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.
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
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
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
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
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
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
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
Ivo Herzog: Ring Theory, Module and Representation Theory, Category Theory, Model Theory
Chris Miller: Logic, Model Theory, Applications to Analytic Geometry & Geometric Measure 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
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
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
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
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
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
David Penneys: Operator algebra, von-Neuman Subfactors, Fusion and Tensor Categories, Mathematical Physics, Non-commutative Geometry
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