Faculty Research

Alphabetical By Research Group

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

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.

Differential equations, asymptotic theory of differential operators

Arithmetic geometry: rational and integral points, motives, anabelian geometry

Motives, p-adic periods, integral points.

Arithmetic geometry and ($p$-adic) $L$-functions

Galois theory, field arithmetic, Galois cohomology, valuation theory

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

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

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

Automorphic representations and L-functions

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

Model theory and applications to algebra and geometry.

Operator algebras.

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.

Singularities, Algebraic Geometry, Commutative Algebra

Set theory, mathematical logic, combinatorics.

Set theoretic topology, functional analysis, topological groups.

Topology, dimension theory, geometric topology, continuum theory

Operator algebras

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

Algebraic Graph Theory, Group Theory, Permutation Groups

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

Function Theory, Differential equations, Number Theory

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

Partial differential equations, geometric measure theory

Automorphic forms, Representation Theory, Harmonic analysis.

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

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

Algebraic geometry, Tropical Geometry, Singularities

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

Operator theory, system theory, algebraic geometry

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

Algebraic geometry, noncommutative algebra

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