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

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

Function Theory, Differential equations, Number Theory

Galois theory, field arithmetic, Galois cohomology, valuation theory

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

Finite group theory, finite geometries, combinatorial topology.

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

Algebraic geometry, Tropical Geometry, Singularities

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.