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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 increasinglybecome cross-disciplinary.

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

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

AngelicaCueto:*Algebraic Geometry, Combinatorics, Non-Archimedean Geometry, Tropical Geometry*

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

EricKatz:*Tropical Geometry, Combinatorial Algebraic Geometry, Arithmetic & Enumerative Geometry*

Hsian-HuaTseng:*Algebraic Geometry, Symplectic Topology & Geometry, Mirror Symmetry, Gromov-Witten Theory*

MirelCaibar:*Algebraic Geometry, Singularity Theory, Hodge Theory*

JamesCogdell:*Number Theory, Analytic Number theory,**L-functions - Converse Theorems*

GhaithHiary:*Computational number theory, analytic number theory, random matrix models for L-functions, asymptotic analysis*

RomanHolowinsky:*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*

WenzhiLuo:*Number Theory, Analytic and Arithmetic Theory of Automorphic Forms and Automorphic L-Functions*

JenniferPark:*Number Theory and Algebraic Geometry, Algebraic Curves and Arithmetic Properties, Number and Function Fields*

StefanPatrikis:*Number theory, Automorphic forms, Arithmetic Geometry,* *Galois representations, and Motives*

IvoHerzog:*Ring Theory, Module and Representation Theory, Category Theory, Model Theory*

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

MohamedYousif:*Rings and Modules, Injective and Continuous Rings and Modules, Pseudo and Quasi-Frobenius Rings*

NathanBroaddus:*Geometric Group Theory, Topology, Low-dim Topology*

JamesFowler:*Topology, Geometric Topology of Manifolds, Geometric Group Theory, Surgery Theory, K-Theory, Mathematics Education*

Jingyin Huang:*Geometric Group Theory, Metric Geometry*

ThomasKerler:*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-FrançoisLafont:*Topology, Differential Geometry, Geometric Group Theory, K-Theory*

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

FacundoMémoli:*Shape comparison, Computational Topology, Topological data analysis, Machine learning*

CrichtonOgle:*Topology - K-Theory*

SergeiChmutov:*Topology, Knot Theory, Quantum Invariants*

MicahChrisman:*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*

NilesJohnson:*Topology, Categorical and Computational Aspects of Algebraic Topology, Picard/Brauer theory*

VidhyanathRao:*Topology - Homotopy Theory - K-Theory*

DonaldYau:*Topology, Algebra, Hom-Lie algebras, Deformations*

AndrzejDerdzinski:*Differential Geometry - Einstein Manifolds*

AndreyGogolyev:*Differential Geometry, Topology, Dynamical Systems, Hyperbolic Dynamics*

BoGuan:*Differential Geometry, Partial Differential Equations - Geometric Analysis*

MatthewStenzel:*Differential Geometry, Several Complex Variables*

CesarCuenca:*Random Matrices, Random Partitions, Asymptotic Representation Theory, and Algebraic Combinatorics*

NeilFalkner:*Probability Theory, Brownian Motion*

MatthewKahle:*Combinatorics, Probability Theory, Geometric Group Theory, Mathematical Physics, Topology, Topological Data Analysis*

HoiNguyen:*Combinatorics - Probability Theory, Random Matrices - Number Theory*

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

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

JohnMaharry:*Graph Theory, Combinatorics*

AurelStan:*Stochastic Analysis, Harmonic Analysis, Quantum Probability, Wick Products*

GabrielConant:*Model theory of Groups, Graphs, and Homogenous structures. Additive Combinatorics*

ChrisMiller:*Logic, Model Theory, Applications to Analytic Geometry & Geometric Measure Theory*

CarolineTerry:*Model theory, Extremal Combinatorics, Graph Theory, Additive Combinatorics*

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

KennethKoenig:*Several Complex Variables, Szegő & Bergman Projections, ∂--Neumann problem*

DustyGrundmeier:*Mathematics Education,Several Complex Variables, andCR manifolds*

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

JanLang:*Analysis, Differential Equations, Harmonic Analysis, Function Spaces, Integral Inequalities, PDE - Function Theory*

RodicaCostin:*Partial Differential Equations, Difference Equations, Orthogonal Polynomials, Asymptotic Analysis*

JohnHolmes:*Partial Differential Equations, Non-Linear PDE, Stochastic Differential Equations, Mathematical Finance, Mathematical Physics*

AdrianLam:*Partial Differential Equations, Mathematical Biology, Evolutionary Game Theory, Free-boundary Problems*

SalehTanveer:*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-RanTian:*Dispersion & Semi-Classical Limits, Whitham Equations, Modulation of Dispersive Oscillations, Free Boundary Problems*

FerideTiglay:*Partial Differential Equations, Mathematical Physics, Dynamical Systems, Wave Equations & Fluid Dynamics*

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

AdrianaDawes:*Mathematical Biology, Mathematical Modeling of Cell Polarization & Chemotaxis, Differential Equations*

IanHamilton:*Behavioral Ecology, Coerced Cooperation, Evolution of Cooperative Behavior, Mathematical Modeling*

MariaHan Veiga:*Numerical Analysis for Hyperbolic PDEs, Probabilistic Machine Learning, Constraint & Privacy aware Machine Learning*

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

JosephTien:*Mathematical Biology, Models of Infectious Disease Dynamics, Differential Equations, Parameter Estimation, Neuroscience*

YulongXing:*Numerical Analysis, Scientific Computing, Wave propagation, Computational Fluid Dynamics*

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

BishunPandey:*Applied Mathematics*

VitalyBergelson:*Ergodic Theory, Combinatorics, Ergodic Ramsey Theory, Polynomial Szemerédi Theorems, Number Theory*

JohnJohnson:*Algebra in Stone-Cech compactification, Dynamics, Combinatorics related to Ramsey Theory*

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

NimishShah:*Ergodic Theory, Ergodic Theory on Homogeneous Spaces of Lie Groups, Applications to Number Theory*

DanThompson:*Ergodic Theory, Dynamical Systems, Symbolic Dynamics, Thermodynamic Formalism, Dimension Theory & Geometry*

LuisCasian:*Rep*r*esentation Theory, Representation Theory of Real Semisimple Lie Groups, Integrable Systems*

SachinGautam:*Representation Theory of Infinite-Dimensional Quantum Groups, Classical and Quantum Integrable Systems*

DustinMixon:*Applied Harmonic Analysis, Mathematical Signal Processing, Compressed Sensing*

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

KrystalTaylor:*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*