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Research Areas
Algebra and Number Theory
Dustin Cartwright - Algebraic Geometry
- Tropical Geometry
- Applied Algebra
Luis Finotti - Arithmetic Geometry
- p-Adic and Local Fields
- Computational Aspects
Marie Jameson - Number Theory: Modular Forms
Shashikant Mulay - Commutative Algebra
- Algebraic Geometry
- Mathematical Physics
Morwen Thistlethwaite - Discrete Subgroups of Lie Groups
- Computational Algebra
Analysis
Michael Frazier - Wavelets
- Harmonic Analysis
- Function Spaces
Joan Lind - Complex Analysis
- Probability
Remus Nicoara - Operator Algebras
- Functional Analysis
Stefan Richter - Complex Analysis
- Functional Analysis
Kenneth Stephenson - Circle Packing
- 2D Particle configurations (graphene, quantum glasses, electron distributions)
- Numerical conformal mapping (planar and surface)
Vyron Vellis - Geometric Function Theory
- Geometric Measure Theory
- Complex Analysis
Computational and Applied Mathematics
Vasilios Alexiades - Biomathematics
- Phase Cange Processes
- Heat & Mass Transfer, CFD
Nina Fefferman - Network Theory
- Distributed Anomaly Detection
- Applied Algebraic Topology
Xiaobing Feng - Numerical PDEs and Scientific Computing
Ohannes Karakashian - Finite Element and discontinuous Galerkin methods
- Fast iterative solvers, Domain Decomposition
- Navier-Stokes equations, nonlinear dispersive equations
Tim Schulze - Materials Science
- Crystal Growth
- Kinetic Monte Carlo Simulation
Kenneth Stephenson - 3D printing
- Discrete Conformal Geometry
Steven Wise - Multi-phase Flows, Moving Boundary Problems
- Numerical Methods for PDE
- Fast Solvers for Nonlinear Elliptic PDE
Differential Geometry
Theodora Bourni - Geometric Analysis
- Geometric measure theory
Alexandre Freire - Geometric Analysis
- Analysis on manifolds
Conrad Plaut - Riemannian Geometry
- Metric Geometry/Alexandrov Spaces
- Geometry of Fractals
Vyron Vellis - sub-Riemannian Geometry
- Metric Geometry
- Geometry of Fractals
Mathematical Biology
Vasilios Alexiades - chemotaxis, action potentials, phototransduction
Judy Day - dynamical systems
- mathematical modeling and control
- model predictive control
Nina Fefferman - Epidemiology & BioSecurity
- Evolution and Stability of Social-Behavioral Systems
- Self-organizing Adaptive Complex Systems
Xiaobing Feng - Systems biology and gene function prediction
Vitaly Ganusov - Immunology
- Infectious diseases
- Within-host dynamics
Sergey Gavrilets - Biological, social, and cultural evolution. Human origins. Social complexity, conflict, and cooperation in historical and modern societies.
Louis Gross - Population and Community Ecology
- Vegetation Modeling
- Quantitative Education In The Life Sciences.
Suzanne Lenhart - Optimal Control of ODEs, PDEs, discrete and integrodifference equations
- Population Models, Infectious Diseases, One Health
- Natural Resource Modeling, Invasive Species, Agent Based Models
Vasileios Maroulas - Statistical Learning Methods in Neuroscience and Molecular Biology
Christopher Strickland - Mathematical Modeling
- Complex Systems
- Population Ecology
Partial Differential Equations
Vasilios Alexiades - Parallel Computing, Computational Science Education
- laser ablation, solidification
Xiaobing Feng - Fully nonlinear PDEs and geometric flows
Alexandre Freire - Geometric flows
- Spectrum of Riemannian manifolds
Mathew Langford - Fully nonlinear elliptic and parabolic equations
Suzanne Lenhart - Parabolic Systems
- First order PDEs for age structure models
- Elliptic equations for population models
Tadele Mengesha - Partial differential equations, system of integral equations applied to mechanics
- Calculus of variations
Tuoc Phan - Partial differential equations
Henry Simpson - Mathematical Elasticity
- Nonlinear Elliptic Partial Differential Equations, Variational and Topological Aspects, Bifurcation.
Grozdena Todorova - Hyperbolic and Parabolic Partial Differential Equations
- Mathematical Physics
Steven Wise - Nonlinear Parabolic PDE
- Existence, Uniqueness, and Regularity of Solutions
Probability and Stochastic Processes
Xia Chen - Large deviation
- Stochastic partial differential equations
- Brownian motions and random walks
Xiaobing Feng - Nonlinear stochastic PDEs and their numerical solutions
Statistics and Data Analysis
Vitaly Ganusov - Data Science
- Statistics
- Computation
Louis Gross
Vasileios Maroulas - Computational Bayesian Statistics
- Topological Data Analysis
- Foundations of Data Science
Topology
Conrad Plaut - Discrete Homotopy Theory
- Topological Groups
- Generalized Covering Spaces