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Research interests

I study geometry of varieties with a "good" action of an algebraic group (main examples are toric varieties, flag varieties and more generally spherical varieties). There is a beautiful and rich theory, known as the theory of Newton polytopes, that studies geometry of a toric variety using combinatorics of its Newton polytope. I would like to extend the theory of Newton polytopes to more general varieties (see [1], [2], [4], [5], [6]).
I am also interested in the theory of algebraic cobordism. This theory is in many aspects similar to complex (topological) cobordism, and one of the main challenges is to find an algebro-geometric replacement for the topological methods of complex cobordism (see [3]).
My past research concerned constructible sheaves on reductive groups (see [7], [8]) and generalized hypergeometric functions (see [9]).