# Faculty News Briefs

### January 2007

A paper by Professor Richard S. Ellis and two former Ph.D. students in our department, Marius Costeniuc and Peter Otto, has been accepted for publication in Journal of Statistical Physics. The 60-page paper is entitled *Multiple Critical Behavior of Probabilistic Limit Theorems in the Neighborhood of a Tricritical Point.* After receiving his Ph.D. in 2005, Marius spent a year as a postdoctoral associate at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany. He is currently enrolled in the Master of Advanced Studies Program in Finance in Zurich, Switzerland. Peter received his Ph.D. in 2004. After holding temporary positions at Gettysburg University and Union College, he now has a tenure-track position at Willamette University in Salem, Oregon.

Professor Rob Kusner was recently invited to serve on a National Science Foundation panel reviewing proposals in geometric analysis.

Visiting Assistant Professor Ralf Schiffler attended the winter meeting of the Canadian Mathematical Society in Toronto. He gave a talk at the meeting entitled *m-Cluster Categories and m-Replicated Algebras*.

### December 2006

Visiting Assistant Professor Ana-Maria Castravet gave a talk on November 7, 2006 in the Harvard-MIT Algebraic Geometry Seminar. The title of her talk was *HilbertÌs 14th problem and Cox Rings,* based on joint work with Jenia Tevelev.

Professor Paul Gunnells gave a talk on November 15, 2006 at the Algebra and Number Theory Seminar at the University of Maryland. The title of his talk was *Quadratic Weyl Multiple Dirichlet Series.*

Professor Farshid Hajir gave a colloquium on November 3, 2006 at McMaster University in Hamilton, Ontario, Canada. The title of his talk was *Galois Groups and Dynamics on the Projective Line.*

Professor Panos Kevrekidis was informed on November 2, 2006 that his paper *Deciding the Nature of the Coarse Equation through Microscopic Simulations: The Baby-Bathwater Scheme* was chosen as the next SIGEST selection from Multiscale Modeling and Simulation, a journal published by the Society for Industrial and Applied Mathematics (SIAM). Cowritten with Ju Li, C.W. Gear, and I. G. Kevrekidis, the paper will appear in issue 49-2 of SIAM Review in June 2007. The purpose of the SIGEST propgram is to make the more than 10,000 readers of SIAM Review aware of exceptional papers published in SIAMÌs specialized journals. The paper by Panos and his collaborators was chosen by the editors of SIAM Review *for the importance of its contributions and topic, its clear writing style, and its broad interest for the SIAM community.*

Professor Jenia Tevelev gave a talk on October 31, 2006 at the Commutative Algebra and Algebraic Geometry Seminar at the University of California at Berkeley. The title of his talk was *Modular, Log Canonical, And Tropical Compactifications.* He gave another talk on November 3 at the Algebraic Geometry Seminar at Stanford University. The title of his second talk was *Geometry of Chow Quotients of Grassmannians*.

### November 2006

Professor George Avrunin has been named a Distinguished Scientist by the Association for Computing Machinery for having *made a significant impact in the fields of computing, computer science and information technology.* One of 49 people given this honor, George is the Associate Head of the Department as well as an adjunct professor in the Department of Computer Science. He is currently investigating finite-state verification techniques as applied to high-performance scientific computing and to complex medical processes. In order to view the list of 2006 ACM Distinguished Members and for information on selection criteria, visit http://distinguished.acm.org.

Professor Tom Braden was co-organizer of a special session at the meeting of the American Mathematical Society in Storrs, CT during the weekend of October 28Ò29, 2006. The title of the special session was "Combinatorial Techniques in Equivariant Topology".

Professor Eduardo Cattani has been appointed to the American Mathematical SocietyÌs Committee on Human Rights of Mathematicians. The appointment, made by AMS President James Arthur, is for a three-year term effective February 1, 2007. The Committee on Human Rights assists the AMS by investigating alleged violations of human rights of foreign mathematicians, whether they may have occurred in the US or abroad, and by recommending appropriate action whenever actions seems warranted.

Eli Cooper spoke on part of his dissertation work at the Storrs AMS special session on Geometric Analysis in October 2006; the special session was co-organized by his advisor, Professor Rob Kusner. Because a scheduled speaker canceled, fellow graduate student, Shabnam Beheshti, gave an impromptu lecture on her dissertation work, which is being directed by Professor Emeritus Floyd Williams. When another speakerÌs flight was delayed, Rob also came off the bench to pinch-speak about his work with session co-organizer Jesse Ratzkin on *Nondegeneracy of CMC Surfaces and Regularity of the CMC Classifying Map,* a talk that he expanded upon at the Valley Geometry Seminar six days later.

