Algebraic Geometry and Number Theory

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

Operator theory, system theory, algebraic geometry

Function Theory, Differential equations, Number Theory

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

Galois theory, field arithmetic, Galois cohomology, valuation theory

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

Finite group theory, finite geometries, combinatorial topology.

Algebraic geometry, Tropical Geometry, Singularities

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

Singularities, Algebraic Geometry, Commutative Algebra

Automorphic forms, Representation Theory, Harmonic analysis.

Algebraic geometry, noncommutative algebra

Automorphic representations and L-functions

Applied Probability, Combinatorial Optimization, Number Theory.

Motives, p-adic periods, integral points.

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

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

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.