#### Primary Fields of Interest.

**Algebra.** Ardila, Gubeladze, Hosten

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

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

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

** Differential Geometry. ** Bao

** Dynamics. ** Cheung, Goetz

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

** Game Theory. ** Langlois

** Fractal Geometry. ** Lai

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

** History. ** Smith*

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

** Statistics. ** He, Hosten, Kafai, Piryatinska

** Topology. ** Ardila, Cheung

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

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.

Tao He’s research interests include large scale genome-wide association studies, statistical inference on high-dimensional data and statistical learning.

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.

Chun-Kit Lai's research is in harmonic analysis and fractal geometry.

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.

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.

Kim Seashore's researches teachers' use of student thinking and formative assessment in order to achieve more equitable learning outcomes in mathematics.

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.