Professor Richard S. Ellis was the main speaker at the International Seminar on Extreme Events in Complex Dynamics, held during the week October 23Ò27, 2006 at the Max Planck Institute for Physics of Complex Systems in Dresden, Germany. At the seminar Richard delivered an eight-hour lecture series entitled *The Theory of Large Deviations and Applications to Statistical Mechanics.*

Professor Franz Pedit participated in the biennial Geometrie Tagung at the Mathematisches Forschungsintitut Oberwolfach in October, 2006.

Visiting Assistant Professor Ralf Schiffler attended the International Conference on Representations of Algebras and Related Topics held at Northeastern University on October 6Ò7, 2006. He gave a talk at the conference entitled *Geometric Realizations of Cluster Categories.*

Visiting Assistant Professor Hao Wu gave a talk on October 27, 2006 in the Topology and Geometry Seminar at University of Wisconsin-Madison. His talk was entitled *Transversal Knots and Khovanov-Rozansky Cohomology.* He also gave a 20-minute condensed version of the same talk in the special session on *Floer Methods in Low-dimensional Topology* during the Fall 2006 Western Section Meeting of the American Mathematical Society held in Salt Lake City, UT. In June 2006 he gave a talk entitled *Legendrian Knots and the Spanning Tree Model of the Khovanov Homology* at the Park City Mathematical Institute.

### October 2006

Professor Farshid Hajir and graduate student Mairead Greene attended the Quebec-Maine Number Theory Conference, which took place in Quebec City on September 30 and October 1. MaireadÌs contributed talk was entitled *On the Index of Cyclotomic Units,* and Farshid gave a plenary address on *Algebraic Properties of Some Hypergeometric Polynomials.* John Cullinan, who obtained his Ph.D. at UMass Amherst under the direction of Professor Siman Wong and is now a visiting assistant professor at Bard College, also gave a lecture at the conference. His lecture was entitled *Divisibility Properties of the Torsion Subgroup of an Abelian Variety.*

Professor Panos Kevrekidis reports on the following activities.

In April 2006 he presented a colloquium jointly sponsored by the Department of Mathematics and the Department of Chemical Engineering at Worcester Polytechnic Institute. His talk was entitled *Discrete Solitary Waves and Applications.*

In July 2006 Panos organized jointly with Mason Porter a mini-symposium entitled *Analysis, Computation, and Experiments in Bose-Einstein Condensates* at the annual SIAM meeting in Boston, MA.

In September 2006, Panos attended the SIAM meeting on Nonlinear Waves in Seattle, WA along with Professor Nate Whitaker and Visiting Assistant Professors Adri∑n EspÃnola-Rocha and Hadi Susanto. At the same meeting, Professor Nate Whitaker and he co-organized a session on *Analysis, Modeling, and Simulation of Biological Systems.* In addition, Panos gave an invited talk at the mini-symposium organized by J. Yang and T. Lakoba and entitled *Advances in Analytical and Numerical Techniques for Nonlinear Waves.* The talk was entitled *Solitary Waves in the Presence of Spatial or Temporal Periodicity: Some Case Examples.*

In September 2006 Panos also attended the conference *SoliQuantum: Solitons and Nonlinear Phenomena in Degenerate Quantum Gases,* which took place in Cuenca, Spain. He also presented an invited talk entitled *Solitons Under Temporal or Spatial Periodicities* at that meeting.

Finally, PanosÌs research work with a CalTech group consisting of Martin Centurion, Mason A. Porter, and Demitri Psaltis has attracted worldwide attention by science and technology news sources. The topic of the research is the first experimental realization of the theoretical concept of *nonlinearity management.* In particular, their paper published in Physical Review Letters, Volume 97, No. 3: 033903 has been featured in Physical Review Focus http://focus.aps.org/story/v18/st1>, a CalTech press release http://pr.caltech.edu/media/Press_Releases/PR12881.html>, and numerous other websites including PhysOrg.com, Science Daily, PhysLink.com, Science News Daily, WhatÌs Next in Science & Technology, Pasadena Independent, Softpedia, and Technology Horizons. Detailed links can be found at the URL http://www.its.caltech.edu/~mason/research/#optics>. Two more articles on this topic are about to appear in Photonics Spectra in October 2006 and in CalTech's research quarterly, Engineering and Science.

Professor Rob Kusner recently participated in the biennial Geometrie Tagung at the Mathematisches Forschungsintitut Oberwolfach, using the opportunity to continue a long-standing collaboration with colleagues from Berlin and Darmstadt, Germany.

