97, and A. Raich ’98. He also had two other papers accepted for publication.

In the fall, Silva gave six lectures on Chaos and Fractals to the Berkshire Institute for Lifetime Learning. This is an organization in the Berkshires that gives classes to retired folk interested in learning new topics. The class met at the Faculty House.

He also was a reviewer for Mathematical Reviews and a referee for several journals.

Colin Adams, Williams College

“Supercrossing Number for Knots”
“Where Number Theory and Ergodic Theory Collide: Hyperbolic Surfaces Stole the Stop Sign”

H. Sanjeeva Balasuriya, Brown University

“The Bubble Bursts: A Vicious Tail”

Olga R. Beaver, Williams College

“Boolean Algebras, Quantum Logics and Hilbert Spaces: Are They Friends?”

Jennifer Beineke, Trinity College

“Splendor in the Graphs”

Hubert Bray, MIT

“Proof of the Riemannian Penrose Conjecture in General Relativity”

Edward B. Burger, Williams College

“Simultaneous Diophantine Approximation in the Vector Space Q+Q”
“Number, Reason, and Life: some Thoughts on 2000.092237442...”

Mikhail Chkhenkeli, Williams College

“The 11/8 Conjecture”

Dietmar Cieslik, University of Greifswald, Germany

“The Steiner Ratio”

Andres Del Junco, University of Toronto

“What is Ergodic Theory and What is it Good For”
“When Does Pairwise Independence Imply Independence?”

Thomas Garrity, Williams College

“Adjunction Formulas”
“How to Give a Prize Winning Talk”
“Partitions of the Plane and Cubic Irrationals”
“On Pseudoconvexity and Complex Function Theory”

Francois Graner, Universite de Grenoble, France

“Physical Foams and the Minimal Perimeter Problem”

Victor E. Hill IV, Williams College

“Change-Ringing: It’s Just Permutation Groups! Well, Not Quite”

Martin Hildebrand ’86, SUNY – Albany

“Probability, Finite Groups, Erdos, and a Case of Murphy’s Law”

Stewart Johnson, Williams College

“Applied Dynamical Systems, Optimal Control, and Applications in Chemotherapy”
“Chemotherapy and Optimal Control”
“Modeling Blood Cell Populations Using Partial, Delayed, and Ordinary Differential Equations”

Susan Loepp, Williams College

“Bad Excellent Rings”

Frank Morgan, Williams College

Mini-double-header: “The Double Bubble Conjecture” and “Mass in General Relativity”
“Some Questions about Hale’s Recent Proof of the Hexagonal Honeycomb Conjecture”

Karin Reinhold, SUNY-Albany

“On Counting Functions and Square Functions in Ergodic Theory”

Jerome Reiter, Williams College

“Borrowing Strength Without Explicit Data Pooling: Estimation with External Constraints”
“Confidentiality and Data Disclosure”

Cesar Silva, Williams College

“Student Research in Ergodic Theory”
“Visualizing Measurable Dynamics”

Robert Tubbs, University of Colorado, Boulder

“A Brief Introduction to Modern Transcendental Number Theory”

Edward Welsh ’94, Duke University

“My Trip to the Grand Canyon, or, Adventures in Modeling Surface Erosion”

Janine Wittwer, University of Chicago

“Math, Music and Fingerprints”

SMALL Commutative Algebra Group

“Completions of Rings”

SMALL Geometry Group

“The Double Bubble Conjecture”

SMALL Knot Theory Group

“Toroidally Alternating Knots”

SMALL Number Theory Group

“On Periodic Sequences and the Hermite Problem”

Katherine Acton ’00

“Impossible Tessellations: How Not to Choose Flagstones for your Patio”

Khaleefah Al-Sabah ’00

“From Duels to Truels: What to Do When You are Slapped in the Face by Two Gloves”

Patrick Andersen ’00

“Random Walk and Ruin Problems”

Lauren Buckley ’00

“Can Math Prevent Species Extinctions? The Mathematics of Species-Area Relations”

Audrey Chen ’00

“(Islamic) A R T (and group theory)”

Tegan Cheslack-Postava ’00

“A Journey into Many Dimensions”

Marlin Chu ’00

“The Problem of Appolonius”

Elise Cucchi ’00

“What you can’t do with a Compass”

William Darrin ’00

“The MARS Algorithm—Finding a Regression in a Mess”

Tom Fleming ’00

“Cubics are our Friends”

Mark Florenz ’00

“Tests of Significance”

Cory Heilmann ’00

“Tracking Computer Error”

Kristen Grippi ’00

“Dangerous Curves Ahead”

Haibo Gu ’00

“A Theory of Epidemics”

Wilmot Harkey ’00

“Jobs for Pat and Wil? Maybe, Maybe Not. An Introduction to Game Theory”

Patricia Hines ’00

“What Happens to Cats When They Get Excited?”

