# Faculty News Briefs

### February 2017

Professors Tom Braden and Eric Sommers, as well as Visiting Assistant Professor Jacob Matherne, attended the 2017 Joint Math Meetings which took place 5-8 January in Atlanta, Georgia. Each spoke in the special session on *Representations and Related Geometry in Lie Theory*. Tom's talk was titled "A sufficient condition for a category of perverse sheaves to be highest weight," while Eric's was "Functions on nilpotent orbit covers," and Jacob's was "A combinatorial Fourier transform for quiver representation varieties in type A." Matherne spoke on this topic earlier in a 2 January research seminar at the Indian Institute of Science Education and Research (IISER) in Pune, India, and later at the Erwin Schrodinger Institute in Vienna, Austria, where he attended the * Geometry and Representation Theory * workshop 16-27 January. While in Pune, Jacob also talked about countability and uncountability with 8th, 9th, and 10th graders at the New English School, and he discussed careers in mathematics with beginning undergraduates at Modern College.

Professor Franz Pedit gave an inaugural address at the vernissage for the University of Tuebingen's perpetual exhibition *Mind and Shape* on 19 January 2017. A trio of computer graphic images - "Dini Surface, Tetranoid, and Twizzled Torus" - produced by Dr. Nicholas Schmitt (who was Prof. Rob Kusner's first Ph.D. student at UMass) were permanently loaned to the exhibition. Franz also received funding (with Michael Wolf from Rice University) to co-organize a 5-day workshop for 42 prticipants on *Higgs Bundles and Harmonic Maps of Riemann Surfaces* at Casa Matematica Oaxaca, Mexico, scheduled for 1-6 July 2018.

On 2 December 2016, Professor HongKun Zhang delivered an invited *Fields Dynamics Day* talk on "Optimal bounds on correlation decay rates for nonuniformly hyperbolic systems" at the Fields Institute in Toronto, Canada. This event brings together experts in the field of dynamical systems to report on the their latest advances. The speakers reflect the broad influence of dynamical systems in all fields of mathematics, with a common theme being the relation between dynamical systems and probability theory. She also co-organized a Special Section on *Stochastic Properties of Dynamical Systems* with Jacopo De Simoi and Ke Zhang (both from U. Toronto) at the 2-4 December 2016 Canadian Mathematical Society winter meeting in Niagara Falls. Dmitry Dolgopyat, a leading expert in dynamical systems from U. Maryland, was among the 13 mathematicians who gave talks in this special section. Dmitry and HongKun (together with Mark Demers and Konstantin Khanin) received funding to hold a workshop on *New Developments in Open Dynamical Systems and Their Applications* at the Banff International Research Station, scheduled for 18-23 March 2018.

A group of faculty, staff, and students in the department has formed a Diversity Committee to celebrate our diverse population. For more information - or to join the group - please contact Professor Krista J Gile.

### November 2016

On November 12, 2016 graduate student Konstantinos Gourgoulias gave a talk at the AMS Fall Southeastern Sectional Meeting in the special session on Recent Advances in Stochastic Processes and Stochastic Computation. The talk, titled "Information Metrics for Parallel Lattice Kinetic Monte Carlo", discussed joint research with Professors Markos Katsoulakis and Luc Rey-Bellet.

On November 11, 2016 Visiting Assistant Professor Jacob Matherne gave a talk in the cluster algebra seminar at the University of Connecticut. His talk was titled "Presentations of Cluster Algebras".

During the time period November 15-30, 2016 Professor Franz Pedit was invited by the Transregional Collaborative Research Centre SFB on Discretization in Geometry and Dynamics at the Technische Universität Berlin for collaborative research on conformal flows of Riemann surfaces with Professor Ulrich Pinkall and on 3 point correlation functions in AdS_3 theories with Professor Alexandre Bobenko. Franz also delivered the SFB colloquium on November 15, 2016, titled "Constant Mean Curvature Surfaces and Hilbert's 21st problem for Loop groups".

On November 18, 2016 Visiting Assistant Professor Yaping Yang gave a talk titled "Cohomology Theories and Affine Quantum Groups" at the Australian National University in Canberra. On November 23 she gave the same talk at the University of Melbourne.

### October 2016

Professor Tom Braden and Visiting Assistant Professor Jacob Matherne attended a workshop on symplectic varieties and geometric representation theory, which was held October 28-30, 2016 at the University of North Carolina, Chapel Hill. Professor Braden gave a talk at the workshop titled "Proving Categories of Perverse Sheaves Are Highest Weight".

On October 20, 2016 Professor Erin Conlon gave a talk in the Department of Biostatistics at Columbia University titled "Parallel Markov Chain Monte Carlo Methods for Bayesian Analysis of Big Data".

