Monday, February 19, 2024
Time  Items 

All day 

4:00pm 
02/19/2024  4:00pm The BatemanHorn conjecture gives a prediction for how often an irreducible polynomial takes on prime values. In this talk, I will discuss the proof of BatemanHorn 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 2group 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 2group 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 Gbundles on X. For G finite and X a Riemann surface, we prove that this gives a categorification of the FreedQuinn line bundle, a mappingclass group equivariant line bundle on Bun_G(X) which plays an important role in DijkgraafWitten theory (i.e. ChernSimons theory for the finite group G). I will not assume background knowledge on 2groups, 2group bundles, or the FreedQuinn line bundle; I will provide the necessary definitions and an outline of the proof of the categorification result. Time permitting, I will discuss workinprogress regarding applications of this result, and generalizations to ChernSimons theory in the case that G is a compact group. This talk is based on joint work with Daniel BerwickEvans, Laura Murray, Apurva Nakade, and Emma Phillips. Location:
KT 217
