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CATEGORIES:Conferences/Seminars/Lectures
DESCRIPTION:Speaker: Tom Gannon (University of California\, Los Angeles)\n\
 nTitle: Quantization of the universal centralizer and central $D$-modules\n
 \nAbstract: We will discuss work\, joint with Victor Ginzburg\, on certain 
 quantizations (or non-commutative deformations) of objects and morphisms of
  interest in the geometric Langlands program. First\, we will discuss the q
 uantization of a morphism of group schemes used by Ngô in his proof of the 
 fundamental lemma\, which confirms a conjecture of Nadler. Afterwards\, we 
 will discuss how this morphism can be used to construct a $D$-module analog
 ue of a recent equivalence proved by Bezrukavnikov--Deshpande in the ℓ-adic
  setting\, identifying a certain braided monoidal subcategory of the catego
 ry of $G$-equivariant $D$-modules on $G$ known as vanishing $D$-modules wit
 h the category of a modules for a ring known as the spherical nil-DAHA. We 
 will also explain the construction of a certain bimodule isomorphism used t
 o construct this braided monoidal equivalence\, whose existence was origina
 lly conjectured by Ben-Zvi--Gunningham. \n\nTime permitting\, we will also 
 discuss another application of our methods: a proof of a conjecture of Brav
 erman and Kazhdan\, known as the exactness conjecture\, in the $D$-module s
 etting.
DTEND:20241023T220000Z
DTSTAMP:20260305T105752Z
DTSTART:20241023T200000Z
GEO:42.358262;-71.090045
LOCATION:Building 2\, 2-142
SEQUENCE:0
SUMMARY:MIT Lie Groups Seminar
UID:tag:localist.com\,2008:EventInstance_47569417223754
URL:https://calendar.mit.edu/event/mit-lie-groups-seminar-6602
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