Most talks will be preceded by a "pre-talk" meant for graduate students and postdocs, starting 40 minutes before the announced time for the main talk and lasting about 30 minutes.
Don't forget to register for Math 209 if you are a UCSD graduate student. Continued department financial support for this seminar is contingent on maintaining sufficient enrollment.
The organizers strive to ensure that all participants in this seminar enjoy a welcoming environment, conducive to the free expression and exchange of ideas. In particular, the pre-talks are meant to provide a safe space for junior researchers to ask questions of the speaker. All participants are expected to cooperate with this effort and encouraged to contact the organizers with any concerns.
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For previous quarters' schedules, click here.
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April 4 |
Organizational meeting |
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April 11 |
Claus Sorensen (UC San Diego)
This talk will be colloquial and geared towards people from other fields. I will talk about smooth mod $p$ representations of $p$-adic Lie groups. In stark contrast to the complex case, these categories typically do not have any (nonzero) projective objects. For reductive groups this is a byproduct of a stronger result on the derived functors of smooth induction. The talk is based on joint work with Peter Schneider. |
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April 18 |
Aranya Lahiri (UC San Diego)
My goal will be to motivate why looking at distribution algebras associated to p-adic lie groups is natural in the context of number theory. More specifically I will try to briefly outline their importance in the p-adic Langlands program. And then I will give a simple example of an overconvergent distribution algebra of certain kinds of p-adic groups with an eye towards illuminating techniques used in my work Dagger groups and p-adic distribution algebras (joint w/ Matthias Strauch and Claus Sorensen). |
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April 25 |
Jon Aycock (UC San Diego)
We will introduce an analytic notion of automorphic forms. These automorphic forms encode arithmetic data by way of their Fourier theory, and we will explore two different families of automorphic forms which have interesting congruences between their Fourier coefficients. |
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May 2 |
Wei Yin (UC San Diego)
The classical Coates-Sinnott Conjecture and its refinements predict the deep relationship between the special values of L-functions and the structure of the étale cohomology groups attached to number fields. In this talk, we aim to delve deeper along this direction to propose what we call the “Higher Coates-Sinnott Conjectures" which reveal more information about these two types of important arithmetic objects. We introduce the conjectures we formulate and our work towards them. This is joint work with C. Popescu. |
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May 9 |
Nandagopal Ramachandran (UC San Diego)
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May 16 |
Bryan Hu (UC San Diego)
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May 23 |
Christian Klevdal (UC San Diego)
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May 30 |
Ellen Eischen (Oregon)
I will discuss recent developments and ongoing work for algebraic and p-adic aspects of L-functions. Interest in p-adic properties of values of L-functions originated with Kummer’s study of congruences between values of the Riemann zeta function at negative odd integers, as part of his attempt to understand class numbers of cyclotomic extensions. After presenting an approach to studying analogous congruences for more general classes of L-functions, I will conclude by introducing ongoing joint work of G. Rosso, S. Shah, and myself (concerning Spin L-functions for GSp_6). I will explain how this work fits into the context of earlier developments, while also indicating where new technical challenges arise. All who are curious about this topic are welcome at this talk, even without prior experience with p-adic L-functions or Spin L-functions. |