## NICK ROZENBLYUM THESIS

I will discuss the notion of crystals and de Rham coefficients that goes back to Grothendieck, the derived D-module functoriality for smooth varieties due to Bernstein and Kashiwara , and some basic ideas of the Gaitsgory-Rosenblum theory. This construction has a number of benefits; for instance, Kashiwara’s Lemma and h-descent are easy consequences of the definition. Crystals, D-modules, and derived algebraic geometry. October 4 Thursday and October 8 Monday. We show that sheaves which are, in a certain sense, equivariant with respect to infinitesimal Hecke functors are exactly D-modules, i. This family of functors, parametrized by the Ran space of X, acts by averaging a quasi-coherent sheaf over infinitesimal modifications of G-bundles at prescribed points of X. Duality and D-modules via derived algebraic geometry.

Beilinson’s talk is intended to be a kind of introduction to those by Rozenblyum. Abstract For an algebraic group G and a projective curve X, we study the category of D-modules on the moduli space Bung of principal G-bundles on X using ideas from conformal field theory. Abstract This is an introduction to a series of talks of Nick Rosenblum on his foundational work with Dennis Gaitsgory that establishes the basic D-module functoriality in the context of derived algebraic geometry hence for arbitrary singular algebraic varieties over a field of characteristic 0. Models for spaces of rational maps Abstract I will discuss the equivalence between three different models for spaces of rational maps in algebraic geometry. The category of D-modules is defined as sheaves in the deRham stack.

So we have plenty of time to think about Nick’s talks!

Thu, 8 Nov Mon, 29 Oct I will discuss the notion of crystals and de Rham coefficients that goes back to Grothendieck, the derived D-module functoriality for smooth varieties due to Bernstein and Kashiwaraand some nixk ideas of the Gaitsgory-Rosenblum theory.

Department Massachusetts Institute of Technology. Mon, 22 Oct JavaScript is disabled for your browser. Connections on conformal blocks Author s Rozenblyum, Nikita. This gives a description of flat connections on a quasi-coherent sheaf on Bung which is local on the Ran space. Beilinson’s talk is intended to be a kind of introduction to those by Rozenblyum. They may be viewed from this source for any purpose, but reproduction or rozzenblyum in any format is prohibited without written permission.

Abstract This is an introduction to a series of talks of Nick Rosenblum on his foundational work with Dennis Gaitsgory that establishes the basic D-module functoriality in the context of derived algebraic geometry hence for arbitrary singular algebraic varieties over a field of characteristic 0.

In particular, I will explain the relation between spaces of quasi-maps and the model for the space of rational maps which Gaitsgory uses in his recent contractibility theorem.

Nick will continue nik Thursday: However, as such spaces are not representable by ind- schemes, the construction of such categories relies on the general theory presented in Nick Rozenblyum’s talks. Sun, 4 Nov Categories of D-modules on spaces of rational maps arise in rozenboyum context of the geometric Langlands program.

Collections Mathematics – Ph. Wed, 7 Nov We show that sheaves which are, in a certain sense, equivariant with respect to infinitesimal Hecke functors are exactly D-modules, i.

## David Ayala

On Hick 12 Monday Jonathan Barlev will begin his series of talks on the spaces of rational maps. The theory of D-modules will be built as an extension of this theory.

October 4 Thursday and October 8 Monday. We describe this category in terms of the action of infinitesimal Hecke functors on the category of quasi-coherent sheaves on Bung.

# David Ayala – David Ayala | Montana State University

Already in Lusztig proposed a very elegant, but still conjectural, geometric construction of twisted parabolic induction for unramified maximal tori in arbitrary nlck p-adic groups. Thu, 11 Oct Other Contributors Massachusetts Institute of Technology. Mon, 8 Oct Mon, 24 Sep Sarnak’s second Albert lecture is at 3 p.

Thursday October 184: This immediately implies the statement for any finite extension of K. Duality and D-modules via derived algebraic geometry.

## Nick rozenblyum thesis –

Some features of this site may not work without it. No previous knowledge of the above subjects is needed. The latter will be devoted to a new approach to the foundations of D-module theory developed by Gaitsgory and Rozenblyum.