MATHEMATICS AND STATISTICS DEPARTMENT

At Reunions 2006, we held our second annual reception. Williams alums were invited to come by to say hello to the old profs, meet some new ones, see some students, and enjoy one more of our famous ‘Teas.’

At the 2006 annual math meetings in San Antonio, Professors Adams, Garrity, and Burger presented their famous “Great /e Debate” to a crowd that packed the room and the adjoining corridor. It was followed by a reception for all friends of Williams. Attendants included present and former faculty and students Colin Adams, Ollie Beaver, Ed Burger, Pippa Charters, Misha Chkhenkeli, Tim Comar, Joe Corneli, David Craft, Carl Erickson, Joel Foisy, Tom Garrity, Jesse Gell-Redman, Gary Gordon, Nathan Kaplan, Brian Katz, David Jensen, Michelle Lee, Liz McMahon, Frank Morgan, Allison Pacelli, Andy Raich, Juan Ramos, Chris and Susan Roosenraad, Vojislav Sesum, Henry Walker, Nick Yates, and many other friends. For more information and pictures, follow the alum link at our webpage at http://www.williams.edu/Mathematics.

The faculty celebrating one of its treasured possessions:
Frank Morgan

ABC’s World News Tonight on February 24, 2006, featured Yale statistician Jay Emerson ‘92, on the effect of dropping three judges’ scores in Olympic figure skating.

Professor Colin Adams became the chair of the Haimo Awards Committee, which decides on the winners of the national mathematics teaching awards each year.

Professor Ollie Beaver spent the past year particularly involved in issues concerning quantitative literacy and diversity in the sciences. In the fall, she was invited to Amherst College to lead a visiting committee to review Amherst’s Quantitative Center. Also in the fall, she participated with other Williams College colleagues in the first series of the national Symposia on Diversity in the Sciences, held at Harvard University. As a result of the discussions in the Harvard Symposium, Beaver initiated a study group pilot project in a spring calculus course. In the January term, Beaver attended a Wellesley workshop on Supplemental Instruction as well as the Joint Mathematics meetings held in San Antonio. At Williams, Beaver was chair of the Calendar and Schedule Committee, continued her involvement with the Mellon Mays Undergraduate Fellowship program, and with the Robert L. Gaudino Memorial Fund as a trustee. She was awarded Williams funding for a CRAAS course (Critical Reasoning and Analytical Skills), which she will apply for developing modules for the Quantitative Studies course. Beaver continues to teach in and coordinate the mathematics component of the Summer Science Program.

This year, Professor Carsten Botts’ research has been an extension of the ideas and concepts developed in his thesis. He submitted a paper with Michael Daniels (at the University of Florida) entitled “Likelihood Approximations in Bayesian Multiple Curve Fitting” this January, and had another paper, “A Shrinkage Estimator for the Spectral Density” appear in Biometrika’s March 2006 issue. He is currently exploring ideas on how to use Markov chain Monte Carlo methods to improve the shrinkage estimator studied in this Biometrika paper.

Professor Burger continued his research in number theory. This summer he was one of the SMALL NSF-REU advisors for a group of four undergraduates including Nicholas Yates ’06 and Ross Kravitz ’07. The group authored the article “Shrinking the period lengths of continued fractions while still capturing convergents” that will be submitted for publication. Burger was also the thesis advisor for Nick Yates ‘06 who produced an honors thesis entitled, “Diophantine Approximation through Nonsimple Continued Fractions and Planar Curves.” He delivered two invited lectures in special sessions on his research at two national mathematics conferences. In the spring term, he offered a new tutorial entitled Explorations in Number Theory and Geometry.

In September, Burger, together with M. Starbird, published a general-audience trade book entitled Coincidences, Chaos, And All That Math Jazz (W.W. Norton & Company). The book will soon appear in Chinese, Korean, and Japanese. He completed his next book, Extending the Frontiers of Mathematics: Inquiries into Proof and Argument (to appear in August). He also completed a series of mathematics videos that accompany six new texts published this year by Holt, Rinehart & Winston, as well as a series of interviews produced by Discovery Education.

Burger served 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 was also reappointed to another term as Associate Editor of the American Mathematical Monthly. In May, he appeared on the Reader’s Digest annual list of “100 Best of America.”

