Research excellence is a prime objective of the Mathematics Department. Faculty members conduct research in a variety of areas in pure and applied mathematics. Grants from the federal and state government support many faculty members' research programs. These grants often include support for graduate students seeking Ph.D. or master degrees. The research areas in the Department of Mathematics may be loosely grouped into:

- Algebra
- Analysis
- Applied and Computational Mathematics
- Dynamical Systems and Ergodic Theory
- Geometry and Topology
- Mathematical Logic and Foundations
- Number Theory
- Statistics

# Algebra

**Areas of Research:**

- Combinatorics
- Group Theory
- Homological algebra
- Representation theory

**Faculty:**

- Lea Beneish (Vertex Algebras)
- Doug Brozovic
- Charles Conley
- Anne Shepler (Deformation Theory, Reflection Groups, Algebraic Combinatorics, Hochschild Cohomology)

# Analysis

**Areas of Research:**

- Functional Analysis
- Measure Theory
- Partial Differential Equations
- Probability
- Real and Complex Analysis

**Faculty:**

- Pieter Allaart (Probability, Fractal Geometry)
- Nicolae Anghel (Complex Analysis of One and Several Variables, Mathematical Physics, Math Education)
- Lior Fishman
- Joe Iaia (Nonlinear Ordinary and Partial Differential Equations)
- Kirill Lazebnik
- Bunyamin Sari (Banach Space Theory, Linear and Nonlinear Geometry of Infinite Dimensional Banach Spaces)
- Mariusz Urbański (Functional Analysis)

# Applied and Computational Mathematics

**Areas of Research:**

- Computational Biology and Bioinformatics
- Machine Learning
- Mathematical Biology
- Numerical Analysis
- Optimization
- Uncertainty Quantification

**Faculty:**

- Serdar Bozdag (Bioinformatics and Computational Biology, Machine Learning, Data Mining, Biological Network Modelling and Analysis, Precision Medicine)
- Yanyan He (Uncertainty Quantification, Uncertainty Modeling, Uncertain Data Fusion, Fuzzy Sets, Fuzzy Measures)
- J. Jianguo Liu (Optimization, Numerical Analysis, Scientific Computation, Data Classification, Machine Learning)
- Shuang Liu (Numerical PDEs, Mathematical Biology, Computational Biology, Computational Moving Boundary Problems, Scientific Computing)
- John Quintanilla (Stochastic Geometry, Percolation, Random Heterogeneous Materials)
- Giordano Tierra Chica (Fluid Mechanics, Modeling, Numerical Analysis, PDEs, Scientific Computing)

# Dynamical Systems and Ergodic Theory

**Areas of Research:**

- Conformal, Holomorphic, and Meromorphic Dynamical systems
- Conformal Iterated Functions Systems
- Ergodic Theory and Topological Dynamics
- Open Dynamical Systems
- Random Dynamical Systems
- Thermodynamic Formalism

**Faculty:**

- Pieter Allaart (Fractal Geometry, Beta Transformations and Symbolic Dynamics)
- Lior Fishman
- Kirill Lazebnik (Geometric Function Theory and Complex Dynamics)
- Mariusz Urbański (Thermodynamic Formalism; Conformal, Holomorphic, and Transcendental Dynamical Systems; Random Dynamical Systems; Open Dynamical Systems; Conformal Iterated Functions Systems and Graph Directed Markov Systems; Hausdorff Dimension; Rational Semigroups)

# Geometry and Topology

**Areas of Research:**

- Topological Groups

**Faculty:**

- Nicolae Anghel (Geometric Analysis, Differential Geometry)
- Mariusz Urbański (Kleinian Groups, Fractal Geometry, Topological Dimension, Circle Packings)

# Mathematical Logic and Foundations

**Areas of Research:**

- Descriptive Set Theory
- Set Theory

**Faculty:**

- Steve Jackson
- John Krueger (Combinatorial Set Theory, Consistency Results, Forcing)
- Nam Trang (Inner models, Determinacy, Forcing, Consistency Results)

# Number Theory

**Areas of Research:**

- Automorphic Forms
- Classical Modular Forms
- Representation Theoretic Methods

**Faculty:**

- Lea Beneish (Modular Generating Series, Arithmetic Statistics of Curves, Modular Forms, Mock Modular Forms)
- William Cherry (Complex Analysis/Geometry, p-adic Analysis/Geometry)
- Lior Fishman
- Jackson Morrow (Arithmetic Geometry, Non-Archimedean Geometry, Algebraic Geometry, Rational Points on Varieties)
- Olav Richter (Automorphic Forms: In particular, Jacobi Forms, Siegel Modular Forms, Maass Forms, Mock Theta Functions and Related Objects)
- Ralf Schmidt (Classical and Adelic Modular Forms, Local and Global Representation Theory, Automorphic L-Functions)
- Mariusz Urbański (Diophantine Approximation, Continued Fractions)

# Statistics

**Areas of Research:**

- Biostatistics

**Faculty:**

- Junhyeon Kwon (Multiscale Methods in Statistics, Spatial Statistics, Time Series Analysis, Environmental Statistics)
- Michael Monticino
- Kai-Sheng Song