Related papers: Derived Categories and Birational Geometry
This is a (mostly expository) paper on Reidemeister classes, twisted Burnside-Frobenius theory, congruences, R-infinity property and all that. It was written in 2005 and published in 2008. We post it as it was, only the bibliography data is…
We discuss what is known about the structure of the bounded derived categories of coherent sheaves on Grassmannians of simple algebraic groups.
Open problems from the 15th Annual ACM Symposium on Computational Geometry.
These are notes for the Bootcamp volume for the 2015 AMS Summer Institute in Algebraic Geometry. They are based on earlier notes for the "Positive Characteristic Algebraic Geometry Workshop" held at University of Illinois at Chicago in…
This work is the first in a series laying the foundations of derived geometry in the $C^{\infty}$ setting, and providing tools for the construction and study of moduli spaces of solutions of Partial Differential Equations that arise in…
This is the fourth (and last) prepublication version of a book on derived categories, that will be published by Cambridge University Press. The purpose of the book is to provide solid foundations for the theory of derived categories, and to…
This article is a comprised version of my doctoral thesis defended at Basel University in 1995. It concerns circle packings on compact surfaces of any genus.
This is the authors doctoral thesis written at the Humboldt-University Berlin. It contains material from the three separate papers: "On the Kodaira dimension of the moduli space of nodal curves", "On quotients of…
These are notes for a summer course given at the PIMS Summer School on Geometric and Topological Aspects of the Representation Theory of Finite Groups in Vancouver, July 27-30 2016.
A working mathematician's summary of many results on the derived category, perverse sheaves, and vanishing cycles. This is the August 2025 version, with a completely revised section on vanishing cycles.
Talk given at Harvard, January 1999, published in the Proceedings of the Harvard Winter School on mirror symmetry, vector bundles and lagrangian cycles, 1999, International Press. Surveys the joint work [ST, KS] with Paul Seidel and Mikhail…
In this expository note, we discuss some results of the author on the structure of derived categories of equivariant coherent sheaves and the derived categories of geometric invariant theory quotients. We take a recent perspective,…
This paper is based on Wald Lectures given at the annual meeting of the IMS in Minneapolis during August 2005. It is a survey of the theory of large deviations.
This paper is an expanded version of two talks given by the author at the Summer School on the Interactions between Homotopy Theory and Algebra at the University of Chicago, July 26 to August 6, 2004. It describes a connection between model…
Another introduction to perverse sheaves with some exercises. Expanded version of five lectures at the 2015 PCMI.
This is an extended version of my earlier articel "Projective and injective objects in symmetric categorical groups. arXiv:1007.0121v1." Several new facts added, including the material on the derived 2-functors and the proof of the…
We discuss a relation between the structure of derived categories of smooth projective varieties and their birational properties. We suggest a possible definition of a birational invariant, the derived category analogue of the intermediate…
This is a survey article on the relationship between algebraic properties of diffeomorphism groups and homotopical properties of foliations, written for the Notices of the AMS.
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
This a slightly expended version of my habilitation thesis, which is an overview of my research activities during the last 4 years, written in a rather informal style.