We introduce the notion of a prism, which may be regarded as a" deperfection" of the notion
of a perfectoid ring. Using prisms, we attach a ringed site---the prismatic site---to a p-adic …

We discuss the Hodge theory of algebraic non-commutative spaces and analyze how this
theory interacts with the Calabi-Yau condition and with mirror symmetry. We develop an …

Tropical geometry provides an explanation for the remarkable power of mirror symmetry to
connect complex and symplectic geometry. The main theme of this book is the interplay …

Abstract We prove the Topological Mirror Symmetry Conjecture by Hausel–Thaddeus for
smooth moduli spaces of Higgs bundles of type SL_n SL n and PGL_n PGL n. More …

In this paper we prove the smoothness of the moduli space of Landau–Ginzburg models. We
formulate and prove a Bogomolov–Tian–Todorov theorem for the deformations of Landau …

Good formal structure for meromorphic flat connections on smooth projective surfaces Page 1
Advanced Studies in Pure Mathematics 54, 2009 Algebraic Analysis and Around pp. 223-253 …

Let k be the algebraic closure of a finite field of odd characteristic p, and X a smooth
projective scheme over the Witt ring W (k) which is geometrically connected in characteristic …

We prove Bogomolov's inequality for Higgs sheaves on varieties in positive characteristic pp
that can be lifted modulo p^ 2 p 2. This implies the Miyaoka–Yau inequality on surfaces of …

Springer resolution of the set of nilpotent elements in a semisimple Lie algebra plays a
central role in geometric representation theory. A new structure on this variety has arisen in …

We discuss a conjecture which says that the automorphism group of the Weyl algebra in
characteristic zero is canonically isomorphic to the automorphism group of the …