#### Primary Fields of Interest.

**Algebra.** Ardila, Gubeladze, Hosten

** Analysis. ** Axler, Hayashi, Li, Schuster

** Applied Mathematics. ** Ellis, Langlois, Li

** Combinatorics. ** Ardila, Beck, Gubeladze, Hosten, Krause, Ovchinnikov

** Differential Geometry. ** Bao

** Dynamics. ** Cheung, Goetz

** Education. ** Hsu, Kysh, Resek*

** Game Theory. ** Langlois

** Geometry. ** Ardila, Beck, Gubeladze, Hosten, Smith*

** History. ** Smith*

** Mathematical Biology. ** Arsuaga, Vazquez

** Number Theory. ** Beck, Cheung, Robbins

** Statistics. ** Hosten, Kafai, Piryatinska, Richards

** Topology. ** Ardila, Arsuaga, Cheung, Vazquez

Federico Ardila investigates objects in algebra, geometry, topology, and applications by understanding their underlying combinatorial structure.

Javier Arsuaga works on the development of quantitative methods to understand 3D chromosome structure, nuclear architecture and the formation of chromosome aberrations. He works closely with experimental groups and uses a wide variety of mathematical methods (knot theory, geometry, probability and stochastic processes), biophysical methods (statistical physics of polymers and diffusion models) and statistics methods.

Sheldon Axler works on functional analysis and complex analysis. He also always seems to be writing another book.

David Bao was trained in mathematical physics and later switched to differential geometry. He works on curvature-driven problems in Riemann-Finsler geometry.

Matthias Beck works in discrete & computational geometry and analytic number theory. He is particularly interested in problems and applications connected with lattice-point enumeration in polytopes.

Yitwah Cheung's current research is in dynamical systems, focusing on the ergodic theory of rational billiards, Teichmuller flows and dynamics on Lie groups.

Arek Goetz's research interests include dynamical systems, symbolic computing, and effective use of cutting edge multimedia technology in teaching.

Joseph Gubeladze works on K-theory of toric varieties and related commutative algebra and discrete geometry topics.

Eric Hayashi's research interests are in complex analysis, operator theory, and frame analysis.

Serkan Hosten works in computational and combinatorial commutative algebra, algebraic geometry and discrete geometry with applications in discrete optimization and algebraic statistics.

Eric Hsu is currently involved with several math education projects, including an NSF Math Science Partnership. He is interested in how teachers use the internet and live communities to learn to teach. He is also interested in how undergraduates learn calculus and use informal representations.

Jean-Pierre Langlois's research is in game-theoretic modeling of deterrence, bargaining, and treaty design. He is the designer of the Gameplan game theory software.

Sergei Ovchinnikov's current research interests are in discrete mathematics and its applications in cognitive sciences.

Alexandra Piryatinska is interested in time series analysis and random fields, and their applications to medicine and oceanography; Levy processes, parametric estimation problems, and models of anomalous diffusion.

Diane Resek* (retired) works on the development and popularisation of innovative curricula for teaching remedial mathematics.

Joey Richards was trained in both astrophysics and statistics. He works at the forefront of big data mining and their numerous socially relevant applications such as fraud detection, healthcare, finance, customer engagement, telecommunications, and industrial safety.

Neville Robbins's current research interests are in number theory, particularly in linear recurrences and the theory of partitions.

Alex Schuster's research interests include spaces of analytic functions of one complex variable, especially the Hardy, Bergman and Bargmann-Fock spaces.

James T. Smith* (retired) His main scholarly project now is a book, The legacy of Mario Pieri in arithmetic and geometry, in collaboration with Elena Marchisotto. Pieri (1860-1913) was a major figure in the Italian research groups in algebraic geometry and logic. A long-standing background project is investigation and implementation of computer techniques for doing and presenting mathematics.

Mariel Vazquez is a mathematical and computational biologist. In one line of research, she applies low-dimensional topology, and in particular of knot theory, to study how certain enzymes change the topology of DNA. She is particularly interested in the action of Type II topoisomerases and of site-specific recombinases. Type II topoisomerases are essential to every known organism, and as such are good targets for antibacterial and anticancer drugs. Professor Vazquez studies their topological mechanism of DNA simplification (NIH SCORE Grant). Site-specific recombinases are used by the cell to rearrange its genetic material. Professor Vazquez has won an NSF CAREER Award to study the action of Xer recombinases and their impact on DNA replication. She is also interested in the effects of packing on the topology of DNA, together with Professor J. Arsuaga she has an NSF Grant to study the packing of DNA by bacteriophage P4. In a second line of research, she uses topological and discrete methods to study chromosomal aberrations in cancer, including rearrangements, amplifications and deletions (NIH RIMI Grant with J. Arsuaga).