Categorical diagonalization
1 hour 7 mins,
256.59 MB,
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44100 Hz,
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About this item
| Description: |
Hogancamp, M
Wednesday 28th June 2017 - 11:30 to 12:30 |
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| Created: | 2017-07-20 13:38 |
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| Collection: | Homology theories in low dimensional topology |
| Publisher: | Isaac Newton Institute |
| Copyright: | Hogancamp, M |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | 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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