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SUMMARY:Categorical diagonalization - Matthew Hogancamp (University of Sou
 thern California)
DTSTART:20170628T103000Z
DTEND:20170628T113000Z
UID:TALK73093@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:It goes without saying that diagonalization is an important to
 ol in linear algebra and representation theory. &nbsp\;In this talk I will
  discuss joint work with Ben Elias in which we develop a theory of diagona
 lization of functors\, which has relevance both to higher representation t
 heory and to categorified quantum invariants. &nbsp\;For most of the talk 
 I will&nbsp\;use small examples to illustrate of components of&nbsp\;the t
 heory\, as well as subtleties which are not visible on the linear algebra 
 level. &nbsp\;I will also state our&nbsp\;Diagonalization Theorem which\, 
 informally\,&nbsp\;asserts that an object in a monoidal category is diagon
 alizable if it has enough ``eigenmaps&#39\;&#39\;.&nbsp\; Time allowing\, 
 I will also mention our&nbsp\;main application\, which is a diagonalizatio
 n of&nbsp\;the full-twist Rouquier complexes acting on Soergel bimodules i
 n type A. &nbsp\;The resulting categorical eigenprojections categorify q-d
 eformed Young idempotents in Hecke algebras\, and are also important for c
 onstructing colored link homology theories which\, conjecturally\, are fun
 ctorial under 4-d cobordisms. &nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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