# Faculty News Briefs

### May 2006

Professor Wei-Min Chen was recently awarded a three-year research grant of $105,540 from the National Science Foundation.

Professor Paul Gunnells authored the cover story in the May 2006 issue of the Notices of the American Mathematical Society. Entitled *Cells in Coxeter Groups,* the article highlights a series of beautiful graphics, which Paul created.

During the period April 5Ò8, 2006 Professor Emeritus Jim Humphreys visited the University of South Alabama in Mobile, where he gave a colloquium lecture as well as a seminar talk. Several UMass Ph.D. students now teach there, including JimÌs former student Cornelius Pillen.

Professor Emeritus Aroldo Kaplan, currently a Researcher for ArgentinaÌs Science Agency, has joined the Mathematics Division of the International Center for Theoretical Physics in Trieste, Italy as Senior Associate.

In the March 2006 News Briefs the following item appeared concerning some research carried out by Professor Markos Katsoulakis and collaborators.

Professor Katsoulakis had an article accepted for publication in the top journal Nature Materials. Entitled *Mechanistic Principles of Nanoparticle Evolution to Zeolite Crystals,* the article was written in collaboration with chemical and materials scientists from the University of Minnesota and the industry.

In April the National Science Foundation recognized the importance of this research by featuring it on the main NSF web page in an article entitled *Crystal Sieves, Born Anew: Hard Data Resolves Decades-old Mystery of How Certain Zeolites Form.* The research was supported by a number of NSF grants and by the NSF National Nanotechnology Infrastructure Network.

Professor William Meeks was recently been awarded a Guggenheim Fellowship for the fall semester of 2006. Professor Meeks was one of 187 out of approximately 3,000 applicants to receive this yearÌs prestigious award from the John Simon Guggenheim Memorial Foundation.

Professor Gregory Pearlstein, formerly at the Institute for Advanced Study and currently a visiting professor at Duke University, has accepted a tenure-track position at Michigan State University. Gregory was the last student at UMass whose Ph.D. dissertation Professor Emeritus Aroldo Kaplan directed.

A number of current and former UMass people participated in the Spring Northeastern Sectional Meeting of the American Mathematical Society held April 22Ò23, 2006 at the University of New Hampshire in Durham. Several special sessions were organized by faculty members at UMass, including a special session on algebraic groups organized by Professors Eric Sommers and George McNinch. At that session, the following faculty members gave talks:

Professor Tom Braden, *Semi-infinite Moment Graphs*

Professor Emeritus Jim Humphreys,*Tilting Modules for Semisimple Groups in Characteristic p*

Professor Ivan Mirkovic, *A t-Structure on Coherent Sheaves on Cotangent Bundle of a Flag Variety*

Visiting Assistant Professor Ralf Schiffler, *Cluster-tilted Algebras*

In addition, Professor Paul Gunnells and Farshid Hajir organized a special session on arithmetic geometry and modular forms, and Professors Weimin Chen, Michael Sullivan, and Hao Wu organized a special session on symplectic and contact geometry. A detailed program listing is available online.

Professor Emeritus Floyd Williams was one of eleven invited plenary speakers at the Fifth International Conference on Mathematical Methods in Physics, held during the period April 24-28, 2006 in Rio de Janeiro, Brazil. The title of his one-hour lecture was *Remarks on the BTZ Instanton with Conical Singularity.*

### September 2005

Professor Weimin Chen gave a talk at a Workshop on Topology held in Banff, Canada during the period August 27ÒSeptember 1, 2005. The title of his talk was *Pseudoholomorphic Curves and Finite Group Actions in Dimension 4.*

Professor Erin Conlon gave an invited talk at the Joint Statistical Meetings in Minneapolis, Minnesota on August 7, 2005. The title of her talk was *Identifying Chromosome Clusters and Over-represented Functions of Differentially Expressed Genes In Complementary cDNA Microarray Experiments.*

Professor Richard S. Ellis gave an invited talk at the Florence Meeting on Long-Range Interactions and Ensemble Inequivalence held at the University of Florence in Florence, Italy on June 28 and June 29, 2005. The title of his talk was *Global Optimization, the Gaussian Ensemble, and Universal Ensemble Equivalence.*

Professor Emeritus David Foulis gave an invited plenary lecture, *Rickart Comparability Groups and Quantum Logics,* at a Workshop on Quantum Information, Computing, and Logic held at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, Canada. At the end of the 7-day workshop and conference, Professor Foulis also participated as a member of a panel to summarize the events of the meeting.

