09:15 AM  09:30 AM


Welcome

 Location
 SLMath: Eisenbud Auditorium
 Video


 Abstract
 
 Supplements



09:30 AM  10:30 AM


Algebraic geometry of topological field theories
David BenZvi (University of Texas, Austin)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
The study of supersymmetric gauge theories in physics has produced an incredibly rich collection of mathematical structures (for example the construction of SeibergWitten 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 6dimensional field theory, Theory X (better known as the (2,0) 6d SCFT), whose structure unifies much of modern geometric representation theory.
 Supplements


10:30 AM  11:00 AM


Tea

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


Poincaré/Koszul duality
David Ayala (Montana State University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
What is Poincaré duality for factorization homology? Our answer has three ingredients: Koszul duality, zeropointed manifolds, and Goodwillie calculus. We introduce zeropointed 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 GoodwillieWeiss calculus.
 Supplements


12:00 PM  02:00 PM


Lunch

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


Poincare'/Koszul duality and formal moduli
John Francis (Northwestern University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 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 nonperturbative.
 Supplements


03:00 PM  03:30 PM


Tea

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



04:10 PM  05:00 PM


Sullivan's conjecture and applications to arithmetic
Kirsten Wickelgren (Duke University)

 Location
 60 Evans Halls, UC Berkeley
 Video


 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 nonderived 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 pgroups. 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

