Joint Colloquium: Anthony Licata -- Positivity and integrality from higher representation theory

Speaker: Dr.  Anthony Licata 

http://maths-people.anu.edu.au/~licatat/Anthony_Licata_homepage/Home.html 

Time: Friday, May 3, 2:00--3:00PM 

Room: Room: RC-4082, Red Centre (UNSW) 

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Title: Positivity and integrality from higher representation theory 

Abstract: One of the important consequences of the geometric methods introduced in
representation theory over the last thirty years has been the discovery that
representations of important algebras in Lie theory often have natural - or "canonical"
bases; when written in these bases, the representation theory of the algebra can be
formulated over the positive integers, instead of, say, over the complex numbers.  One
byproduct of such positive integrality is that a wealth of combinatorics emerges.  Of
course, proving these various positivity and integrality statements is sometimes hard
work.  In this talk we will explain how ideas from "higher representation theory" can be
used to prove positivity and integrality statements.  In particular, we will explain
some of the mathematics behind the recent proof by Elias-Williamson of the positivity of
Kazdhan-Lusztig polynomials in the representation theory of the Hecke algebra.  

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Lunch with speaker: we meet around 12:30PM at the entrance to the East Wing of Red
Centre Building.  

One choice of commuting from Sydney: meet at Carslaw 620 around 12:05PM and share taxi
to UNSW.  The round trip is covered by department colloquium fund.  

Joint Colloquium web site: 

http://www.maths.usyd.edu.au/u/SemConf/JointColloquium/index.html