A paper, authored by graduate student Konstantinos Gourgoulias, Professor Markos Katsoulakis, and Professor Luc Rey-Bellet, was recently accepted for publication in the *Journal of Computational Physics*. The paper, titled "Information Criteria for Quantifying Loss of Reversibility in Parallelized KMC", can be view at https://arxiv.org/abs/1605.02375. In this work, the authors continue their study of schemes for parallel Lattice Kinetic Monte Carlo in the context of simulating time-reversible systems. Time reversibility is an important physical property that unfortunately is not preserved during parallelized simulation. Through information metrics, they relate the loss of reversibility to parameters of the scheme, such as the time step and the lattice decomposition, which naturally leads to potential comparisons among schemes, decompositions, time steps, and other quantities.

On October 13, 2016 Professor Rob Kusner lectured about "CMC surfaces & CSC Metrics with Cylindrical Ends" in the MIT Geometric Analysis Seminar. He also delivered two lectures this month in the Penn Minimal Surfaces Seminar (October 18 and 25) and another lecture about "Critical Configurations of Hard Disks on the Sphere" at the October 28-30 AMS Meeting in Minneapolis in a special session honoring Professor Ken Millett on his 75th birthday.

During the period October 23-25, 2016 Visiting Assistant Professor Gufang Zhao visited SUNY at Buffalo. On October 24 he gave a talk in the algebra seminar titled "Cohomological Hall Algebras and Affine Quantum Groups".

### September 2016

On September 24, 2016 Visiting Assistant Professor Stathis Charalampidis gave a talk at the Fall Eastern Sectional Meeting of the American Mathematical Society titled "Multi-Component Nonlinear Waves in One and Two Dimensional Coupled Nonlinear Schroedinger Systems: Theory and Numerical Computations". The meeting was held at Bowdoin College in Brunswick, Maine.

A paper, authored by graduate student Konstantinos Gourgoulias, Professor Markos Katsoulakis, and Professor Luc Rey-Bellet, was accepted for publication in the *SIAM Journal on Scientific Computing*. The paper, titled "Information Metrics for Long-Time Errors in Splitting Schemes for Stochastic Dynamics and Parallel KMC", can be viewed at https://arxiv.org/abs/1511.08240. In this work, the authors study the long-time properties of the parallel Kinetic Monte Carlo algorithm, which is a high-performance computing algorithm used to simulate stochastic models on a lattice with applications as varied as computational physics, traffic modeling, and systems biology. An information criterion connected with path-space relative entropy is derived. Through this information criterion, practitioners can assess the appropriateness of different versions of the algorithm and select the one that is best suited to their application of choice. The proposed methodology extends the numerical analysis of the algorithm to the long-time regime while still providing a tractable computational diagnostic that can be computed during a simulation.

Professor Rob Kusner lectured on "CMC Surfaces and CSC Metrics with All Ends Cylindrical" in the Penn Minimal Surfaces Seminar on September 27, 2016.

### August 2016

Covering June, July, and August 2016

With collaborators in the UMass College of Information and Computer Sciences and at Harvard Medical School, Massachusetts General Hospital, and Brigham and Women's Hospital, Professor George Avrunin received a grant from the National Institutes of Health titled "Developing Standardized Intraoperative Process Models to Enhance Surgical Safety". The project involves modeling key parts of cardiac surgery using a programming language designed for systems in which human experts interact with hardware and software devices, validating the safety of those models using techniques developed for analyzing concurrent computer programs, and then generating context-aware online guidance for the surgical teams from the models. George is the PI on the UMass part of the grant, which is a subcontract to Harvard Medical School.

Graduate student Isabelle Beaudry, working with Professor Krista J Gile, won the Best Student Paper in Applied Statistics at the International Indian Statistical Association (IISA), as part of the IISA 2016 Conference held in Corvallis, OR during the period August 18-21.

In June 2016 Professor Tom Braden gave talks at the University of Glasgow and the University of Edinburgh titled "Modular Representation Theory and Hypertoric Varieties".

Visiting Assistant Professor Stathis Charalampidis and Dr. Chris Gong from Bowdoin College, a former VAP in our department, organized a session titled "Analysis and Applications of the Nonlinear Schroedinger Equation" during the SIAM Conference on Nonlinear Waves and Coherent Structures held in Philadelphia. On August 9, 2016 Stathis gave a talk at this session titled "Dark-Bright Solitons and Their Two-Dimensional Counterparts in Coupled Nonlinear Schrodinger Systems". Information about the session is available at http://meetings.siam.org/sess/dsp_programsess.cfm?SESSIONCODE=23215.

Professor Erin Conlon and a team of researchers from UMass Amherst, the University of New Hampshire, and Hampshire College recently received a three-year $1.9 million award from the U.S. Department of Energy titled "The Who and How of Microbial Control over Soil Carbon Dynamics: a Multi-omics, Stable Isotope, and Modeling Approach". Kristen DeAngelis of the Department of Microbiology at UMass is the PI on the grant, and Erin is the co-PI. The project involves a systems-biology approach to the study of regulatory and metabolic networks of microbes. The long-term goal of the project is to predict the fate of soil carbon by developing mathematical and ecosystem models of soil organic-matter decomposition. These models will incorporate genetic and physiologic information on carbon-use efficiency by microbes, laying the groundwork for expanding predictions of microbial carbon-use efficiency to additional ecosystems. This work is based on experimental samples from Harvard Forest.