During the past summer Professor Paul Gunnells participated in three workshops. The first was Variations on MahlerÌs Measure held in Luminy, France during the period 30 May 30ÒJune 3, 2005. The next was Multiple Dirichlet Series held in Bretton Woods, NH during the period July 11Ò14 July,2005. The third was Explicit Methods in Number Theory held in Oberwolfach, Germany during the period July 17Ò23, 2005.

Professor Emeritus Floyd Williams was an invited speaker at the 16th Latin-America Colloquium on Algebra held in Colonia, Uruguay during the period August 1Ò9. The title of his lecture was *Conical Defect Zeta Function for the BTZ Black Hole.* Other speakers at the Uruguay meeting were the former department members Aroldo Kaplan, Frank Sottile, and Sarah Witherspoon. Professor Williams also spent the period July 25Ò30 as a visitor at the Universidad Nacional de Cordoba in Cordoba, Argentina, where he continued to do research on an ongoing project with Professor Roberto Miatello on problems in non-commutative harmonic analysis on higher rank semisimple Lie groups.

### September 2004

Along with Lori Clarke (CMPSCI), Lee Osterweil (CMPSCI), and Elizabeth Henneman (Nursing), Professor George Avrunin has been awarded a 4-year ITR grant from NSF, which is being funded at the level $1,448,242. This is a collaborative grant with Philip Henneman, Chair of the Department of Emergency Medicine both at Tufts University Medical School and at Baystate Medical Center. The project will apply, to medical processes, techniques developed to represent and analyze computer systems, with the goal of reducing medical errors and cost. George was also the General Chair of the ACM International Symposium on Software Testing and Analysis, held in Boston in July, 2004. In addition to its three days of sessions, two one-day workshops were held in association with the symposium, and there were several joint activities with the co-located 16th International Conference on Computer-Aided Verification.

In June 2004, Professor Tom Braden spoke at the SIAM conference on discrete mathematics in Nashville, TN. The title of his talk was *Cohomology of Intersections of Opposite Bruhat Cells.* He also participated in this summerÌs Park City Math Institute, where Professor R. MacPherson gave graduate lectures on equivariant localization techniques and mentioned some of his joint work with Tom. At the institute, Tom helped run a discussion section associated with the lectures and demonstrated computer algebra code to calculate with these techniques.

Professor Erin Conlon gave a talk at the Functional Genomics 2004 Reunion Conference at IPAM at UCLA on June 3, 2004. She also gave a talk at the Statistics in Functional Genomics Workshop in Ascona, Switzerland on June 30. The topic of both talks was motif-finding using DNA sequence and expression information.

At MathFest 2004, the national meeting of the Mathematical Association of America in August, Professor Murray Eisenberg delivered a 20-minute paper entitled *The OWL System with webMathematica in Applied Calculus.* The paper, selected for the session *Uses of the WWW that Enrich and Promote Learning,* was co-authored with David M. Hart of the Center for Computer-Based Instructional Technology at UMass and Alan R. Peterfreund and Kenneth A. Rath of Peterfreund Associates. The talk discussed adaptation of the OWL on-line, web-based learning system to the introductory calculus course for management and the life and social sciences, and it evaluated the results of its use there.

Professor Richard S. Ellis gave a talk on June 23, 2004 in Berlin at the Berlin Stochastics Colloquium, a joint colloquium with the Technishe Universitât, Humboldt University, and the Weierstrass Institute. The title of his talk was *Generalized Canonical Ensembles, Universal Ensemble Equivalence, and Global Optimization.*

On the occasion of his 65th birthday, Professor Emeritus Jim Humphreys was honored at the Joint Summer Research Conference on Representations of Algebraic Groups, Quantum Groups, and Lie Algebras for his contributions to the fields of Lie algebras, algebraic groups, and representation theory. At the conference, which took place at the Snowbird Ski Resort in Utah during the period July 11Ò16, 2004, Jim gave a talk entitled *Representations of Reduced Enveloping Algebras and Cells in the Affine Weyl Group,* Professor Eric Sommers chaired an afternoon session, and Professor Ivan Mirkovic gave a featured talk entitled *Beilinson-Bernstein Localization for Quantum Groups at Roots of Unity.* During the lively dinner in JimÌs honor, speeches were made by a number of people including Professor Mirkovic and JimÌs former UMass doctoral students, Cornelius Pillen and Zongzhu Lin. Zongzhu was a principal organizer of the conference.

