Related papers: Introduction to staggered sheaves

These are (mostly) expository notes for lectures on affine Stanley symmetric functions given at the Fields Institute in 2010. We focus on the algebraic and combinatorial parts of the theory. The notes contain a number of exercises and open…

Survey written for the Proceedings of the AMS Meeting on Algebraic Geometry, Seattle, 2005. Based on the talk delivered at this occasion, but a few comments on recent developments are added.

This paper is based on a course given by the author at the University of Rome ``La Sapienza'' in the Academic year 2000/2001. The intended aim of the course was to rapidly introduce, although not in an exhaustive way, the non-expert PhD…

In this paper, we describe a general theory of "spaces with structure sheaves." Specializations of this theory include the classical theory of schemes, the theory of Deligne-Mumford stacks, and their derived generalizations.

This is an expanded version of the author's lecture at the Conference in Commutative Algebra and Algebraic Geometry in Messina Italy in June 1999. The purpose of the talk was to give a brief introduction to the subject of tight closure,…

We give a geometric construction of tilting perverse sheaves using stratified Morse theory, torus actions, and nearby cycles.

This is the text of a series of five lectures given by the author at the "Second Annual Spring Institute on Noncommutative Geometry and Operator Algebras" held at Vanderbilt University in May 2004. It is meant as an overview of recent…

These notes are based on an introductory minicourse on Poisson geometry given at CRM, Barcelona, in July 2022. They mostly contain foundational material, including motivating questions and key examples of Poisson structures, and highlight…

In these lecture notes we give an introduction to Bridgeland stability conditions on smooth complex projective varieties with a particular focus on the case of surfaces. This includes basic definitions of stability conditions on derived…

This is an expanded version of the notes for the lectures given by the author at RIMS in the summer of 1999 to give a detailed account of the proof for the (weak) factorization theorem of birational maps by…

This is a series of lecture notes explaining topos theory and its application in physics.

This expository article presents an overview of research, conducted mostly between the mid-1990s and late 2000s, that explores a link between commutation relations among a family of asymptotically stable vector fields and stability…

Lecture notes of lectures delivered at the Hodge Theory Summer School in ICTP Trieste, June 2010.

The brief review of the duality between gauge theories and closed strings propagating in the curved space is based on the lectures given at ITEP Winter School - 2005

Much of the recent progress in String Theory can be traced to a precise strategy: a careful study of the few models known since the beginnings of the subject, and the abstraction from them of basic properties that one would like to demand…

This survey on the topology of Stein manifolds is an extract from our recent joint book. It is compiled from two short lecture series given by the first author in 2012 at the Institute for Advanced Study, Princeton, and the Alfred Renyi…

These are the notes for my 2017 Takagi lectures on DT counts of curves in algebraic threefolds. We discuss the fundamentals of the subject, its origins, open questions, and certain recent advances.

We discuss how to formulate a staggered chiral perturbation theory. This amounts to a generalization of the Lee-Sharpe Lagrangian to include more than one flavor (i.e. multiple staggered fields), which turns out to be nontrivial. One loop…

An overview of some of the developments in string theory over the past two years is given, focusing on four topics: realistic (standard model like) models from string theory, geometric engineering and theories with fluxes, the gauge…

In these notes, an introduction to derived categories and derived functors is given. The main focus is the bounded derived category of coherent sheaves on a smooth projective variety.