Professor Patrick Flaherty is part of a research team that has developed a rapid, low-cost screening method to decipher the gene mutations behind drug resistance. The new method addresses how some chemotherapy agents used on tumors and cancer can stop working because they become resistant to the drug’s effect. For details see *ScienMag*

<http://scienmag.com/deciphering-the-mutations-behind-drug-resistance/> and *Medical Xpress* <http://medicalxpress.com/news/2016-07-deciphering-mutations-drug-resistance.html>.

In June 2016 Professor Nestor Guillen was a speaker at the Conference on Recent Trends on Elliptic Nonlocal Equations, held at the Fields Institute in Toronto. He was also a speaker at the 3rd Conference on Nonlocal Operators and Partial Differential Equations, held at the Stefan Banach International Mathematical Center in Bedlewo, Poland. In July Nestor taught a minicourse on Stochastic Homogenization of Elliptic Equations aimed at graduate students as part of the 2016 Gene Golub Summer School in Philadelphia.

During the summer Professor Rob Kusner was a research member of MSRI in Berkeley. He delivered a small lecture on the Hyperbolic Geometry of Relationships to a large gathering that celebrated the Montague wedding of colleagues Franz Pedit and Allison Tanguay in June.

On June 27, 2016 Professor Michael Lavine gave a talk at the Army Research Office titled "WHIM: Function Approximation Where It Matters".

Professor Yao Li, together with Molei Tao from Georgia Tech, organized a special session "SS82: Numerical Simulations and Computations for Stochastic Dynamics" at the 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications. The conference was held in Orlando, FL during the period July 1-5, 2016. Yao also gave two talks at the conference. The first, given in the special session that he organized, was titled "A Fast Simulation Method for Markov Jump Processes. The second, given in another special section, was titled “Systematic Measures of ODE-Modeled Complex Networks". In August 2016 Yao gave two invited talks both titled “Polynomial Convergence Rate to Nonequilibrium Steady-State”. The first talk was given on August 1, 2016 in Shenzhen, China at the International Conference on Statistical Properties of Nonequilibrium Dynamical Systems. The second talk was given on August 30 at the PIMS/AMI Seminar at the University of Alberta in Edmonton, Canada.

Professor Franz Pedit organized the session "Progress in Surface Geometry" at the 2016 Differential Geometry and Applications Conference held in Brno, Czech Republic during the period July 11-15, 2016. As an editor of the *Journal of Differential Geometry and Applications*, he was invited and participated in the editorial meeting of the journal.

Professor Eric Sommers gave an invited talk at the "Nilpotent Orbits and Representation Theory" workshop, held June 13-16, 2016 at the Scuola Normale in Pisa, Italy. His talk was titled “A Family of Weyl Group Representations”. In August he visited Japan for the Summer Conference on Hyperplane Arrangements, held August 8-12, 2016 at Hokkaido University (our own President William S. Clark became the first leader of Hokkaido University in 1876). At this conference Eric gave a talk titled "From Hyperplane Arrangements to Families of Weyl Group Representations". While there, he also visited the new Global Station for Data Science and Cybersecurity, which will host long-term visits by faculty from UMass Amherst and other institutions.

From May 17 until August 3, 2016 Visiting Assistant Professor Yaping Yang visited Professor Marc Levine at the University Duisburg-Essen in Essen, Germany. On August 5 she gave a talk at Zhejiang University in Hangzhou, China. The title of her talk was "Quantum Groups and Cohomology Theories".

Professor Hongkun Zhang had a busy summer organizing an international conference as well as a workshop. The International Conference on Statistical Properties of Nonequilibrium Dynamical Systems was held in the South University of Science and Technology of China (SUSTC) in Shenzhen, China, from July 27 until August 2, 2016. In conjunction with that conference a workshop was held during the period July 4-26, 2016. Visiting Assistant Professor Jianyu Chen helped Hongkun organize both the conference and the workshop. The goal of the workshop and conference was to bring together an excellent group of researchers from around the world to discuss new research results and to explore new ideas and powerful new mathematical tools to deepen our theoretical understanding of the dynamical underpinnings of non-equilibrium systems and classical statistical physics. More than 120 people participated in the conference, including many leading world-experts in several research fields. At the workshop Hongkun gave a series of lectures on "Ergodic and Statistical Properties of Billiards". The conference and workshop were sponsored by SUSTC as well as Hongkun's NSF conference grant, which is funded by the Analysis Program in the Division of Mathematical Sciences at NSF.

From May 17 until August 3, 2016 Visiting Assistant Professor Gufang Zhao visited the University of Duisburg-Essen in Essen, Germany. During August 2016 Gufang visited Zhejiang University. On August 5 he gave a seminar talk titled "Elliptic Quantum Groups and Affine Grassmannians over an Elliptic Curve".