Professor Markos Katsoulakis was awarded an NSF grant that is being funded at the level $314,000 by the Applied Mathematics, Statistics, Computational, and MSPA/Material Programs of DMS. The title of his project is *Multiscale Stochastic Modeling, Analysis and Computation.*

Professor Panos Kevrekidis had a busy spring and summer, visiting the University of Chicago in February, Georgia Tech and University of Kansas in March, and Boston University in April. As part of these visits, he lectured on his recent work on Bose-Einstein condensates and a dynamic renormalization approach to self-similar problems. Panos was also invited to spend two weeks during the summer at the Los Alamos National Laboratory. He combined this visit with a visit to San Francisco State University and the AIMS June meeting in Pomona, CA, where he delivered an invited talk in the session on dynamical systems; this session was organized by Yuri Latushkin and Carmen Chicone.

During the academic year 2003Ò2004, Professor Rob Kusner was a member of the Mathematical Sciences Research Institute (MSRI) in Berkeley and a Visiting Research Professor at the University of California, Berkeley. He also had month-long invitations to the Federal University of Ceara in Fortaleza, Brazil in February, to the University of Utah in Salt Lake City in March, to the Technical University in Darmstadt, Germany in May, and to the Center for Theoretical Physics in Aspen, Colorado in June, where he delivered a series of lectures and collaborated with colleagues. Perhaps the highlight of RobÌs year was a major breakthrough concerning the nondegeneracy, in the sense of Morse theory, of constant mean curvature surfaces. Done in collaboration with Nick Korevaar and Jesse Ratzkin of the University of Utah, this work has led to a series of papers, the first of which was submitted to Inventiones Mathematicae during the summer. Eli Cooper, RobÌs new Ph.D. student, spent the year as a graduate student at UC Berkeley. Eli is working on a dissertation about the geometry of a constant-mean-curvature-surface moduli space as a Lagrangian submanifold.

Professor Matvei Libine participated in the American Institute of Mathematics workshop on Moment Maps and Surjectivity in Various Geometries, held in the AIM Research Conference Center in Palo Alto, CA during the period August 9Ò13, 2004. The workshop was organized by T. Holm, E. Lerman, and S. Tolman.

Professor Franz Pedit recently completed a three-month visit at TU-Berlin in Germany, where he was supported by a $10,000 Alexander von Humboldt Senior Research Grant. While in Germany, he gave a three-hour lecture series on *Conformal Tori in the 4-Sphere* at the annual workshop on "Integrable Systems and Quantum Field Theory in Peyresque, France. He also gave two colloquia on the same topic at the University of Cologne and at the University of Freiburg in Germany.

Professor Tom Weston was awarded a joint NSF grant with Robert Pollack of Boston University for 2004Ò2006. The title of their project, which is being funded at the level $93,715, is *p-adic Variation of Supersingular Iwasawa Invariants.* Tom also gave a talk entitled *Iwasawa Invariants of Galois Deformations* at the special session on arithmetic geometry at the meeting of the Canadian Number Theory Association in Toronto.

In July 2004 the department had a large contingent at the Park City Mathematics Institute in Utah. Focusing on geometric combinatorics, this three-week program had different subprograms for undergraduates, graduate students, faculty, and high school teachers. Professor Nate Whitaker was involved in recruitment for the program. Heather Harrington, a rising junior, was in the undergraduate program. Professors Tom Braden, Amit Khetan, Eric Sommers, Evgenia Soprunova, and Ivan Soprounov participated in the faculty program, as did former Professors Frank Sottile and Sarah Witherspoon. In the graduate program, Patrick Boland, Chris McDaniel, Marianna Pereira, and Jim Ruffo represented the department. Professors Sommers, Soprunova, and Soprounov gave research talks, and Professor Braden led a session on a software program that he developed.

At the biennial meeting in July 2004 of the International Quantum Structures Association (IQSA) in Denver, CO, Dr. Alex Wilce was awarded the IQSA prize for his mathematical research, his service to the IQSA, and his work as coeditor of the book Operational Quantum Logic, published by Kluwer in 2000. Dr. Wilce received his Ph.D. in our department in 1998. After receiving the prize, Dr. Wilce gave a plenary lecture entitled *Symmetry and Topology in Quantum Logic.*

Professor Floyd Williams had a busy summer and reports on the following activities.