Professor Burger gave over thirty invited addresses at various conferences and institutions including the Smithsonian Institution. In addition, he went on a seven-city book tour and give 27 radio and television interviews including WABC-TV, WABC-AM, KERA-AM, WPFW-FM, WAMU-FM, WTMD-FM, and the ABC Syndicated Radio Network.

Professor Satyan Devadoss spent this year on sabbatical leave at the Ohio State University. Other than working on research, he was the senior thesis advisor to Tomio Ueda, a Williams math major working on flat-folding origami using thick paper.

Professor Tom Garrity has continued his research in number theory. He participated in a debate about the relative merits of e and pi with Colin Adams and Ed Burger, at a Summer Science Lunch and for the First Year Family weekend in October. They redid the debate at the national joint meeting of mathematician in January of 2006 in San Antonio. He organized an all day event in January, called the Szemeredi festival, during which many faculty members discussed aspects of Terrence Tao’s “The Dichotomy between Structure and Randomness, Arithmetic Progression, and the Primes.” Outside of Williams, he spoke in the Valley Geometry Seminar, at the University of Massachusetts, Amherst; at a special session for continued fractions at the AMS-MAA Meeting, in San Antonio; and at Tulane. He became the director of Williams’ Project for Effective Teaching (Project PET) in January.

Professor Stewart Johnson continues his research in dynamical systems, modeling, and optimal control with a focus on optimal periodic switching strategies. 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. Professor Johnson is continuing to explore generic forms and the types of behavior possible in degenerate cases.

Professor Johnson supervised a thesis by Christina Brakken-Thal ‘06 on implementing variation in maturation time in a blood cell model. Applying this model to cyclic variations, she has demonstrated that stochasticity has a dramatic effect on the amplitude of oscillations, contrary to current assumptions in this research area. Her work contributes to better modeling of blood cell populations, which can be applied to a variety of blood disorders and may lead to more efficient use of chemotherapy and blood cell stimulants. 

Professor Johnson continues as a statistical consultant for research conducted at Neurological Consultants of Bennington by Dr. Keith Edwards, ‘69. This research establishes the safety and efficacy of Galantamine as treatment for dementia with Lewy bodies. Results are being prepared for publication.

Professor Johnson remains active in the college wide Quantitative Studies program that provides early identification and intervention for students with quantitative deficiencies.

Professor Bernhard Klingenberg published two papers with Alan Agresti on the analyses of multivariate binary data with application to drug safety evaluation: The paper “Multivariate Tests Comparing Binomial Probabilities, with Application to Safety Studies for Drugs” appeared in The Journal of the Royal Statistical Society, Series C, Applied Statistics, and the paper “A Multivariate Extension of McNemar’s Test” will appear in Biometrics.

Further, Bernhard gave an invited talk about statistical drug safety analyses at the meeting of the International Biometric Society, Section Austria-Swiss, in Graz, Austria.

Professor Susan Loepp, along with her students, continued working on research in commutative algebra. The paper, “Controlling Formal Fibers of Principal Prime Ideals,” written by her SMALL 2003 commutative algebra group, Ariana Dundon, David Jensen, Susan Loepp, John Provine, and Jordan Rodu, was accepted for publication in the Rocky Mountain Journal of Mathematics. In addition, the paper “Chains of Rings with Local Formal Fibers,” by Kai Chen, Susan Loepp, and John Provine, was accepted for publication in Communications in Algebra.

Loepp and William Wootters (Physics) will once again teach their interdisciplinary course on protecting information in the spring of 2007. Their book, Protecting Information: From Classical Error Correction to Quantum Cryptography, based on the course, was published by Cambridge University Press in 2006.

During the summer of 2005, Loepp advised the SMALL commutative algebra group. The members consisted of John Chatlos, Brian Simanek, Sherry Wu, and Nathaniel Watson. They have written two manuscripts based on their work over the summer and plan to submit them to refereed research journals in mathematics.

Professor Frank Morgan published two texts for the pure and applied versions of the mathematics major core requirement in real analysis. The applied text includes Fourier series and the calculus of variations: minimal surfaces, physics, economics, Riemannian geometry, and general relativity. He launched a new course in Investment Mathematics, including the Nobel-Prize-winning Black-Scholes equation for pricing stock options.

