Speaker: Andy Senger (Harvard University) 4:30 PM in 2-131

Speaker: Cameron Krulewski (MIT)  6:00 PM in 2-131

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Speaker: Andy Senger (Harvard University)  

Title: Synthetic algebras and THH

Abstract: In this talk, I'll introduce a category of synthetic E_n-algebras, discuss some of its properties, indicate its relation to normed motivic spectra, and give some applications to the even filtration on THH. This is preliminary work in progress with Devalapurkar, Hahn and Raksit.

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Speaker: Cameron Krulewski (MIT)   

Title: Invertible Functorial Field Theory for Symmetry Breaking and Interactions in Quantum Field Theory

Abstract: I will discuss two applications of invertible field theories to quantum field theory. Functorial field theories, which are functors from a bordism category to a target category, are invertible when they factor through the Picard groupoid of the target. After additionally imposing reflection positivity, such theories are classified, due to results of Freed-Hopkins, by Anderson-dual bordism groups.

The first application we study is toward a certain form of spontaneous symmetry breaking. We model three physical processes using a twisted Gysin sequence of Anderson-dual bordism groups. Using generalized Euler classes, we study the Smith maps of Madsen-Tillmann spectra that underlie the sequence, and use them to draw physical predictions. The second application we study is toward fermionic symmetry-protected topological phases (SPTs). Generalizing work of Freed-Hopkins, we define and compute twisted Atiyah-Bott-Shapiro maps from twisted spin bordism to shifts of K-theory in order to compare two models of SPTs. This talk represents several joint projects with Antolín Camarena, Debray, Devalapurkar, Liu, Pacheco-Tallaj, Sheinbaum, Stehouwer, and Thorngren.