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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.


David AndersonAlgebraic geometry, Combinatorics, Representation theory, Schubert varieties and Toric Varieties, Equivariant Cohomology and its Applications

Angelica CuetoAlgebraic Geometry, Combinatorics, Non-Archimedean Geometry, Tropical Geometry

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

Eric KatzTropical Geometry, Combinatorial Algebraic Geometry, Arithmetic & Enumerative Geometry

Hsian-Hua TsengAlgebraic Geometry, Symplectic Topology & Geometry, Mirror Symmetry, Gromov-Witten Theory

Mirel CaibarAlgebraic Geometry, Singularity Theory, Hodge Theory

James CogdellNumber Theory, Analytic Number theory,
 L-functions - Converse Theorems

Ghaith HiaryComputational number theory, analytic number theory, random matrix models for L-functions, asymptotic analysis

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

Michael LipnowskiNumber Theory, Automorphic Forms, Representation Theory, and Low-dim Topology

Wenzhi LuoNumber Theory, Analytic and Arithmetic Theory of Automorphic Forms and Automorphic L-Functions

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

Stefan PatrikisNumber theory, Automorphic forms, Arithmetic Geometry, Galois representations, and Motives

Ivo HerzogRing Theory, Module and Representation Theory, Category Theory, Model Theory

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

Mohamed YousifRings and Modules, Injective and Continuous Rings and Modules, Pseudo and Quasi-Frobenius Rings

Nathan BroaddusGeometric Group Theory, Topology, Low-dim Topology

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

Jingyin HuangGeometric Group Theory, Metric Geometry

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

Sanjeevi KrishnanDirected Algebraic Topology and Applications to Optimization, Data Analysis, and dynamics

Jean-François LafontTopology, Differential Geometry, Geometric Group Theory, K-Theory

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

Facundo MémoliShape comparison, Computational Topology, Topological data analysis, Machine learning

Crichton OgleTopology - K-Theory

Sergei ChmutovTopology, Knot Theory, Quantum Invariants

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

John HarperTopology, Homotopy Theory, Modules over Operads, K-Theory & TQ-Homology

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

Vidhyanath RaoTopology - Homotopy Theory - K-Theory

Donald YauTopology, Algebra, Hom-Lie algebras, Deformations

Andrzej DerdzinskiDifferential Geometry - Einstein Manifolds

Andrey GogolyevDifferential Geometry, Topology, Dynamical Systems, Hyperbolic Dynamics

Bo GuanDifferential Geometry, Partial Differential Equations - Geometric Analysis

Matthew StenzelDifferential Geometry, Several Complex Variables

Cesar CuencaRandom Matrices, Random Partitions, Asymptotic Representation Theory, and Algebraic Combinatorics

Neil FalknerProbability Theory, Brownian Motion

Matthew KahleCombinatorics, Probability Theory, Geometric Group Theory, Mathematical Physics, Topology, Topological Data Analysis

Hoi NguyenCombinatorics - Probability Theory, Random Matrices - Number Theory

Grzegorz RempalaComplex Stochastic Systems Theory, Molecular Biosystems Modeling, Mathematical and Statistical Methods in Epidemiology and in Genomics

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

John MaharryGraph Theory, Combinatorics

Aurel StanStochastic Analysis, Harmonic Analysis, Quantum Probability, Wick Products

Gabriel ConantModel theory of Groups, Graphs, and Homogenous structures. Additive Combinatorics

Chris MillerLogic, Model Theory, Applications to Analytic Geometry & Geometric Measure Theory

Caroline TerryModel theory, Extremal Combinatorics, Graph Theory, Additive Combinatorics

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

Kenneth KoenigSeveral Complex Variables, Szegő & Bergman Projections, ∂--Neumann problem

Dusty GrundmeierMathematics Education, Several Complex Variables, and CR manifolds

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

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

Rodica CostinPartial Differential Equations, Difference Equations, Orthogonal Polynomials, Asymptotic Analysis

John HolmesPartial Differential Equations, Non-Linear PDE, Stochastic Differential Equations, Mathematical Finance, Mathematical Physics

Adrian LamPartial Differential Equations, Mathematical Biology, Evolutionary Game Theory, Free-boundary Problems

Saleh TanveerApplied 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 TianDispersion & Semi-Classical Limits, Whitham Equations, Modulation of Dispersive Oscillations, Free Boundary Problems

Feride TiglayPartial Differential Equations, Mathematical Physics, Dynamical Systems, Wave Equations & Fluid Dynamics

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

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

Ian HamiltonBehavioral Ecology, Coerced Cooperation, Evolution of Cooperative Behavior, Mathematical Modeling

Maria Han VeigaNumerical Analysis for Hyperbolic PDEs, Probabilistic Machine Learning, Constraint & Privacy aware Machine Learning

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

Joseph TienMathematical Biology, Models of Infectious Disease Dynamics, Differential Equations, Parameter Estimation, Neuroscience

Yulong XingNumerical Analysis, Scientific Computing, Wave propagation, Computational Fluid Dynamics

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

Bishun PandeyApplied Mathematics

Vitaly BergelsonErgodic Theory, Combinatorics, Ergodic Ramsey Theory, Polynomial Szemerédi Theorems, Number Theory

John JohnsonAlgebra in Stone-Cech compactification, Dynamics, Combinatorics related to Ramsey Theory

Alexander LeibmanErgodic Theory, Dynamics on Nil-Manifolds, Polynomial Szemerédi & van der Waerden Theorems

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

Dan ThompsonErgodic Theory, Dynamical Systems, Symbolic Dynamics, Thermodynamic Formalism, Dimension Theory & Geometry

Luis CasianRepresentation Theory, Representation Theory of Real Semisimple Lie Groups, Integrable Systems

Sachin GautamRepresentation Theory of Infinite-Dimensional Quantum Groups, Classical and Quantum Integrable Systems

Dustin MixonApplied Harmonic Analysis, Mathematical Signal Processing, Compressed Sensing

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

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

Scott ZimmermanAnalysis on Metric Spaces, Geometric Measure Theory, Harmonic Analysis, PDEs