Research | Department of Mathematics (2024)

Research | Department of Mathematics (1)
Research | Department of Mathematics (2)
Research | Department of Mathematics (3)

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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: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

Research | Department of Mathematics (2024)

FAQs

What is the most difficult branch of math? ›

Calculus

One of the most complex and highly advanced branches of mathematics, which in fact itself has levels to it, be it Pre-calculus, advanced calculus, Accelerated Multivariable Calculus, differential calculus, integral calculus, etc.

What is research in mathematics? ›

Mathematics research is the long-term, open-ended exploration of a set of related mathematics questions whose answers connect to and build upon each other. Problems are open-ended because students continually come up with new questions to ask based on their observations.

Which field is best for research in mathematics? ›

Research Areas
  • Algebra, Combinatorics, and Geometry. ...
  • Analysis and Partial Differential Equations. ...
  • Applied Analysis. ...
  • Mathematical Biology. ...
  • Mathematical Finance. ...
  • Numerical Analysis and Scientific Computing. ...
  • Topology and Differential Geometry.

Which topic is best for research in mathematics? ›

  • Algebraic topology and Homotopy theory. ...
  • Algebraic topology, Combinatorial topology. ...
  • Low dimensional topology. ...
  • Geometric group theory and Hyperbolic geometry. ...
  • Manifolds and Characteristic classes. ...
  • Moduli spaces of hyperbolic surfaces. ...
  • Systolic topology and Geometry. ...
  • Topological graph theory.

What is the easiest branch of math? ›

Probability and Statistics is one of the most important and underrated branches of mathematics. Probability and Statistics is also one of the easiest, or at least easier when compared to other branches like calculus.

How much do math researchers make? ›

What are Top 10 Highest Paying Cities for Research Mathematician Jobs
CityAnnual SalaryHourly Wage
Sunnyvale, CA$83,124$39.96
Santa Cruz, CA$81,085$38.98
Livermore, CA$80,987$38.94
Manhattan, NY$80,917$38.90
6 more rows

Is mathematical research hard? ›

Asking good mathematical questions is not easy, and in many cases it may be the most difficult part of doing research. In fact, the rest of the research process can become surprisingly easy once you've found the right question to work on.

How to become a research mathematician? ›

Requirements and Qualifications
  1. Master's degree in mathematics; doctorate preferred.
  2. Laboratory or other research experience.
  3. Computer proficiency.
  4. Physics knowledge and experience.
  5. Strong analytical problem-solving skills.

Is there a high demand for mathematicians? ›

The Bureau of Labor Statistics projects 2.2% employment growth for mathematicians between 2022 and 2032. In that period, an estimated 100 jobs should open up. A mathematician can be anyone from your middle school algebra teacher to a computer programmer.

Who are the largest employers of mathematicians? ›

Work Environment

The top employers of mathematicians and statisticians are the federal government and scientific research and development companies. Mathematicians and statisticians may work on teams with engineers, scientists, and other specialists.

What is the hardest mathematical topic to learn? ›

Calculus: Calculus is a branch of the discipline investigating the relative rate of change, also known as differential calculus. It also helps summate infinite particles to find a conclusive result, known as integral calculus.

What kind of research do mathematicians do? ›

As a research mathematician, you can work in a variety of areas, however, you'll typically be involved in proving deep and abstract theorems, developing mathematical descriptions (models) to explain or predict real phenomena, and applying mathematical principles to identify trends in data sets.

Why do we do research in mathematics? ›

Finally, outside of its direct applicability to the world around us, mathematical research helps us to improve and refresh the quality of what we teach, and certainly the world needs a large number of graduates with a wide variety of mathematical skills to fill the wide variety of positions that require some ...

What is the hardest type of maths? ›

Algebra: Algebra is considered one of the most challenging topics in mathematics that help in the studies of different types of symbols and also the different rules which help in controlling these symbols.

What is the hardest math of all time? ›

  • Fermat's Last Theorem. Getty Images. ...
  • The Classification of Finite Simple Groups. Wikimedia Commons. ...
  • The Four Color Theorem. ...
  • (The Independence of) The Continuum Hypothesis. ...
  • Gödel's Incompleteness Theorems. ...
  • The Prime Number Theorem. ...
  • Solving Polynomials by Radicals. ...
  • Trisecting an Angle.
Dec 28, 2023

What is the most difficult maths degree? ›

Part III of the Mathematical Tripos (officially Master of Mathematics/Master of Advanced Study) is a one-year master's-level taught course in mathematics offered at the Faculty of Mathematics, University of Cambridge. It is regarded as one of the most difficult and intensive mathematics courses in the world.

Is calculus the hardest math? ›

Calculus is widely regarded as a very hard math class, and with good reason. The concepts take you far beyond the comfortable realms of algebra and geometry that you've explored in previous courses. Calculus asks you to think in ways that are more abstract, requiring more imagination.

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