Past Representation Theory Seminar

29 May 2014
14:00
to
16:00
Emily Cliff
Abstract
<p><span>We will define the Ran space as well as Ran space versions of some of the prestacks we've already seen, and explain what is meant by the homology of a prestack. Following Gaitsgory and possibly Drinfeld, we'll show how the Ran space machinery can be used to prove that the space of rational maps is homologically contractible.</span></p>
  • Representation Theory Seminar
22 May 2014
14:00
to
16:00
Abstract
I will give a survey of some parts of Barlev's paper on moduli problems of generic data in algebraic geometry, such as moduli of generically defined maps between varieties, and moduli of generic reductions of the structure group of a principal bundle.
  • Representation Theory Seminar
15 May 2014
14:00
to
16:00
Abstract
This talk will be an introduction to the notion of D-modules on prestacks. We will begin by discussing Grothendieck's definition of crystals of quasi-coherent sheaves on a smooth scheme X, and briefly indicate how the category of such objects is equivalent to that of modules over the sheaf of differential operators on X. We will then explain what we mean by a prestack and define the category of quasi-coherent sheaves on them. Finally, we consider how the crystalline approach may be used to give a suitable generalization of D-modules to this derived setting.
  • Representation Theory Seminar
8 May 2014
14:00
to
16:00
Tobias Dyckerhoff
Abstract
<p>Infinity categories simultaneously generalize topological spaces and categories. As a result, their study benefits from a combination of techniques from homotopy theory and category theory. While the theory of ordinary categories provides a suitable context to analyze objects up to isomorphism (e.g. abelian groups), the theory of infinity categories provides a reasonable framework to study objects up to a weaker concept of identification (e.g. complexes of abelian groups). In the talk, we will introduce infinity categories from scratch, mention some of the fundamental results, and try to illustrate some features in concrete examples.</p>
  • Representation Theory Seminar
1 May 2014
14:00
to
16:00
Dario Baraldo
Abstract
<div></div> <div>In the first meeting of this reading group, I will begin with an overview of the statement of the geometric Langlands conjecture. Then, following&nbsp;Arinkin and Gaitsgory,&nbsp;I will outline a strategy of the proof in the case of GL_n. Some ingredients of the proof are direct translations of number theoretic constructions, while others are specific to the geometric situation. No prior familiarity with the subject is assumed. However, a&nbsp;number of technical tools is necessary for both the statement and the proof; in this talk I intend to list these tools (to be explained in future talks) and motivate why they are essential.</div>
  • Representation Theory Seminar
27 March 2014
14:00
Nick Rosenblyum
Abstract
We will describe a generalization of the algebra of differential operators, which gives a geometric approach to quantization of cotangent field theories. This construction is compatible with "integration" thus giving a local-to-global construction of volume forms on derived mapping spaces using a version of non-abelian duality. These volume forms give interesting invariants of varieties such as the Todd genus, the Witten genus and the B-model operations on Hodge cohomology.
  • Representation Theory Seminar
5 December 2013
14:00
Robert Laugwitz
Abstract

In this talk, two concepts are brought together: Algebras with triangular decomposition (as studied by Bazlov & Berenstein) and pointed Hopf algebra. The latter are Hopf algebras for which all simple comodules are one-dimensional (there has been recent progress on classifying all finite-dimensional examples of these by Andruskiewitsch & Schneider and others). Quantum groups share both of these features, and we can obtain possibly new classes of deformations as well as a characterization of them.

  • Representation Theory Seminar
5 November 2013
14:00
Chris Dodd
Abstract
<p>I will explain some ongoing work on understanding algebraic D-moldules via their reduction to positive characteristic. I will define the p-cycle of an algebraic D-module, explain the general results of Bitoun and Van Den Bergh; and then discuss a new construction of a class of algebraic D-modules with prescribed p-cycle.</p>
  • Representation Theory Seminar

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