Research

Research

Research in Mathematics at Ohio State


The Mathematics Department offers a vast array of research opportunities in both theoretical and applied mathematics, which you can explore in the list below. The organization by subject area in the list is often somewhat arbitrary as various research areas have increasingly become cross-disciplinary. 

Interested students should feel free to contact faculty directly with questions about their research.

 

Actuarial Mathematics & Risk Management

Zhenzhen Huang: Actuarial Science, Quantitative Finance, Quantitative Risk Management

Kenneth Ng: Actuarial Science, Stochastic Control, Mean Field Games

Linfeng Zhang: Actuarial Science, Cyber Risk Analytics, Privacy Risk, Pandemic Risk

Algebraic Geometry

David Anderson: Algebraic geometry, Combinatorics, Representation theory, Schubert varieties and Toric Varieties, Equivariant Cohomology and its Applications

Angelica Cueto: Algebraic Geometry, Combinatorics, Non-Archimedean Geometry, Tropical Geometry

Roy Joshua: Algebraic and Arithmetic Geometry, K-Theory, Singular Varieties, Computational aspects of geometry, Quantum computation

Eric Katz: Tropical Geometry, Combinatorial Algebraic Geometry, Arithmetic & Enumerative Geometry

Hsian-Hua Tseng: Algebraic Geometry, Symplectic Topology & Geometry, Mirror Symmetry, Gromov-Witten Theory

Mirel Caibar: Algebraic Geometry, Singularity Theory, Hodge Theory

Combinatorics, Probability, & Graph Theory

Cesar Cuenca: Random Matrices, Random Partitions, Asymptotic Representation Theory, and Algebraic Combinatorics

Neil Falkner: Probability Theory, Brownian Motion

Jimmy He: Probability Theory, Combinatorics

Yifan Jing: Combinatorics and Graph Theory, Harmonic Analysis, Additive and Combinatorial Number Theory, Discrete Probability

Matthew Kahle: Combinatorics, Probability Theory, Geometric Group Theory, Mathematical Physics, Topology, Topological Data Analysis

Hoi Nguyen: Combinatorics - Probability Theory, Random Matrices - Number Theory

Grzegorz Rempala: Complex Stochastic Systems Theory, Molecular Biosystems Modeling, Mathematical and Statistical Methods in Epidemiology and in Genomics

Michael Roysdon: Convex Geometry, Harmonic Analysis, Geometric Functional Analysis, Geometric Tomography, and Probability

David Sivakoff: Stochastic Processes on Large Finite Graphs, Probability Theory, Applications to Percolation Models, Particle Systems, Cellular Automata, Epidemiology, Sociology, and Genetics

John Maharry: Graph Theory, Combinatorics

Aurel Stan: Stochastic Analysis, Harmonic Analysis, Quantum Probability, Wick Products

Differential Geometry

Andrzej Derdzinski: Differential Geometry - Einstein Manifolds

Andrey Gogolyev: Differential Geometry, Topology, Dynamical Systems, Hyperbolic Dynamics

Bo Guan: Differential Geometry, Partial Differential Equations - Geometric Analysis

Matthew Stenzel: Differential Geometry, Several Complex Variables

Ergodic Theory & Dynamical Systems

Vitaly Bergelson: Ergodic Theory, Combinatorics, Ergodic Ramsey Theory, Polynomial Szemerédi Theorems, Number Theory

John Johnson: Algebra in Stone-Cech compactification, Dynamics, Combinatorics related to Ramsey Theory

Alexander Leibman: Ergodic Theory, Dynamics on Nil-Manifolds, Polynomial Szemerédi & van der Waerden Theorems

Nimish Shah: Ergodic Theory, Ergodic Theory on Homogeneous Spaces of Lie Groups, Applications to Number Theory

Dan Thompson: Ergodic Theory, Dynamical Systems, Symbolic Dynamics, Thermodynamic Formalism, Dimension Theory & Geometry

Mathematical Biology, Scientific Computing, & Data Science

Janet Best: Applied Mathematics, Mathematical Biology, Dynamical Systems, Circadian Rhythms, Probability Theory, Stochastic Processes on Random Graphs

Adriana Dawes: Mathematical Biology, Mathematical Modeling of Cell Polarization & Chemotaxis, Differential Equations

Ian Hamilton: Behavioral Ecology, Coerced Cooperation, Evolution of Cooperative Behavior, Mathematical Modeling

Maria Han Veiga: Numerical Analysis for Hyperbolic PDEs, Probabilistic Machine Learning, Constraint & Privacy aware Machine Learning

Wonjun Lee: Applied Mathematics, PDE-based Machine learning and Image Processing, Optimization, Optimal transport

Thomas O'Leary-Roseberry: Scientific Computing, Numerical Mathematics, Applied Mathematics

Bishun Pandey: Applied Mathematics

Grzegorz Rempala*: Complex Stochastic Systems Theory, Molecular Biosystems Modeling, Mathematical and Statistical Methods in Epidemiology and in Genomics

Joseph Tien: Mathematical Biology, Models of Infectious Disease Dynamics, Differential Equations, Parameter Estimation, Neuroscience

Yulong Xing: Numerical Analysis, Scientific Computing, Wave propagation, Computational Fluid Dynamics

Dongbin Xiu: Scientific Computing, Numerical Mathematics, Stochastic Computation, Uncertainty Quantification, Multivariate approximation, Data Assimilation, High-order Numerical Methods

Anna Yesypenko:  Applied Mathematics, Numerical Analysis, Numerical PDE, Scientific Computing

Mathematical Logic, Model Theory

Ivo Herzog: Ring Theory, Module and Representation Theory, Category Theory, Model Theory

Chris Miller: Logic, Model Theory, Applications to Analytic Geometry & Geometric Measure Theory

