Algebra Seminar
(Mon 3:30-4:30pm, Kap 265)
Organizer: Cris Negron
Topics include (but are not limited to):
Algebra, representation theory, algebraic and arithmetic geometry, homotopy theory, and mathematical physics.
Fall 2025
| Date | Location | Speaker | Abstract |
|---|---|---|---|
| Sept 8 | Yifeng Huang (USC) | Coh zeta functions for quadratic orders Abstract: The Coh zeta function, a 1/|Aut|-weighted count of a ring's finite modules, is a basic invariant that unifies problems in enumerative algebra such as counting matrices and representations. While these zeta functions for (germs of) singular curves have revealed surprising connections to q-series, making precise predictions has remained challenging. This talk provides a unified picture for the known y2=xn singularities by re-interpreting them as quadratic orders: ramified for odd n and split for even n. This algebraic viewpoint reveals a crucial missing piece in the landscape---the inert quadratic orders---which is necessary to complete the picture (via quadratic twists), and is the focus of the new work. |
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| Sept 15 | Vesselin Dimitrov (CalTech) | A new approach to effective Diophantine approximation Abstract: I will introduce you to the method of arithmetic holonomy bounds which we currently develop in collaboration with Frank Calegari and Yunqing Tang. To stick to a simple but fundamental example, I will explain how to effectivize the Thue—Siegel theorem for the special case of high order roots from a rational number, using an analysis surprisingly close to the traditional hypergeometric method but now cast within our new framework of multivalent holonomy bounds. The two other known ways to effectivize this ‘binomial' case of Thue—Siegel are Baker’s theory of linear forms in logarithms of algebraic numbers, and Bombieri’s equivariant Thue—Siegel method. Our holonomy bounds method begins with the original line of Axel Thue and adds to it a technique of David and Gregory Chudnovsky (originally used in the 1980s in their study of the Grothendieck—Katz p-curvature conjecture about the algebraicity of the solutions of certain linear ODEs). |
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| Sept 22 | Anton Kapustin (CalTech) | Homotopy theory, Quantum Field Theory, and Quantum Lattice Systems Abstract: It is now widely accepted in the theoretical physics community that any local QFT must account for higher or generalized symmetries, and that the mathematical structure which describes them is not a group, but a higher group, i.e. a connected homotopy type. Yet the origin of homotopy-theoretic notions in QFT remains poorly understood. I will discuss this issue in the context of quantum lattice systems. They share many similarities with QFT but their theory can be put on a solid mathematical footing using operator-algebraic methods. I will show that homotopy-theoretic structures naturally appear when one considers restrictions of symmetry transformations to spatial regions. Specifically, higher groups arise through their algebraic models: crossed modules in one spatial dimension, crossed squares of groups in two dimensions, and crossed cubes in general dimensions. |
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| Sept 29 [organizer away] |
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| Oct 6 [organizer away] |
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| Oct 13 | Davide Passaro (CalTech) | ||
| Oct 20 | |||
| Oct 27 | |||
| Nov 3 | Sam Qunell (UCLA) | ||
| Nov 10 | Mark Walker (U Nebraska) | ||
| Nov 17 | Matt Young (Utah State) | ||
| Nov 24 | pre-Holiday | ||
| Dec 1 |
Mailing list: Contact me if you want to be added to the seminar mailing list.
See our friends at the Geometry seminar (M 2:00 pm) and the Combinatorics seminar (W 2:00 pm).