Morgan published five research papers and has seven others in process. With Garrity, he wrote a note on “Teaching Tips” for the American Mathematical Society website. His two honors thesis students, Michelle Lee and Vojislav Sesum, both veterans of his undergraduate research Geometry Group, studied isoperimetric problems. His joint paper with his 2004 honors thesis student Jonathan Lovett (now Hillary Clinton’s speech writer) will appear in The American Mathematical Monthly. For summer 2006 his Geometry Group includes Colin Carroll ‘07 and Conor Quinn ‘07. Morgan serves as Director of the Williams College National Science Foundation SMALL undergraduate research project.

Morgan has given over twenty talks this year, including an invited lecture at the Geometry Festival and some lectures at the National Autonomous University in Mexico. For his 2006-2007 sabbatical, Morgan is considering visits to Spain, Portugal, Italy, Switzerland, Germany, Canada, Korea, Vietnam, Singapore, and Hong Kong.

Professor Allison Pacelli continued her research in algebraic number theory. She had one paper appear in the Journal of Number Theory, while another (with Yoonjin Lee) was accepted by the Journal of Pure and Applied Algebra. She received two travel grants this year from the Association for Women in Mathematics including a mentoring travel grant to work with Florian Luca.

Last summer, she supervised the SMALL 2005 Algebraic Number Theory group who did work on class groups of number fields and function fields. The resulting paper (with Carl Erickson, Nathan Kaplan, Neil Mendoza ’07, Allison M. Pacelli, and Todd Shayler ’06) was submitted for publication. The students won awards for presenting their work at Mathfest 2005 and the Joint Mathematics Meetings in January 2006. During the year, Pacelli advised the senior honors thesis of Elizabeth Adams ’06.

In addition to speaking at the department’s Faculty Seminar in March, Pacelli was invited to speak at the Number Theory Inspired by Cryptography Workshop at the Banff International Research Station, the Colby College Undergraduate Mathematics Seminar, the Union College 2005 Mathematics Conference, the Union College Undergraduate Mathematics Seminar, the Front Range Number Theory Seminar at the University of Wyoming, and the Centre de Recherches Mathématiques at the University of Montréal.

In fall 2005, Silva taught a linear algebra tutorial and a course on chaos and fractals. In the spring, he taught the second semester calculus course. For the chaos and fractals course, Robin Stewart, a student in the class, wrote a nice fractals program that will be made available in the future. He continued his research in ergodic theory and the writing of a book that he plans to use in his ergodic theory tutorial in fall 2006. 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. In summer 2005, he supervised SMALL research group in ergodic theory consisting of J. Kingsbery ‘06, A. Levin, and A. Preygel.

Professor Mihai Stoiciu taught calculus, linear algebra and a new senior seminar class called Functional Analysis with Applications to Mathematical Physics. He continued his research in mathematical physics and was invited to give talks at the Centre de Recherches Mathématiques Montréal, Banff International Research Station, Oberwolfach Mathematics Institute, Wesleyan University, University of Michigan and Northeastern University. His paper “The Statistical Distribution of the Zeros of Random Paraorthogonal Polynomials on the Unit Circle” was published in the Journal of Approximation Theory.

Stoiciu gave a Science Lunch talk at Williams in November 2005 and two Faculty Seminars in September 2005 and February 2006. He also gave a lecture at the Joint Physics-Astronomy-Mathematics Colloquium and a talk at the Szemeredi Festival organized by the Mathematics and Statistics Department.

During the year, Stoiciu organized and ran a weekly math problem-solving club called “Math Puzzle Night.” Its purpose was to attract students interest in solving math quizzes and olympiad-type problems and to prepare them for various mathematics competitions. This year, the Williams College Mathematics Team won the traditional Green Chicken Mathematics Competition and had a good performance in the Putnam Competition.

Professor Kristopher Tapp attended a conference in Muenster, Germany on “Curvature and Global Shape.” He spoke there about his recent research on positive curvature obstructions. During the academic year, his research focused on left-invariant metrics on Lie groups, in part with collaborators at Dartmouth and Middlebury. He has just finished writing up his discoveries for publication. He plans to do follow-up research with a team of five undergraduates this summer. He also recently completed and submitted for publication an article on large holonomy groups.