He was an invited speaker at the Sixth Alexander Friedmann International Seminar on Gravitation and Cosmology, which was held in CargÀse, France during the period June 28ÒJuly 3, 2004. The title of his 30-minute lecture was *An Alternate Formulation of Einstein-Friedmann Equations with Scalar Field and Perfect Fluid Matter Source.*

As part of a week-long visit to the Department of Mathematics, he gave two one-hour, invited lectures at the City University in Cordoba, Argentina. The two lectures, given on August 4 and 5, were entitled *Patterson-Selberg Zeta Function for a Hyperbolic Cylinder-Application to the BTZ black hole* and *Solitons and 2-Dimensional Gravity.*

He served as a member of the Scientific Committee for the Fourth International Winter Conference on Mathematical Methods in Physics held at the Physics Institute CBPF (Centro Brasileiro de Pesquisas Fisicas) in Rio de Janerio, Brazil during the period August 9Ò13. As one of the plenary speakers, he gave a one-hour lecture entitled *Further Thoughts on First Generation Solitons and Jackiw-Teitelboim Gravity.*

He gave mini piano-recitals at the Institut dÌEtudes Scientifiques de CargÀse in CargÀse, France on July 1 and at a private home in Cordoba, Argentina on August 7. The programs consisted of American hymns, modern jazz, and original compositions, one of which was a variation on a theme of S. Rachmaninoff.

The paper of Professor Robin Young entitled *Solutions to Isentropic Gas Dynamics with Arbitrarily Large BV Data* contains a major result that he presented at James GlimmÌs 70th birthday conference held in Stony Brook, New York during the period August 3Ò5. Robin will also present the result at HYP2004 held in Osaka, Japan during the period September 13Ò16 and at several AMS and SIAM conferences during the next few months.

### September 2003

On March 12, 2004 Professor Tom Braden spoke on *Toric Koszul Duality* in the special session *Algebraic Geometry and Topology* at the Spring AMS Southeastern Section Meeting in Tallahassee, FL.ÜÜ

Professor Emeritus Ed Connors reports on the following activities.

### September 2002

In June, Professor Tom Braden gave a talk in the conference on Computational Lie Theory at the Centre de Recherches Mathematiques at the University of Montreal. The title of his talk was *Torus Actions and Singularities of Schubert Varieties.* Visiting Assistant Professor Greg Warrington also spoke at the same conference.

In June, Professor Richard S. Ellis was awarded a 3-year, $227,000 National Science Foundation grant entitled *Research in Large Deviations and Applications to Statistical Mechanical Models of Turbulence.* He also gave two talks at the Swiss Federal Institute of Technology in Lausanne and two talks at University of Paris VI.

At a convocation held on September 3, 2002, Professor Ellis received the 2001-2002 Outstanding Faculty Award for Research in the College of Natural Sciences and Mathematics. The citation that accompanied the award was the following.

\tRichard Ellis is an acknowledged world leader in the study of large deviations, an important field having numerous applications including the analysis and design of high-speed communication networks. His most recent innovative work on statistical theories of turbulence is an outgrowth of his previous research on statistical mechanics and large deviations.

Ü Ü Ü ÜProfessor Ellis has produced a considerable body of published work, including two major research monographs on probability theory and applications, a well known theorem carrying the name *Gârtner-Ellis Theorem,* and many frequently cited papers on probability theory and statistical mechanics. In 1999 he was elected to be a Fellow in the Institute of Mathematical Statistics in honor of his outstanding research contributions.

Ü Ü Ü Ü As important and impressive as Richard's scientific accomplishments are, his intellectual activities extend beyond science. UMass Magazine recently highlighted his numerous contributions to the field of Judaic studies. As the article points out, *Ellis performs a remarkable and rare intellectual juggling act, straddling what the British writer C. P. Snow called the Îtwo culturesÌ of science and the humanities.* We are indeed fortunate that Professor Ellis has chosen to spend his highly creative research career here at UMass.

During the summer of 2002, Professor Farshid Hajir was awarded a 3-year National Science Foundation grant from the program in algebra, number theory, and combinatorics. He was invited to give a special session talk at the meeting of the American Mathematical Society in Boston in October 2002. The special session, entitled *Number Theory and Arithmetic Geometry,* is organized by Professor Siman Wong.

Professor H. K. Hsieh presented a paper entitled *A Proof for a Continuity Property of Positive Definite Matrices Used in Linear Models* at the ICSA 2002 Applied Statistics Symposium held in Philadelphia on June 6-8, 2002.

Professor Markos Katsoulakis accepted an invitation to join the editorial board of the SIAM Journal in Mathematical Analysis. He was recently awarded a $420,000 grant from the National Science Foundation for the development of mesoscopic Monte Carlo simulation methods. Co-PIÌs on the grant are David Horntrop, Department of Mathematics, New Jersey Institute of Technology, and Dionisios Vlachos, Department of Chemical Engineering, University of Delaware.

