09:15 AM - 09:30 AM
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Welcome
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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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Algebraic geometry of topological field theories
David Ben-Zvi (University of Texas, Austin)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
The study of supersymmetric gauge theories in physics has produced an incredibly rich collection of mathematical structures (for example the construction of Seiberg-Witten integrable systems and their quantization). I will explain (following work in progress with D. Nadler, A. Neitzke and T. Nevins) how to see such structures directly from the formalism of extended topological field theory. The main (and utterly conjectural) example is provided by a 6-dimensional field theory, Theory X (better known as the (2,0) 6d SCFT), whose structure unifies much of modern geometric representation theory.
- Supplements
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10:30 AM - 11:00 AM
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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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11:00 AM - 12:00 PM
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Poincaré/Koszul duality
David Ayala (Montana State University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
What is Poincaré duality for factorization homology? Our answer has three ingredients: Koszul duality, zero-pointed manifolds, and Goodwillie calculus. We introduce zero-pointed manifolds so as to construct a Poincaré duality map from factorization homology to factorization cohomology; this cohomology theory has coefficients the Koszul dual coalgebra. Goodwillie calculus is used to prove this Poincaré/Koszul duality when the coefficient algebra is connected. The key technical step is that Goodwillie calculus is Koszul dual to Goodwillie-Weiss calculus.
- Supplements
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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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Poincare'/Koszul duality and formal moduli
John Francis (Northwestern University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
For g a dgla over a field of characteristic zero, the dual of the Hochschild homology of the universal enveloping algebra of g *completes* to the Hochschild homology of the Lie algebra cohomology of g. In this talk we will resolve this completion discrepancy through considerations of formal algebraic geometry. This will be an instance of our main result, which is a version of Poincare' duality for factorization homology as it interacts with Koszul duality in the sense of formal moduli. This can be interpreted as a duality among certain topological field theories that exchanges perturbative and non-perturbative.
- Supplements
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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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04:10 PM - 05:00 PM
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Sullivan's conjecture and applications to arithmetic
Kirsten Wickelgren (Duke University)
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- Location
- 60 Evans Halls, UC Berkeley
- Video
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- Abstract
One can phrase interesting objects in terms of fixed points of group actions. For example, class numbers of quadratic extensions of Q can be expressed with fixed points of actions on modular curves. Derived functors are frequently better behaved than their non-derived versions, so it is useful to consider the associated derived functor, called the homotopy fixed points. Sullivan's conjecture is an equivalence between appropriately completed spaces of fixed points and homotopy fixed points for finite p-groups. It was proven independently by H. Miller, G. Carlsson, and J. Lannes. This talk will present Sullivan's conjecture and its solutions, and discuss analogues for absolute Galois groups conjectured by Grothendieck.
- Supplements
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