Visiting Assistant Professor Ralf Schiffler gave a sixty-minute talk at the International Meeting on Representation Theory of Algebras, which took place in Sherbrooke, Canada on September 22Ò24. The title of his talk was *Geometric Realizations of Cluster Categories.* He also participated in a Meeting on Homology and Deformations in Algebra, Geometry and Representations at the CIRM in Luminy, France on September 25Ò29, where he gave a thirty-minute talk entitled *Les Categories Amass»es et les Algebres Repliqu»es*.

### September 2006

Professor Erin Conlon organized an invited session entitled *Statistical Methods in Genetics and Public Health* for the International Chinese Statistical Association 2006 Applied Statistics Symposium, which was held during the period June 14Ò17, 2006 in Storrs, Connecticut.

During June 2006 Professor Murray Eisenberg attended the 8th International Mathematica Symposium in Avignon, France, where he gave a talk entitled *Visualizing Complex Functions with the Cardano3 Application.* This talk was based upon joint work with David J. M. Park, Jr.

On June 27, 2006 Professor Richard S. Ellis gave a talk in the Seminar in Probability and Stochastic Processes at the TechnionÒIsrael Institute of Technology in Haifa, Israel. The title of his talk was *Double-Chai (18?2) Limit Theorems for Sums of Dependent Random Variables Occurring in Statistical Mechanics.*

Professor Paul Gunnells participated in the workshop *Multiple Dirichlet Series* that took place during the period July 8Ò16, 2006 at Stanford University. He also gave a short course of four lectures on the cohomology of arithmetic groups at the MSRI Summer Graduate Workshop on Computing with Modular Forms, which took place during the period July 31 Ò August 11 2006 at the Mathematical Sciences Research Institute in Berkeley, California.

Professors Paul Gunnells, Hans Johnston, Markos Katsoulakis, Panayotis Kevrekidis, and Bruce Turkington were awarded a $84,000 NSF SCREMS grant (Scientific Computing Research Environments for the Mathematical Sciences). The grant will be used to purchase a Beowulf computer cluster to support computationally intensive research in the mathematical sciences. The cluster will initially be used for research in several areas, including the following.

computational investigation of cohomology of arithmetic groups and Kazhdan-Lusztig cells in Coxeter groups;

investigation of heat transfer and turbulent shear flows in viscous incompressible fluids via direct numerical simulations;

development of multiscale computational methods for hydrid deterministic/stochastic systems;

simulation of nonlinear multi-dimensional phenomena in optics and condensed matter physics;

development and testing of novel closure strategies using equilibrium and nonequlibrium statistical mechanics.

These projects will also have a significant impact on the education and training of both students and young researchers in the mathematical sciences at UMass Amherst. As such, the equipment in this grant is part of a continuing effort of the department to build its computational program and to bring the frontier of research in mathematics to all levels of university education.

Along with three co-authors, Professor Panayotis Kevrekidis published an article in the July 21, 2006 issue of Physical Review Letters, which is the premier journal of the American Physical Society. Entitled *Nonlinearity Management in Optics: Experiment, Theory, and Simulation,* this article was chosen to be a focus article by the journal. It is featured on the website Physical Review Focus http://focus.aps.org/story/v18/st1>.

The new design for the International Mathematical Union, unveiled during August 2006 at the International Congress of Mathematicians in Madrid, is based on the example of Professor Rob Kusner of an optimal configuration of the Borromean rings. This optimal configuration appeared in a paper published in Inventiones Mathematicae several years ago and co-written with Jason Cantarella and John Sullivan; it was elaborated upon in a recent paper that Rob wrote with Jason Cantarella, Joe Fu, John Sullivan, and Nancy Wrinkle. This recent paper will soon appear in the journal Geometry and Topology.

Professor Franz Pedit co-organized the London Mathematical Society Durham Symposium on Methods of Integrable Systems in Geometry, which was held during the period August 11Ò21, 2006. He also gave a lecture at the symposium in honor of T. J. Willmore (1919Ò2005) on the history and developments of the so-called Willmore Conjecture. Professor Willmore was the long time chairman of the Mathematical Institute at the University of Durham.

Visiting Assistant Professor Ralf Schiffler gave a talk at the CBMS Conference on Cluster Algebras at the North Carolina State University, which was held during the period June 13Ò16, 2006 in Raleigh. The title of his talk was *Introduction to Cluster Categories.* He also spent the period June 25 Ò July 1, 2006 at the University of Sherbrooke, where he continued his joint research with I. Assem and T. Bruestle.

Professor Emeritus Floyd Williams was one of hundreds of speakers at the 11th Marcel Grossmann Meeting on General Relativity held at the Free University in Berlin, Germany during the period July 23Ò29, 2006. Floyd presented a 10-minute abstract entitled *A Non-linear Schràdinger-type Formulation of FLRW Scalar Field Cosmology.*