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University of Cambridge > Talks.cam > Junior Algebra/Logic/Number Theory seminar > Kazhdan-Lusztig Positivity Conjectures - The Algebraic Viewpoint

## Kazhdan-Lusztig Positivity Conjectures - The Algebraic ViewpointAdd to your list(s) Download to your calendar using vCal - Robert Spencer, University of Cambridge
- Friday 14 February 2020, 15:00-16:00
- CMS, MR13.
If you have a question about this talk, please contact Liam Jolliffe. Kazhdan-Lusztig polynomials are easy to compute elements of Z[v] giving the coefficients of the “Kazhdan-Lusztig basis” of the Hecke algebra in terms of the standard basis. A famous conjecture called the Kazhdan-Lusztig Positivity Conjecture states that the coefficients of the polynomials are non-negative. This was proven in the 1980s using D-modules, perverse sheaves and other geometrical constructions. Much later in the 2010s, a more algebraic proof based off Soergel bi-modules and Hodge theory emerged. In this introductory talk we will define the Kazhdan-Lusztig polynomials from the ground up, give an overview of the conjectures (some true, some false) surrounding them, define the basics of Soergel bi-module theory and give a very light sketch of the algebraic proof of the Positivity Conjecture (and a couple of others). Time permitting, we will mention some of the offshoots from this theory of current interest. This talk is part of the Junior Algebra/Logic/Number Theory seminar series. ## This talk is included in these lists:- All CMS events
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