Research in the Department of Mathematics | Department of Mathematics

Research in the Department of Mathematics

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

Areas of Research:

  • Combinatorics
  • Group Theory
  • Homological algebra
  • Representation theory

Faculty:

Analysis

Areas of Research:

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

Faculty:

Applied and Computational Mathematics

Areas of Research:

  • Mathematical Biology
  • Numerical Analysis
  • Optimization
  • Uncertainty Quantification

Faculty:

  • Rajeev Azad (Bioinformatics and Computational Biology, Probabilistic Modeling of Biomolecular Sequences, Machine Learning, Gene Network Analysis)
  • 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)
  • 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:

  • Lior Fishman
  • Su Gao (Ergodic Theory and Topological 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)
  • Su Gao (Noncompact Transformation Groups)
  • Mariusz Urbański (Kleinian Groups, Fractal Geometry, Topological Dimension, Circle Packings)

Mathematical Logic and Foundations

Areas of Research:

  • Descriptive Set Theory
  • Set Theory

Faculty:

Number Theory

Areas of Research:

  • Automorphic Forms
  • Classical Modular Forms
  • Representation Theoretic Methods

Faculty:

  • William Cherry (Complex Analysis/Geometry, p-adic Analysis/Geometry)
  • Lior Fishman
  • 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:

  • Han Hao
  • Michael Monticino
  • Kai-Sheng Song
  • Xuexia Wang (Statistical Methods Development and Applications in Cancer Genomics, Genome Wide Association Studies, Genetic Risk Prediction, RNA Sequencing Data Analysis, Single Cell Analysis, Image Analysis, Biological Network Modeling and Analysis, Disease Biomarker Identification)

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