Faculty Research

Alphabetical By Research Group

Partial differential equations, geometric measure theory

Differential equations, asymptotic theory of differential operators

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

Set theory, mathematical logic, combinatorics.

Discrete Geometry, Combinatorics, Dynamical Systems, Ergodic Theory, Diophantine Approximations, Computational Geometry

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

Representation Theory: Lie algebras and superalgebras, representations of finite groups, tensor categories, representation stability, diagram categories, categorical actions

Algebraic Graph Theory, Group Theory, Permutation Groups

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

Ergodic theory and dynamical systems,  in particular symbolic dynamics and related aspects of probability theory. 

Random walks on groups, Geometric Group Theory, Ergodic Theory and Operator Algebras

Discrete Geometry, Combinatorics, Dynamical Systems, Ergodic Theory, Diophantine Approximations, Computational Geometry

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

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

Operator theory, system theory, algebraic geometry

operator algebras, noncommutative convexity, function theory, several complex variables, real and complex algebraic geometry

Operator algebras.

Operator algebras

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

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

Partial differential equations, geometric measure theory

Set theoretic topology, functional analysis, topological groups.

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.

Topology, dimension theory, geometric topology, continuum theory

Algebraic geometry, Tropical Geometry, Singularities

Set theory, mathematical logic, combinatorics.

Set theoretic topology, functional analysis, topological groups.

Model theory and applications to algebra and geometry.

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.

Probability: random walks, interacting particle systems, discrete analysis. Geometric group theory: spaces of harmonic functions on groups, random walks on groups, boundaries.