# Faculty News Briefs

### March 2017

Professor Erin Conlon delivered the keynote address "Parallel Markov Chain Monte Carlo Methods for Bayesian Analysis of Big Data" at the Heidelberg University *Workshop on Monte Carlo Methods and Big Data* in Heidelberg, Germany, 10-11 February 2017.

During 31 January - 1 February, Associate Professor Krista J Gile participated in a consultation on *Population Size Estimation in Hard-to-Reach High-Risk Populations* at the Centers for Disease Control and Prevention in Atlanta.

Visiting Assistant Professor Robin Koytcheff gave two research-related talks last month: “From linking numbers to Taylor towers” (University at Albany, Monday 30 January) and “Knots, links, linking numbers, and generalizations” (West Chester University, Tuesday 21 February).

In January, Professor Ivan Mirkovic lectured in the Number Theory and the Representation Theory seminars at the University of Zagreb, Croatia. He also gave three talks during the 16-27 January workshop on *Geometry and Representation* *Theory* at the Schrödinger Institute in Vienna, Austria.

As part of its THEMATIC MONTH ON DYNAMICAL SYSTEMS AND INTERACTIONS, Professor HongKun Zhang was invited to participate in two workshops at CIRM Luminy (Centre International de Rencontres Mathématiques) in the environs of Marseille, France, between 13-24 February:

• *Teichmüller Space, Polygonal Billiards, Interval Exchanges*

• *Non-Uniformly Hyperbolic Dynamical Systems, Coupling and Renewal Theory* ;

in the latter, she delivered a talk on "Diffusion behavior of Lorentz gas with flat points" based on her two recent publications.

On 23 February, the faculty adopted by unanimous vote the following statement on equity, inclusion and diversity:

*The Department of Mathematics and Statistics includes and serves faculty, staff, and students from a wide range of personal and professional backgrounds. It has long been a pillar of academic thought that diversity of perspectives fosters enhanced ability to advance science. We know that having a department of teachers, mentors, staff, researchers, and colleagues from a range of personal and professional backgrounds also enhances our ability to effectively serve our educational mission. We embrace the diversity of our department and community, including persons of varying age, disability, ethnicity, family status, gender, gender identity, geographic region, national origin, political affiliation, race, religion, sexual orientation, and socioeconomic status. *

### 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 Schröedinger 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.