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Categorical diagonalization

Presented by: 
Matthew Hogancamp University of Southern California
Wednesday 28th June 2017 - 11:30 to 12:30
INI Seminar Room 1
It goes without saying that diagonalization is an important tool in linear algebra and representation theory.  In this talk I will discuss joint work with Ben Elias in which we develop a theory of diagonalization of functors, which has relevance both to higher representation theory and to categorified quantum invariants.  For most of the talk I will use small examples to illustrate of components of the theory, as well as subtleties which are not visible on the linear algebra level.  I will also state our Diagonalization Theorem which, informally, asserts that an object in a monoidal category is diagonalizable if it has enough ``eigenmaps''.  Time allowing, I will also mention our main application, which is a diagonalization of the full-twist Rouquier complexes acting on Soergel bimodules in type A.  The resulting categorical eigenprojections categorify q-deformed Young idempotents in Hecke algebras, and are also important for constructing colored link homology theories which, conjecturally, are functorial under 4-d cobordisms.  
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons