Research

My research area is number theory and arithmetic algebraic geometry. I am interested in connections between them. Specifically, geometric counter part of some arithmetic information. For example one of this arithmetic information is studying L-values and multiple zeta values which are completely related to geometric motives. I am also interested in the connection between (usual) geometry and p-adic geometry. On the arithmetic side, some sort of connection is called local-global principle. I can mention the following keywords for my research interests: arithmetic of 1-motives, period space and p-adic periods, geometrization of Langlands program, non-abelian reciprocity, modular curves, Galois and representations, perfectoid spaces, class field theory of arithmetic schemes.

•  P-adic integration and de Rham-crystalline period pairing, in preparation. 

•  P-adic version of subgroup theorem and Grothendieck period conjecture, in preparation. 

• Beilinson-Deligne conjecture for 1-motives

• On the theory of motivic Galois groups and (tilted) perfectoid fields

• Motivic modular curves

• Motives, periods and Beilinson-Deligne conjecture on automorphic side

• Classifying certain supersingular 1-motives

• Galois theory of motives