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. Thu, 18 Oct This immediately implies the statement for any finite extension of K. The category of D-modules is defined as sheaves in the deRham stack. A key player in the story is the deRham stack, introduced by Simpson in the context of nonabelian Hodge theory.

Thu, 8 Nov 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. Mon, 29 Oct Sun, 4 Nov An analysis of Lusztig’s construction and of the Lubin-Tate tower of K leads to interesting new varieties that provide an analogue of Deligne-Lusztig theory for certain families of unipotent groups over finite fields.

This construction has a number of benefits; for instance, Kashiwara’s Lemma and h-descent are easy consequences of the definition. An analysis of Lusztig’s construction and of the Lubin-Tate tower of K leads to interesting new varieties that provide an analogue of Deligne-Lusztig theory for certain families of unipotent groups over finite fields.

The theory of D-modules will be built as an extension of this theory. Sun, 4 Nov October 4 Thursday and October 8 Monday. A key player in the story is the deRham stack, introduced by Simpson in the context of nonabelian Hodge theory. So we have plenty of time to think about Nick’s talks!

## Nick rozenblyum thesis –

Models for spaces of rational maps. Thursday October 184: The latter will be devoted to a new approach rozenboyum the foundations of D-module theory developed by Gaitsgory and Rozenblyum.

See provided URL for inquiries about permission. D-modules in infinite type. Thu, 15 Nov Categories of D-modules on spaces of rational maps arise in the context of rozenblyjm geometric Langlands program. I will explain how each of the different models for these spaces exhibit different properties of their categories of D-modules.

# Nick rozenblyum thesis

Some features of this site may not work without it. Sarnak’s second Albert lecture is at 3 p. 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.

Other Contributors Massachusetts Institute of Technology.

## David Ayala

Beilinson’s talk is intended to be a kind of introduction to inck by Rozenblyum. Mon, 22 Oct I make there two additional assumptions, which are not really necessary: Mon, 29 Oct Connections on conformal blocks Author s Rozenblyum, Nikita.

One uses here the following fact: Part of the talk will be based on joint work with Jared Weinstein Boston University. I will begin with an overview of Grothendieck-Serre duality in derived algebraic geometry via the formalism of ind-coherent sheaves.

Collections Mathematics – Ph. Mon, 12 Nov Nick will continue next Thursday: The category of D-modules is defined as sheaves in the deRham stack. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission.

nck

Thu, 8 Nov Thu, 11 Oct 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. We describe this category in terms of the action of infinitesimal Hecke functors on the category of quasi-coherent sheaves on Bung.