Stefan Hwang ’00

“The EM Algorithm: Dealing with Missing Data”

Jonathan Kallay ’00

“The Unsolvable 15-Puzzle”

SungHwan Kim ’00

“Sylow’s Theorem”

Brendan Kinnell ’00

“Implementation of Hamming Codes, or How to Win the Office Pool”

Vikram Lamba ’00

“Bargaining”

Douglas Marshall ’00

“Many-Valued Logics”

Campbell Miller ’00

“Continued Fractions”

Suela Nako ’00

“Having Trouble to the nth Degree? There is Still Hope”

Anthony Ndirango ’00

“On Proceeding Purely Formally, or Why I am NOT a Mathematician”

Dawn Nelson ’00

“A Cantor Set Turns Golden”

Shara Pilch ’00

“A Geometric Meaning for Prime Ideals”

Ravi Purushotham ’00

“Chaos: Its Not All That Complicated”

Virginia Pyle ’00

“An Exploration in Cumulative Voting”

Joshua Rathmell ’00

“Definitions of Chaos”

Kamille Richards ’00

“How to Raise a Winning Chicken”

Tanisha Salmon ’00

“Lanchester Combat Model”

Adam Schuyler ’00

“All You Need is a Few Turbles and Some Colorful Snargles”

Kevin See ’00

“Polya’s Theory of Counting”

Boudhayan Sen ’00

“Testing the Distributions of Progressively Longer Sequences”

Tessa Smith ’00

“The Struggle for Life”

Anita Spielman ’00

“Some Painless Operations on Polynomials”

Andrew Speck ’00

“The Sum of the Reciprocals of Primes, the Infinite Product of 1-1/p, and the Number of Primes”

Wayne Stephens ’00

“A Pulse Process Model of Athletic Financing”

Nathan Tefft ’00

“Do You Really Know What It Means to Be “Inside” and “Outside”

Reed Townsend ’00

“Factoring Large Integers”

Sarah White ’00

“Bayesian and Classical Statistics, Opposites Attract”

Junghee Yang ’00

“Tiling Rectangles”

Leila Zelnick ’00

“Money and Marriage: An Optimal Stopping Romance”

Colin Adams

“Newest Inductee in Number Hall of Fame”
Opening banquet presentation, Mathfest Summer Math Meetings, Providence, RI

“Supercrossing Number for Knots and Links”
Low Dimensional Topology Session, AMS Meeting, Austin, TX

“Why Knot?”
Canisius College, Buffalo, NY
Westfield State College, Westfield, MA
Portage Northern High School, Portage, MI
Kalamazoo Area Mathematics and Science Center, Kalamazoo, MI
Union College, Schenectady, NY

“The Knot Theory Workshop”
Canisius College, Buffalo, NY

“Mel Slugbate’s Real Estate in Hyperbolic Space”
Connecticut Valley Undergraduate Mathematics Colloquium, Amherst College
Cal State-Northridge, Northridge, CA
Quinnipiac College, Hamden, CT
Harvey Mudd College
Ohio MAA Sectional Meeting, Marshall University, Huntington, WV
Michigan MAA Meeting, Central Michigan University, Mt. Pleasant, MI
Florida Sectional Meeting of the MAA, Tampa, FL

“Vital Sines”
Opening banquet presentation, AMS/MAA/SIAM Math Meetings, Washington, D.C.
Harvey Mudd College

“Alternating Knots in Surface x I”
Special Session on Knots, AMS/MAA/SIAM Math Meetings, Washington, D.C.

“Hyperbolic 3-Manifolds for Fun and Profit: A Photo Album”
Claremont College, Claremont, CA

“Making Calculus Fun: How to Entertain at Parties”
Ohio MAA Sectional Meeting, Marshall University, Huntington, WV

Edward B. Burger

“Something Old, Something New, Something Borrowed, Something Blue: Becoming Engaged in Diophantine Approximation”
Macquarie University, Sydney, Australia

“On a Question of Mordell and a Spectrum of Linear Forms”
Macquarie University, Sydney, Australia

“‘This is NOT the Title of My Talk’ A Look at Paradoxes...The Dark Side of Mathematics”
Williams Alumni Association of Worcester
Rivier College
Williams Alumni Association of Cleveland
Williams Alumni Association of Toledo
Williams Alumni Association of Delaware
Williams Alumni Association of Washington, DC
Williams Alumni Association of Northeastern New York

