Printer-friendly versionAbstracts
Week of December 7, 2025
| Geometry, Symmetry and Physics | Higher geometric class field theory and moduli spaces of zero cycles |
2:00pm -
KT 801
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Global class field theory provides a universal abelian reciprocity laws for 1-dimensional global fields. It has been generalized in a number of different directions. In the geometric setting, it manifests as a duality between (different kinds of) sheaves on the moduli spaces of line bundles and 1-dimensional representations of the fundamental group of a curve. In a different direction, Kato and Saito gave a generalization to higher dimensional varieties. I will describe a categorification of the Kato-Saito higher class field theory, in which the moduli space of line bundles is generalized to the moduli space of zero cycles. This is joint work in progress with Elmanto. |
| Hahn Lecture Series | Entropy: From algebraic integers to dynamics on surfaces |
4:00pm -
KT 101
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These lectures will describe connections between dynamical systems and topics including algebraic geometry, number theory, All talks will be for a general audience, and no talk is a prerequisite for any other. |
| Geometry & Topology | Cusp cross-sections of arithmetic hyperbolic manifolds |
11:00am -
KT 211
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The ends of finite-volume hyperbolic (n+1)-manifolds are cusps of the form B x R+ for some compact, flat n-manifold B. In 2009, McReynolds built on work on Long and Reid to prove that every such n-manifold arises as the cusp cross section of some hyperbolic (n+1)-manifold using an arithmetic construction. A natural further question to ask is under what conditions each cross-section can arise. In this talk, we give an algebraic condition that describes exactly when a given flat manifold arises (as a cusp cross-section) in a commensurability class of cusped arithmetic hyperbolic manifolds. Time permitting, we will also discuss some applications, including a potential new way to prove a hyperbolic manifold is non-arithmetic. This is joint work with Duncan McCoy. |
| Hahn Lecture Series | Billiards and moduli spaces |
3:30pm -
KT101
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These lectures will describe connections between dynamical systems and topics including algebraic geometry, number theory, All talks will be for a general audience, and no talk is a prerequisite for any other. |
| Hahn Lecture Series | The question mark function, welding and complex dynamics |
3:30pm -
KT 14th floor
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These lectures will describe connections between dynamical systems and topics including algebraic geometry, number theory, All talks will be for a general audience, and no talk is a prerequisite for any other. |
| Friday Morning Seminar | Friday Morning Seminar |
10:00am -
KT 801
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We have impromptu and (sometimes) scheduled talks, on topics in probability, combinatorics, geometry, and dynamics. Everyone is welcome! |
| Geometry, Symmetry and Physics | Factorization algebras and Frobenius kernels |
3:00pm -
KT 801
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An influential conjecture of Finkelberg–Mirkovic identifies the regular block of representations of a reductive group in positive characteristic with Iwahori constructible perverse sheaves on the affine Grassmannian. We will review the statement and history of this conjecture, including its recent resolution by Bezrukavnikov–Riche. We will then discuss a second conjecture, made at the same time by Finkelberg–Mirkovic, which identifies the regular block of representations of a Frobenius kernel with Iwahori constructible perverse sheaves on the semi-infinite flag variety, as well as its proof, which is work in progress with Achar, Riche, and Taylor.
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