Colin Adams, Williams College

“Making Your Bed and Sleeping in It: How Rumpled Is That Surface?”
“Layered Surfaces in Alternating Knot Complements”
BArT

“BArT Charter School Student Presentations: Problems of the Week”
Robert Benedetto, Amherst College

“Counting Rational Points in Polynomial Dynamics”
Carsten Botts, University of Florida

“Likelihood Approximations in Bayesian Multiple Curve Fitting”
Edward Burger, Williams College

“Conjugate Coupling”
David Craft, Williams College

“Multiobjective Optimization for Radiation Treatment Planning in Cancer Therapy”
Robert L. Devaney, Boston University

“Chaos Games and Fractal Images”
Thomas Garrity, Williams College

“Multidimensional Continued Fractions and Elementary Toric Geometry”
Edward Gollin, Williams College

“Structures and Properties: A Mathematical View of Some Musical Materials”
Martin Hildebrand, SUNY, Albany

“On a Question of Chung, Diaconis, and Graham”
Theron Hitchman, Rice University

“Having a Lot of Symmetry Is Difficult”
Michael Keane, Wesleyan University

“On Spontaneous Emergence of Opinions: Results and Conjectures Concerning Reinforced Random Walks”
Stephen Kennedy and Deanna Haunsperger, Carleton College

“Halving Your Cake”
Bernhard Klingenberg, Williams College and Aldo Solari

“Analysis of Multivariate Categorical Data with Applications to Safety Studies for Drugs”
Susan Loepp, Williams College

“Generic Formal Fibers”
“Principal Prime Ideals and Their Formal Fibers”
“An Introduction to Szemeredi’s Theorem”
Szemerdi Festival
Florian Luca, Instituto de Matematicas de la UNAM

“What We Know and Don’t Know about Heron Triangles”
Russ Merris, Williams College

“Graphic Sequences”
Frank Morgan, Williams College

“Gauss Space”
“Manifolds with Density”
Omayra Ortega, University of Iowa

“Cost-Benefit Analysis of a Rotavirus Immunization Program in the Arab Republic of Egypt”
Allison Pacelli, Williams College

“Algebraic Number Theory: From Fermat to Function Fields”
“Class Groups of Quadratic Fields”
David Park, Williams College

“The Random Distribution of Primes”
Michael Rosen, Brown University

“Integral Polynomials Modulo p”
Cesar Silva, Williams College

“Introduction to Measurable Dynamics”
“Sensitive Dependence and Measurable Dynamics”
Ben Stephens, MIT

“Thread-Wire Surfaces”
Mihai Stoiciu, Williams College

“Random Matrices and the Riemann Hypothesis”
“The Distribution of the Eigenvalues of Random CMV Matrices”
“An Introduction to the Knowledge Space Theory”
Craig Sutton, Dartmouth College

“The Length Spectrum and the Torus Method”
Kristopher Tapp, Williams College

“Symmetry and Positive Curvature”
“Lie Groups and Positive Curvature”

Select SMALL Groups, Williams College

“SMALL Undergraduate Mathematics Research Group Reports”
Elizabeth Adams ’06

“Elliptic Curves, Rational Points, and an Old Greek Guy”
Adam Ain ’06

“The Ideal Lifespan”
Syed Akhtar ’06

“Fundamental Solution of Partial Differential Equations”
Nasser Al-Sabah ’06

“Newton’s Kissing Problem”
Alexander Bal ’06

“Waiting Times for Patterns”
Katherine Belshe ’06

“FM Sound Waves and Chowning Synthesizers”
Kathleen Beutel ’06

“Dynamical Systems, Iterated Maps and the Feigenbaum Constants: Finding Order in Chaos”
Joshua Bolton ’06

“The Cake-Cutting Dilemma”
Christina Brakken-Thal ’06

“Modeling the Effect of HIV Vaccines on Controlling the HIV Epidemic”
Andrea Burke ’06

“The Rationality of Irrationals: An Introduction to Continued Fractions and Quadratic Irrationals”
Caroline Byrnes ’06

“Modeling the Anomalies of Human Decision-Making”
Margaret Carr ’06

“Synchronization of Pulse-Coupled Biological Oscillators”
Heather Casteel ’06

“The Weierstrass Approximation Theorem”
Elizabeth Cowen ’06

“Normed Vector Spaces”
Seth Daniels ’06

“An Unmeasurable Set”
Jonathan Dowse ’06

“The Harmony of the Spheres”
Christopher Geissler ’06

“Modelling a Nash Equilibrium in 2x2 Games where Complexity Is Costly”
Eric Gottenborg ’06

