V. Gritsenko makes research in three different areas: the theory of modular forms; algebraic geometry (in particular the theory of moduli spaces); the theory of Lorentzian Kac--Moody Lie algebras (or Borcherds algebras.The main research interests are applications of automorphic forms in arithmetic, algebraic geometry, the theory of Lie algebras, topology, mathematical physics. He has more than 70 mathematical papers.
In 2015 and 2016, Valery Gritsenko is an international chief research fellow of the Bogomolov Laboratory of Algebraic Geometry of the National Research University "High School of Economics" in Moscow. He leads a research seminar “Automorphic forms and their applications”.
In 2015, V. Gritsenko gave two semester courses on Jacobi modular forms and their applications. The current course at Coursera reflects the method of teaching of Russian mathematical school and the new traditions of the Department of Mathematics of HSE.