# Faculty Research

## Algebraic Geometry and Number Theory

#### Research Interests

Number theory, applied probability

#### Research Interests

number theory, arithmetic geometry, p-adic integration, p-adic cohomology, Shimura varieties, automorphic forms, algebraic cycles, algebraic K-theory.

#### Research Groups

#### Graduate Students

#### Research Groups

#### Research Interests

Automorphic representations and L-functions

#### Research Groups

#### Postdoctoral Fellows

#### Research Interests

Model theory (a branch of mathematical logic), and its interactions with other areas of mathematics, especially algebraic geometry, representation theory and differential equations. I also like algebraic geometry in general, as well as category theory and related subjects.

#### Graduate Students

#### Research Interests

Singularities, Algebraic Geometry, Commutative Algebra

#### Research Groups

#### Postdoctoral Fellows

#### Research Interests

Representation theory.

#### Research Groups

#### Postdoctoral Fellows

#### Graduate Students

#### Research Interests

Function Theory, Differential equations, Number Theory

#### Research Groups

#### Research Interests

Algebraic geometry: polynomial automorphisms, geometric function theory, external problems in complex analysis.

#### Research Groups

#### Research Interests

Automorphic forms, Representation Theory, Harmonic analysis.

#### Research Groups

#### Research Interests

Algebraic geometry, Tropical Geometry, Singularities

#### Research Groups

#### Postdoctoral Fellows

#### Research Interests

Operator theory, system theory, algebraic geometry

#### Research Interests

Algebraic geometry, noncommutative algebra

#### Research Groups

## Applied Mathematics and Differential Equations

#### Research Interests

Differential Equations, differential-functional and difference equations

#### Research Groups

#### Research Interests

Differential equations, asymptotic theory of differential operators

#### Research Groups

#### Research Interests

Functional differential equations and their applications in spectral theory of Schroedinger operator, dynamical systems and probability theory.

#### Research Interests

Functional-Differential and hybrid systems, control and optimization problems, neural networks, operator theory

#### Research Groups

#### Research Interests

Free boundary and variational problems, numerical methods, mathematical modeling, granular mechanics, applied super- conductivity

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#### Research Interests

Theory of nonlinear transport processes in continuous media, specific interests: mass and momentum transfer in electrolyte solutions, synthetic ion-exchange membranes, reaction-diffusion, free boundary problems in heat and mass transfer.

#### Research Groups

#### Research Interests

Dualitative properties of partial differential equations. mathematical models of water disalination by electro-dialysis

#### Research Groups

## Combinatorics and Discrete Mathematics

#### Research Interests

Number theory, applied probability

#### Research Interests

Geometric groups theory, Locally compact groups and their lattices, Invariant random subgroups, Permutation groups, Expanding graphs.

#### Research Groups

#### Graduate Students

#### Research Interests

Computational and combinatorial geometry, sensor and wireless networks, online algorithms, discrete math.

#### Research Groups

#### Postdoctoral Fellows

## Functional Analysis, Operator Theory and Operator Algebras

#### Research Interests

- Quaternionic analysis. Function theory on Riemann surfaces. Linear system theory
- Infinite dimensional analysis, Hida’s white noise space, Gaussian processes

#### Research Interests

Functional analysis, geometry of Banach spaces, extremal structure of convex bodies, infinite-dimensional polytopes

#### Research Groups

#### Research Interests

Topological groups (general theory), abstract harmonic analysis, topological dynamics

#### Research Groups

#### Research Interests

Operator algebras.

#### Research Groups

#### Postdoctoral Fellows

#### Graduate Students

#### Research Interests

Operator algebras

#### Research Groups

#### Postdoctoral Fellows

#### Research Interests

Operator theory, system theory, algebraic geometry

## Mathematical and Computational Logic

#### Research Interests

Model theory and applications to algebra and geometry.

#### Research Groups

#### Graduate Students

#### Research Interests

Model theory (a branch of mathematical logic), and its interactions with other areas of mathematics, especially algebraic geometry, representation theory and differential equations. I also like algebraic geometry in general, as well as category theory and related subjects.

#### Graduate Students

#### Research Interests

Set theoretic topology, functional analysis, topological groups.

#### Research Groups

## Other

#### Research Interests

Knot Theory: Vassiliev invariants, Heegaard Floer and Khovanov homologies.

Symplectic geometry and low-dimensional topology.

Braid groups, mapping class groups and transformation groups of smooth manifolds: quasi- morphisms, norms.

Geometric group theory: quasi-isometric embeddings of finitely generated groups, bi-invariant word metrics.

#### Postdoctoral Fellows

#### Research Interests

Galois theory, field arithmetic, Galois cohomology, valuation theory

#### Research Interests

Set theory, mathematical logic, combinatorics.

#### Postdoctoral Fellows

#### Research Interests

Topology, dimension theory, geometric topology, continuum theory

#### Postdoctoral Fellows

#### Research Interests

Theory of Lie algebras, constructive algebraic geometry, algorithmic problems in the theory of rings.

#### Research Interests

Semigroup theory, semigroup identities, completely o-simple semigroups, transformation semigroups, universal algebra

#### Research Interests

Partial differential equations, geometric measure theory

#### Postdoctoral Fellows

#### Research Interests

Finite group theory, finite geometries, combinatorial topology.

#### Research Interests

Geometric analysis: Sobolev spaces theory. Quasiconformal analysis. Geometric measure theory. Analysis on metric measure spaces.