“Generalized Reed Solomon Codes”
Kathleen Harkey ’06

“The Hat Game”
Neal Holtschulte ’06

“Adaptation and Optimization in Complex Domains”
Raphael Seunghyun Jeong ’06

“Understanding Musical (Complex) Tone”
James Kingsbery ’06

“Cellular Automata: From Pretty Pictures to Rigorous Mathematics”
Daniel Klein ’06

“A New Estimate for the Stretchiness of Square Matrices”
Michelle Lee ’06

“Algebraic Geometry”
David Letzler ’06

“Applying the Fredholm Alternative to Integral Operators”
Ruoweng Liu ’06

“Transcending Hilbert’s Seventh Problem”
Adrian Martinez ’06

“The Implications of a Walk through Manhattan on Tiling Aztec Diamonds”
Karl Naden ’06

“Duality in Linear Programming”
Brian O’Connor ’06

“Optimal Linear Predictors”
Aaron Pinsky ’06

“Bayesian Statistics and Applications”
George Price ’06

“The abc Conjecture”
Susan Reid ’06

“Laplace Transforms”
Hyejin Rho ’06

“Fermat Primes and the Sides of Heron Triangles”
David Rodriguez ’06

“Digital Image Compression Using Wavelets”
Carol Rosenberg ’06

“Polygonal Numbers and an Old Claim of Fermat’s”
Vojislav Sesum ’06

“The Anderson’s Localization: A Mathematical Proof”
Lisetta Shah ’06

“Evolutionarily Stable Strategies in Symmetric 2-Player Games”
Todd Shayler ’06

“Smashed Crossings”
Megan Smedinghoff ’06

“How to Cheat at Solving Differential Equations”
Alexander Smith ’06

“The Continued Fraction Expansion of e”
Christopher Steverson ’06

“Gödel’s Completeness Theorem”
Tomio Ueda ’06

“The Million Dollar Sudoku Puzzle”
Leah Weintraub ’06

“Reconstructing Pascal’s Triangle for Twin Primes”
Ya Xu ’06

“Bayesian Curve-Fitting with Piecewise Cubic Splines”
Nicholas Yates ’06

“You Can Never Be Past Your Prime: Dirichlet’s Theorem on Primes in Arithmetic Progressions”

Colin Adams

“Mel Slugbate’s Real Estate in Hyperbolic Space”
University of Colorado, Boulder

“A Pictorial Introduction to Hyperbolic 3-Manifolds”
University of Colorado, Boulder
Friends of Mathematics Lectures, Kansas State University

“Blown Away: What Knot to Do When Sailing”
Friends of Mathematics, Lectures, Kansas State University
American University; Illinois Sectional MAA Meeting, North Central College, Naperville, IL
AMTNYC Summer Workshop Conference, Plattsburgh, NY
Wellesley College; Sacred Heart University, Fairfield, CT

“The Great pi Debate”
AMS/MAA National Meetings, San Antonio, TX

“Knot Theory Workshop”
Illinois Sectional MAA Meeting, North Central College, Naperville, IL
Edward B. Burger

Conferences Lectures:
Metropolitan Mathematics Club of Chicago, Annual Address, Chicago, IL
CAMT Conference, Hour Address, Dallas, TX
MAA PMET Workshop, Invited Speaker, Bowling Green State University
IDS Leadership Conference, Keynote Address, Dallas, TX
Special Session in Gems of Number Theory, Invited Speaker, Albuquerque, NM
NCTM Regional Meeting, Keynote Address, Hartford, CT
44^th Northwest Mathematics Conference, Keynote Address, Portland, OR
8^th Annual Michigan Undergraduate Mathematics Conference, Keynote Address, University of Michigan-Flint
NCTM Regional Meeting, Keynote Address, Harrisonburg, PA
AMS Special Session on Continued Fractions, Invited Speaker, AMS/MAA Meetings, San Antonio, TX
West Virginia Higher Education Math Symposium, Keynote Address, Marshall University
28^th Pi Mu Epsilon Conference, Keynote Addresses, Saint John’s University
NCTM Annual Meeting, Invited Address, Saint Louis, MO
4^th Annual Northeastern Section of the MAA Regional Meeting in Memory of K.J. Preskenis, Keynote Address, Framingham State College

Mathematics Colloquia:
United States Coast Guard Academy
Emma Willard School
Fordham University
University of Hartford
American Community Schools of Athens, Greece
St. John Fisher College
The University of the South

