# Faculty Research

## Algebraic Geometry and Number Theory

#### Research Interests

Applied Probability, Combinatorial Optimization, Number Theory.

#### 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

<p>Galois theory, field arithmetic, Galois cohomology, valuation theory</p>

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<p>Automorphic representations and L-functions</p>

#### Research Groups

#### 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.

#### Postdoctoral Fellows

#### Graduate Students

#### Research Interests

Singularities, Algebraic Geometry, Commutative Algebra

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#### Research Groups

#### 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

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Automorphic forms, Representation Theory, Harmonic analysis.

#### Research Groups

#### Research Interests

Finite group theory, finite geometries, combinatorial topology.

#### Research Interests

<p>Algebraic geometry, Tropical Geometry, Singularities</p>

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Operator theory, system theory, algebraic geometry

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#### Postdoctoral Fellows

#### Research Interests

Algebraic geometry, noncommutative algebra

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## Applied Mathematics and Differential Equations

#### Research Interests

Differential Equations, differential-functional and difference equations

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#### 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.

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#### Research Groups

#### Research Interests

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

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#### Research Interests

Partial differential equations, geometric measure theory

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#### Graduate Students

#### Research Interests

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

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#### Research Interests

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

#### Research Groups

## Combinatorics and Discrete Mathematics

#### Research Interests

Applied Probability, Combinatorial Optimization, Number Theory.

#### Research Interests

Set theory, mathematical logic, combinatorics.

#### Research Interests

Geometric Group theory, Expander graphs and High Dimensional Expanders, Coarse geometry

#### Research Groups

#### Research Interests

Finite group theory, finite geometries, combinatorial topology.

#### Research Interests

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

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#### 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

<p>Topological groups (general theory), abstract harmonic analysis, topological dynamics</p>

#### Research Groups

#### Research Interests

<p>Operator algebras.</p>

#### Research Groups

#### Graduate Students

#### Research Interests

Operator algebras

#### Research Groups

#### Research Interests

Partial differential equations, geometric measure theory

#### Research Groups

#### Graduate Students

#### Research Interests

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

#### Research Groups

#### Research Interests

Operator theory, system theory, algebraic geometry

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#### Postdoctoral Fellows

## Geometry and Topology

#### 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.

#### Research Groups

#### Research Interests

Topology, dimension theory, geometric topology, continuum theory

#### Research Groups

## 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.

#### Postdoctoral Fellows

#### Graduate Students

#### Research Interests

Set theory, mathematical logic, combinatorics.

#### Research Interests

Set theoretic topology, functional analysis, topological groups.

#### Research Groups

#### Research Interests

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