Monday, February 19, 2024
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All day |
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4:00pm |
02/19/2024 - 4:00pm The Bateman-Horn conjecture gives a prediction for how often an irreducible polynomial takes on prime values. In this talk, I will discuss the proof of Bateman-Horn for two new polynomials – the determinant polynomial on nxn matrices and the determinant polynomial on nxn symmetric matrices. A key tool in the proof is the input of homogeneous dynamics to count the number of integral points on level sets. This talk is based on joint work with Giorgos Kotsovolis. Location:
KT205
02/19/2024 - 4:30pm Abstract: A 2-group is a categorical generalization of a group: it's a category with a multiplication operation which satisfies the usual group axioms only up to coherent isomorphisms. The isomorphism classes of its objects form an ordinary group, G. Given a 2-group G with underlying group G, we can similarly define a categorical generalization of the notion of principal bundles over a manifold (or stack) X, and obtain a bicategory Bun_G(X), living over the category Bun_G(X) of ordinary G-bundles on X. For G finite and X a Riemann surface, we prove that this gives a categorification of the Freed--Quinn line bundle, a mapping-class group equivariant line bundle on Bun_G(X) which plays an important role in Dijkgraaf--Witten theory (i.e. Chern--Simons theory for the finite group G). I will not assume background knowledge on 2-groups, 2-group bundles, or the Freed--Quinn line bundle; I will provide the necessary definitions and an outline of the proof of the categorification result. Time permitting, I will discuss work-in-progress regarding applications of this result, and generalizations to Chern--Simons theory in the case that G is a compact group. This talk is based on joint work with Daniel Berwick-Evans, Laura Murray, Apurva Nakade, and Emma Phillips. Location:
KT 217
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