Vasily Krylov

Vasily Krylov is a Benjamin Peirce Fellow at Harvard University, affiliated with the Department of Mathematics. He is mentored by Prof. Dan Freed and supported by the Simons Foundation through the Simons Collaboration on Global Categorical Symmetries. His research interests lie at the intersection of representation theory, mathematical physics, and geometry, with a focus on symplectic resolutions of singularities, integrable systems, 3D-mirror symmetry, and Coulomb branches. Krylov's work is accessible through his website, where he also provides information on his teaching, seminars, and mathematical notes.

Vasily Krylov is a researcher specializing in Geometric Representation Theory. His work explores connections between geometric objects and representation-theoretic structures, with a focus on topics such as quiver varieties, loop Grassmannians, nilpotent cones, and affine Grassmannians. He investigates integrable crystals, generalized slices, and their applications to representation theory. His research also includes the study of Bethe subalgebras, Yangians, and geometric realizations of asymptotic affine Hecke algebras. Krylov's contributions span areas like character formulas for modules over affine Lie algebras, geometric Satake equivalence, and the interplay between symplectic singularities and symplectic duality. His publications highlight the deep relationships between algebraic geometry and representation theory.