09:15 AM - 09:30 AM
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Welcome to MSRI
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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09:30 AM - 10:30 AM
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Hopf Algebras I
Sarah Witherspoon (Texas A & M University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Hopf algebras arise naturally in many different areas of mathematics, such as combinatorics, topology, and mathematical physics. Many commonly studied algebraic structures are either Hopf algebras themselves or are directly related to them: for example, groups, Lie algebras, and quantum groups. Hopf algebras act on rings, generalizing the notion of a group of automorphisms. Modules for a Hopf algebra can be added (direct sum) and multiplied (tensor product), giving their categories of modules the structure of tensor categories. In this first talk, we will define Hopf algebras and their actions on rings, give examples, and explain how their modules fit into this larger picture of tensor categories.
- Supplements
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Notes
796 KB application/pdf
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10:30 AM - 11:00 AM
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Break
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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11:00 AM - 12:00 PM
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Introduction to fusion categories I
Victor Ostrik (University of Oregon)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
This series of talks will be devoted to the theory of fusion categories which is one way to give a mathematical description of quantum symmetries. We will discuss basic definitions, examples and constructions of such categories, as well as some structure theory and classification results.
- Supplements
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Notes
333 KB application/pdf
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12:00 PM - 02:00 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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02:00 PM - 03:00 PM
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An introduction to modular tensor categories I
Eric Rowell (Texas A & M University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Modular tensor categories encode the topological symmetries of 2-dimensional bosonic topological phases of matter, as the algebraic underpinnings of (2+1)D TQFTs. I will describe the main constructions of modular tensor categories, a few classification results and some open questions.
Reference List for Introduction to Modular Categories (compiled by E. Rowell)
- Supplements
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Notes
216 KB application/pdf
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03:00 PM - 03:30 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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03:30 PM - 04:30 PM
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Subfactors and Planar Algebras
Emily Peters (Loyola University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
- --
- Supplements
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Notes
248 KB application/pdf
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