During my PhD, I mainly studied applications of derived algebraic geometry and algebraic topology in the context of the geometric Langlands program, and in particular to the role of the affine Grassmannian and its variants. I also studied stratified topological spaces and constructible sheaves over them from the point of view of homotopy theory.
As part of the ongoing project "Foundations of motivic real K-theory", I am focusing on the problem of topological rigidity of manifolds. Techniques include the theory of assembly maps in algebraic K- and L-theory from the point of view of Poincaré $\infty$-categories and hermitian K-theory.

Keywords: Algebraic geometry, Algebraic topology, Category theory, Derived algebraic geometry, Geometric topology, Geometric representation theory, Homotopy theory, K-theory, $\infty$-category theory.