Topology Seminar
Upcoming Talks
The seminar will meet at 4:30 on Monday in 2-131 unless otherwise noted.
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If you use a different calendar program, the ics file for this seminar is here:
http://math.mit.edu/topology/topology_seminar.ics
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Andy Senger (Harvard University)
$\begingroup $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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Cameron Krulewski (MIT)
$\begingroup $The seminar will meet at 6:00 PM in 2-131.
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.
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Melody Chan (Brown University)
$\begingroup $I will discuss aspects of joint work with Brown, Galatius, and Payne. In particular, we identify a Hopf algebraic structure in the weight 0 cohomology with compact supports of the moduli space of abelian varieties, and we deduce exponential growth results as a corollary. A key role is played by the moduli space of tropical abelian varieties, which is stratified by locally symmetric spaces GL_n(Z)\GL_n(R)/O(n). I will try to emphasize aspects of this work not discussed in Galatius' talk in this seminar.
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Ishan Levy (University of Copenhagen)
$\begingroup $TBA
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