Number Theory

Ghaith Hiary: Computational number theory, analytic number theory, random matrix models for L-functions, asymptotic analysis

Roman Holowinsky: Number Theory: Analytic Methods, Automorphic forms, L-functions, Sieve Methods, Quantum Unique Ergodicity

Michael Lipnowski: Number Theory, Automorphic Forms, Representation Theory, and Low-dim Topology

Wenzhi Luo: Number Theory, Analytic and Arithmetic Theory of Automorphic Forms and Automorphic L-Functions

Jennifer Park: Number Theory and Algebraic Geometry, Algebraic Curves and Arithmetic Properties, Number and Function Fields

Stefan Patrikis: Number theory, Automorphic forms, Arithmetic Geometry, Galois representations, and Motives

Partial Differential Equations

Rodica Costin: Partial Differential Equations, Difference Equations, Orthogonal Polynomials, Asymptotic Analysis

John Holmes: Partial Differential Equations, Non-Linear PDE, Stochastic Differential Equations, Mathematical Finance, Mathematical Physics

Adrian Lam: Partial Differential Equations, Mathematical Biology, Evolutionary Game Theory, Free-boundary Problems

Saleh Tanveer: Applied Mathematics, Asymptotics, Nonlinear Free boundary problems in Fluid Mechanics and Crystal Growth, PDEs in Fluid Mechanics & Mathematical Physics, Singularity & regularity questions in PDEs

Fei-Ran Tian: Dispersion & Semi-Classical Limits, Whitham Equations, Modulation of Dispersive Oscillations, Free Boundary Problems

Feride Tiglay: Partial Differential Equations, Mathematical Physics, Dynamical Systems, Wave Equations & Fluid Dynamics

Zhuolun Yang: Partial Differential Equations, Fluid Dynamics, Analysis

Pure & Applied Harmonic Analysis

Dustin Mixon: Applied Harmonic Analysis, Mathematical Signal Processing, Compressed Sensing

Krystal Taylor: Harmonic Analysis, Geometric Measure Theory, Harmonic Analysis on Fractals, Applications to Analytic Number Theory

Scott Zimmerman: Analysis on Metric Spaces, Geometric Measure Theory, Harmonic Analysis, PDEs

Pure & Applied Topology & Geometry

Nathan Broaddus: Geometric Group Theory, Topology, Low-dim Topology

James Fowler: Topology, Geometric Topology of Manifolds, Geometric Group Theory, Surgery Theory, K-Theory, Mathematics Education

Jingyin Huang: Geometric Group Theory, Metric Geometry

Thomas Kerler: Low-dimensional Topology, Quantum Algebras and their Representations, Invariants of 3-dim Manifolds and Knots, Topological Quantum Field Theories

Sanjeevi Krishnan: Directed Algebraic Topology and Applications to Optimization, Data Analysis, and dynamics

Jean-François Lafont: Topology, Differential Geometry, Geometric Group Theory, K-Theory

Beibei Liu: Hyperbolic Geometry, Kleinian Groups, Geometric Group Theory, Topology and Geometry of 3-, 4-manifolds, Heegaard Floer Homology

Crichton Ogle: Topology - K-Theory

Sergei Chmutov: Topology, Knot Theory, Quantum Invariants

Micah Chrisman: Knot Theory, Low-Dimensional Topology, Virtual knots, Finite-type Invariants, Knot Concordance, Generalized Cohomology Theories

John Harper: Topology, Homotopy Theory, Modules over Operads, K-Theory & TQ-Homology

Niles Johnson: Topology, Categorical and Computational Aspects of Algebraic Topology, Picard/Brauer theory

Donald Yau: Topology, Algebra, Hom-Lie algebras, Deformations

Real & Complex Analysis

Ovidiu Costin: Analysis, Asymptotics, Borel Summability, Analyzable Functions, Applications to PDE and difference equations, Time dependent Schrödinger equation, Surreal numbers

Marjorie Drake: Analysis, Interpolation and Approximation Theory, Geometric Analysis, Whitney-type extension and trace problems, Convexity, Sobolev spaces

Kenneth Koenig: Several Complex Variables, Szegő & Bergman Projections, ∂--Neumann problem

Dusty Grundmeier: Mathematics Education, Several Complex Variables, and CR manifolds

Liz Vivas: Holomorphic Dynamical Systems, Several Complex Variables, Complex Geometry & Affine Algebraic Geometry, Monge-Ampere equations and CR manifolds

Jan Lang: Analysis, Differential Equations, Harmonic Analysis, Function Spaces, Integral Inequalities, PDE - Function Theory

Representation Theory, Operator Theory, & Quantum Information

Kaifeng Bu: Quantum Information and Computation, Mathematical Physics

Luis Casian: Representation Theory, Representation Theory of Real Semisimple Lie Groups, Integrable Systems

Sachin Gautam: Representation Theory of Infinite-Dimensional Quantum Groups, Classical and Quantum Integrable Systems

Roberto Hernandez Palomares: Operator algebras, Quantum Information and Quantum Symmetries

David Penneys: Operator algebra, von-Neuman Subfactors, Fusion and Tensor Categories, Mathematical Physics, Non-commutative Geometry

Rings & Modules

Ranthony Clark: Commutative Ring Theory, Applied Algebraic Topology, Data Science, Mathematics Education, and the History of Black Mathematicians

Ivo Herzog: Ring Theory, Module and Representation Theory, Category Theory, Model Theory

Cosmin Roman: Ring Theory, Module Theory, Injectivity-Like Properties, Relations Between Modules and Their Endomorphisms Ring, Theory of Rings and Modules

Mohamed Yousif: Rings and Modules, Injective and Continuous Rings and Modules, Pseudo and Quasi-Frobenius Rings