Calendar

We will discuss an elementary way of detecting some global anomalies from the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory, give a physical description of the imprint of the “layers” that enter in the cobordism classification of anomalies and discuss applications, including how anomalies can imply a supersymmetric spectrum in strongly coupled (nonsupersymmetric) gauge theories.

Zoom: https://harvard.zoom.us/j/977347126

There is a long standing connection between the Tate conjecture in codimension 1 and finiteness properties, which first appeared in Tate’s seminal work on the endomorphisms of abelian varieties. I will explain how one can possibly extend this connection to codimension 2 cycles, using the theory of Brauer groups, moduli of twisted sheaves, and twisted derived equivalences, and prove the Tate conjecture for K3 squares. This recovers an earlier result of Ito-Ito-Kashikawa, which was established via a CM lifting theory, and moreover provides a recipe of constructing all the cycles on these varieties by purely geometric methods.

Zoom: https://harvard.zoom.us/j/99334398740

Password: The order of the permutation group on 9 elements.

We will begin by discussing hyperbolic geometry, and how it can be used to build “evenly curved” metrics on a donut with one point removed. We will then discuss Maryam Mirzakhani’s computation of the “size” of the universe of all such metrics (the Weil-Petersson volume of the moduli space of complete hyperbolic metrics on a punctured torus)

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