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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 Cohom*ology 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 hom*ology
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 Cohom*ology Theories
John Harper:Topology, hom*otopy Theory, Modules over Operads, K-Theory & TQ-hom*ology
NilesJohnson:Topology, Categorical and Computational Aspects of Algebraic Topology, Picard/Brauer theory
VidhyanathRao:Topology - hom*otopy 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 hom*ogenous 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 hom*ogeneous Spaces of Lie Groups, Applications to Number Theory
DanThompson:Ergodic Theory, Dynamical Systems, Symbolic Dynamics, Thermodynamic Formalism, Dimension Theory & Geometry
LuisCasian:Representation 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