“Playing Dodge Ball: Can It Take Us Far Beyond What We Would Expect?”
Keynote Address, 10^th Annual Sonia Kovalevsky Day, Rivier College

“Transforming Anxiety into Hatred” (with M. Starbird)
AMS-MAA-SIAM Meetings, Washington, DC

“The Y2.1K Problem: What Can the Research and Teaching Community Do to Inspire a Song Other than Math Suks?”
Keynote Address, AMS-MAA-SIAM Meetings, Washington, DC
Plenary Lecture, 2000 New York State Mathematics Association of Two Year Colleges Annual Conference, Hofstra University
Keynote Address, The Pennsylvania State System of Higher Education
Mathematics Conference, Clarion University

“Is There a Fourth Dimension? Can You See It?”
The United States Coast Guard Academy

“Can We Sum Some of the Series All of the Time?”
Marist College

“Fun and Games”
University of Hartford

“Rethinking the Standard Model of Liberal Arts Mathematics”
Invited Workshop, 2000 Intermountain Section Meeting of the Mathematical Association of America, Southern Utah University

“Innovations in Mathematics”
Keynote Address, 2000 Intermountain Section Meeting of the Mathematical Association of America, Southern Utah University

“Discovery Learning from Both Sides of the Classroom”
Discovery Seminar, The University of Texas at Austin

“Making Mathematics a Meaningful Part of a Liberal Arts Education”
Massachusetts College of Liberal Arts

“Magic with Mathematics: Is the Equation Faster than the Eye?”
University of Colorado at Boulder
Keynote Address, National Mathcounts Competition, Washington, DC

“What is Infinity?” and “What is Calculus”
Walt Whitman High School, Bethesda, MD

Richard De Veaux

“Neural Networks for Chemometrics, a Critical Evaluation”
Fall Technical Conference, American Society for Quality, Houston

“Successful Data Mining”
Short Course, Chicago

“A Guided Tour of Data Mining Tools”
Henry Stewart Conference, San Francisco
Washington, DC
Dresden Lecture II, Swarthmore College
American Statistical Association, Indianapolis

“Data Mining: An Overview”
Freddie Mac, Washington, DC
Long Beach

“Experimental Design”
Short Course, Washington, DC

“Data Mining: Fools Gold or Mother Lode?”
Dresden Lecture I, Swarthmore College

“Data Mining for Customer Relationship Management”
Short Course, ICM, Amsterdam, Netherlands

Thomas Garrity

"Factoring Polynomials”
Skidmore College

"Goals of REU Programs"
REU Conference, Washington, DC

“On Algebraic Number and Triangle Sequences”
Hudson River Undergraduate Research Conference, Siena College

Victor E. Hill IV

“Nearly So and Nearly Not: A Survey of Many-Valued Logics”
“Mathematical Aspects of the Music of Bach”
Kalamazoo College

Susan Loepp

Panelist, Project NexT Panel on Designing and Teaching Interdisciplinary Courses
Mathfest, Brown University

“Completions of Local Rings: A Bit of History and Background”
Commutative Algebra Seminar, Michigan State University

“Detecting and Correcting Errors on a Compact Disk: Useful Application of Algebra”
Fall Festival, Bethel College

“Badly Behaved Excellent Rings”
Commutative Algebra Seminar, Michigan State University

“Where Algebra and Analysis Collide: The Complete Polynomial Story”
Colloquium, Swarthmore College

“What they Didn’t Teach You in High School: The Complete Story”
Colloquium, Agnes Scott College

“Rational Numbers and Polynomials: The Complete Story”
Colloquium, Hope College

“Excellent Local Rings with Low Dimensional Generic Formal Fibers”
Centennial Celebration of Commutative Algebra, University of Nebraska

Frank Morgan

“Very Undergraduate Research”
AMS/NSA Undergraduate Research Conference, Washington, DC

“The Double Bubble Conjecture”
University of Delaware

“Recent Breakthroughs on Soap Bubble Geometry by Mathematicians and Students”
Williams and Princeton Alumni, Hanover, New Hampshire

“The Soap Bubble Geometry Contest”
Notre Dame
University of Western Michigan
Math Counts, Hartford, Connecticut
Rose-Hulman Institute of Technology
Richmond School, Hanover, New Hampshire

“Recent Breakthroughs on Three Conjectures”
Notre Dame

“Students and Mathematics in the News and on TV”
University of Western Michigan

“ContesTV 1”
Water Street Books

“ContesTV 2”
Williamstown Public Library

“Bursting the Double Bubble”
Moravian College Student Conference

“The Double Bubble Conjecture”
Rose-Hulman Institute of Technology
Worcester Polytechnic Institute

