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SUMMARY:Kazhdan-Lusztig Positivity Conjectures - The Algebraic Viewpoint -
  Robert Spencer\, University of Cambridge
DTSTART:20200214T150000Z
DTEND:20200214T160000Z
UID:TALK139690@talks.cam.ac.uk
CONTACT:Liam Jolliffe
DESCRIPTION:Kazhdan-Lusztig polynomials are easy to compute elements of Z[
 v] giving the coefficients of the "Kazhdan-Lusztig basis" of the Hecke alg
 ebra in terms of the standard basis.  A famous conjecture called the Kazhd
 an-Lusztig Positivity Conjecture states that the coefficients of the polyn
 omials are non-negative.  This was proven in the 1980s using D-modules\, p
 erverse sheaves and other geometrical constructions.  Much later in the 20
 10s\, a more algebraic proof based off Soergel bi-modules and Hodge theory
  emerged.  In this introductory talk we will define the Kazhdan-Lusztig po
 lynomials from the ground up\, give an overview of the conjectures (some t
 rue\, some false) surrounding them\, define the basics of Soergel bi-modul
 e theory and give a very light sketch of the algebraic proof of the Positi
 vity Conjecture (and a couple of others).  Time permitting\, we will menti
 on some of the offshoots from this theory of current interest.\n
LOCATION:CMS\, MR13
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