Public Addresses:
Barnes and Noble Bookstore, Manhattan, NY
Harvard Book Store, Cambridge, MA
The Smithsonian Institute, Washington, DC
New York State Writers Institute, Albany, NY
Powell’s Bookstore, Portland, OR
Amherst Books, Amherst, MA
Authors at the Athenaeum Series, Lenox, MA
Williams Alumni Association of Northern California
Berkshire Institute of Lifetime Learning, Lenox, MA
ABC News Now, WABC-TV, New York, NY
Thomas Garrity

“How to Lecture”
Project NeXT, Providence, RI

“Toric Varieties and Multidimensional Continued Fractions”
Valley Geometry Seminar, University of Massachusetts, Amherst
Special Session on Continued Fractions, AMS-MAA Meeting, San Antonio, TX
Tulane University
Frank Morgan

“Soap Bubbles and Mathematics”
Harvey Mudd College; MathCounts, Hartford, CT

“The Double Bubble Theorem”
University of Houston

“Geometric Measure Theory and Isoperimetric Problems”
Graduate Student Seminar, University of Houston

“Manifolds with Density”
Rice University; Geometry Festival, University of Pennsylvania
National Mathematics Meetings, San Antonio; Vanderbilt University

“Undergraduate Mathematics Research”
National Mathematics Meetings, San Antonio

“Double Bubbles in the Torus” (Mathematics Club)
Vanderbilt University

“The Mathematics of Soap Bubbles”
Ensworth High School, Nashville, TN

“Soap Bubbles, Mathematics, and Williams”
Hilton Head Mini-Reunion Class of 1957

“Bounds on the Partition Function”
Hudson River Undergraduate Mathematics Conference; Westfield State College

“Geometric Measure Theory and Open Problems”
Universidad Nacional Autónoma de México

“Isoperimetric Problems: An Introduction and Challenge”
Lafayette College

“Isoperimetric Problems, Including Open Problems for Mathematicians and Undergraduates”
Invited Speaker, Geometry-Topology Conference, Lehigh University

“Double Bubbles and Gauss Space”
MAA Invited Speaker, California State University, Channel Islands

“National High School Calculus Student Award”
Jackson Preparatory School, Mississippi
Allison Pacelli

“High n-Rank in Class Groups of Global Fields”
Number Theory Inspired by Cryptography Workshop, Banff International Research Station
Union College Mathematics Conference

“Polynomials, Primes, and Fermat’s Last Theorem”
Colby College Undergraduate Mathematics Seminar

“Algebraic Number Theory: My “Ideal” Summer”
Union College Undergraduate Mathematics Seminar

“Unit Rank and the Rank of the Class Group of a Global Function Field”
Front Range Number Theory Colloquium, University of Wyoming

“Class Groups with High n-Rank”
Centre de Recherches Mathématiques, University of Montreal
Cesar Silva

“On Measure-Preserving C^1 Transformations of Compact-Open Subsets of Non-Archimedean Local Fields”
Special Session in Measurable, Symbolic and Tiling Dynamical Systems, American Mathematical Society
Fall Eastern Meeting, Bard College, October 2005.

“Mixing Rank-One Actions of Locally Compact Abelian Groups,”
International Conference on Harmonic Analysis and Ergodic Theory, DePaul University, Chicago, December 2005.

“Measure-Preserving Locally Scaling Transformations of Compact-Open Subsets of Non-Archimedean Local Fields” Canadian Mathematical Society Winter Meeting, Victoria, BC, Canada, December 2005.

“Mixing Notions And Examples on the Class of Zero Entropy Processes”
Center for Applied Mathematics Colloquium, Cornell University, March 2006.
Mihai Stoiciu

Probability and Mathematical Physics Conference, Centre de Recherches Mathématiques, Montreal, Quebec

Order, Disorder, and Transport - Conference on Recent Advances in Schrödinger Operator Theory,
Banff International Research Station, Banff, Alberta

L²-Spectral Invariants and the Integrated Density of States Workshop
Oberwolfach Mathematics Institute - Oberwolfach, Germany

Ergodic Theory and Topological Dynamics Seminar
Wesleyan University, Middletown, CT

Complex Analysis Seminar, University of Michigan, Ann Arbor, MI

Analysis and Geometry Seminar, Northeastern University, Boston, MA
Kristopher Tapp

“Obstructions to Positive Curvature on Homogeneous Bundles”
Muenster, Germany