“News on the Double Bubble Conjecture, including Work by Undergraduates”
Worcester Polytechnic Institute

“The First National High School Calculus Student Award”
Half Hollow Hills High School West, Long Island

“Double Bubbles and Crystals, Minimizing Surface Area and More General Norms”
AMS meeting, University of Lowell, New Hampshire

“Proof of the Double Bubble Conjecture”
University of Connecticut, Storrs

“Soap Bubbles and Mathematics”
University of Connecticut, Storrs

“La Geometri'a de Pompas de Jabo'n 2000 [Soap Bubble Geometry 2000]”
University of Alicante, Spain
University of Murcia, Spain
University of Valencia, Spain
University of Cartagena, Spain

“Geometric Measure Theory” (four lectures)
University of Murcia, Spain

Jerome Reiter

“Borrowing Strength Without Explicit Data Pooling”
Interface 2000 New Orleans, International Society for Bayesian Analysis Meetings, Crete

Cesar E. Silva

“Power Weakly Mixing Infinite Measure Transformations”
Retirement Conference in Honor of J. R. Choksi, McGill University, Montreal

“Examples of Rank One Z^d Actions”
Special Session in Ergodic Theory and Dynamics of Z^d and R^d, AMS Annual Meeting, Washington, DC

“An Infinite Ergodic Index Measure Preserving Transformation that is not Multiply Recurrent”
Ergodic Theory Seminar, University at Albany

“On Nonsingular Chacon Transformations”
Special Session in Ergodic Theory and Dynamical Systems, AMS Meeting, Lowell

Katherine Acton
Khaleefah Al-Sabah
Patrick Andersen	Working in investment banking in technology group for Morgan Stanley Dean Witter, Boston.
Lauren Buckley	Conducting ecological field research in Yosemite National Park with the Sierra Nevada Aquatic Research Lab in Mammouth Lakes, CA in the summer. Then working at the Ecology Center in Missoula, MT in conservation biology to wildlands preservation. Then onto graduate school in biology/mathematical ecology.
Audrey Chen	Working for artist, Jenny Holzer in New York.
Tegan Cheslack-Postava
Marlin Chu	Working at Merrill Lynch in NYC in the investment banking division.
Elise Cucchi	Pursuing a Masters degree in elementary and special education at Wheelock College Graduate School of Education, Boston.
William Darrin	Working at State Street Bank and Trust in their mutual funds department as a fund accountant in Boston, MA.
Thomas Fleming	Pursuing a Ph.D. in Mathematics at the University of California, San Diego.
Mark Florenz	Peace corps
Kristen Grippi	Working in investment banking at Goldman Sachs in New York City.
Haibo Gu	Working in Hong Kong
Wilmot Harkey	Working at Village Venture Services, Inc. in Williamstown, MA.
Cory Heilmann	Graduate School in Statistics at Iowa State
Patricia Hines	Working for an asset management firm in Boston for one year to be followed by graduate school in environmental engineering
Stefan Hwang	Working at IT Consulting, American Management Systems in Fairfax, VA.
Jonathan Kallay	Giving bike tours this summer then moving to Chicago.
SungHwan Kim	Pursuing a Masters in Architecture Design at Harvard University.
Vikram Lamba	Working for the acquisition finance group of CIBC (part of the Oppenheimer Group), in New York City.
Douglas Marshall	Living in Somerville, MA applying to graduate schools in philosophy.
John Miller	Working at CIP Capital in Wayne, PA.
Suela Nako
Anthony Ndirango	Pursuing a Ph.D. in theoretical physics at the University of Capetown (South Africa)
Dawn Nelson	Teaching math at the Bromfield School in Harvard, MA.
Shara Pilch	Teaching math while receiving a masters in curriculum instruction and classroom education at Mississippi Teacher Corps on the Mississippi Delta in Webb, MS.
Ravi Purushotham
Virginia Pyle	Working as a litigation assistant at Conley and Hodge in Boston, MA.
Joshua Rathmell
Kamille Richards
Tanisha Salmon	Working in management consulting at A.T. Kearney in Atlanta, GA.
Adam Schuyler	Pursuing a Ph.D. in Mechanical Engineering at Johns Hopkins University, Baltimore, MD.
Kevin See	Teaching mathematics in New England.
Boudhayan Sen	Working in financial/statistical analyses at Mercer Management Consulting in Lexington, MA.
Andrew Speck	Attending graduate school in Physics at Harvard University.
Anita Spielman
Nathan Tefft
Reed Townsend	Working on computer graphics for Microsoft in Seattle, WA.
Sarah White
Junghee Yang
Leila Zelnick	Working in community tourism development with the Peace Corps in Bolivia.