Professor Panayotis Kevrekidis gave an invited talk in the 15th Conference on Nonlinear Dynamics, Chaos and Complexity held in Patras, Greece on August 20, 2002. He was also invited to present a colloquium talk at the Department of Physics, Rutgers University on September 25. His talk is entitled *A Dynamic Renormalization Approach to Blowups: the Nonlinear Schràdinger Equation Paradigm.*

This summer Professor Rob Kusner participated in workshops on geometric analysis and its applications at the Euler Institute in St. Petersburg, Russia, the Isaac Newton Institute in Cambridge, England, and the Max Planck Institute for Complex Systems in Dresden, Germany. Professor Kusner delivered several plenary lectures at each institute (3 at Newton, 2 at Max Planck, and 1 at Euler) and also lectured in August at the University of Warwick. Some of the work on which he lectured was recently announced in the Proceedings of the National Academy of Sciences, and some is appearing just now in the journal Inventiones Mathematicae.

The music research of Professor Chris Raphael was the subject of a short radio program on *Science Update* which aired on July 22, 2002. This is a syndicated program sponsored by the American Association for the Advancement of Science. His music research is the focus both of a short article in the June 15, 2002 issue of New Scientist Magazine and of an article in the September 17, 2002 online edition of Discover.

A recent statistical technique and algorithm developed by Professor Paola Sebastiani and her collaborators at Harvard Medical School has received a remarkable amount of attention lately. By analyzing the expression level of thousands of genes with microarrays, molecular biologists hope to identify genes that collaborate in cell functions. Machine learning methods such as clustering or self-organizing maps are typically used to discover groups of genes with similar expression levels in repeated experiments. The method developed by Professor Sebastiani and her collaborators is the first principled solution to clustering gene expression data measured in temporal experiments. The method uses a novel, model-based, Bayesian clustering algorithm to identify gene-expression profiles that are likely to be generated by the same process.

The method is implemented in the program Caged, which is available at http://www.genomethods.org/caged, and was published in the paper by M. Ramoni, P. Sebastiani and I. S. Kohane entitled *Cluster Analysis of Gene Expression Dynamics,* Proc. Nat. Acad. Sci. USA 99(14):9121-9126 (2002).

Out of the 93 papers published in this issue, this paper is one of 6 appearing on the cover page,. It has already been reviewed in the Netwatch section of Science, volume 29, July 2002, and in Bio. IT World; additional reviews are to appear in The Scientist and the ISBA Bulletin. The paper was the *most frequently read paper* on PNAS online across all fields of science during the month of August; the PNAS website is said to receive over 4 million hits a month. Details about the method, the program, and articles in the press are available at http://www.genomethods.org/caged/docs/index.html.

Professor Eric Sommers was recently awarded a 3-year National Science Foundation grant entitled *Nilpotent Orbits in Representation Theory.*

During July, Professor Frank Sottile participated in the conference on Formal Power Series and Algebraic Combinatorics in Melbourne, Australia, was a plenary speaker at the conference on Symbolic Computational Algebra in London, Ontario, and spoke at the workshop on Algebraic Geometry and Geometric Modeling in Vilnius, Lithuania. Professor Sottile was recently awarded a grant from the National Security Agency to organize a series of meetings on Discrete Mathematics in New England. In addition, he had a proposal accepted for a program at the Mathematical Science Research Institute in the spring semester of 2004 on Topological Aspects of Real Algebraic Geometry. He is the chair of the organizing committee.

Professor John Staudenmayer will attend the NSF-sponsored Frontiers in Statistics Conference at Texas A&M in Oct 10-13, 2002. His topic will be *Robust Smoothing for Designed Experiments.* On July 15, 2002, he gave an invited talk on this topic at the International Conference on Current Advances and Trends in Non-Parametric Statistics in Crete, Greece. The title of his talk was *The t-Linear Mixed Model for Smoothing and More.* Professor Staudenmayer has also been invited to give a talk at the Yale Biostatistics seminar on November 12, 2002. The title of his talk is *Robust Smoothing for Designed Experiments in Toxicology.*

Professor Floyd Williams was invited to deliver a Convocational Address to faculty and students of the School of Architecture at Valparaiso University in Valparaiso,Chile. The address, given August 1, 2002, focused on successes and failures of Einstein and the architecture of the early universe. Professor WilliamsÌs new book, entitled Topics in Quantum Mechanics, is scheduled for publication by Birkhâuser this fall.