Harvard Number Theory Seminar, Spring 2019

Wednesdays 3-4pm at Science Center 507

Date Speaker Title
Feb 6 Rong Zhou (IAS) Motivic cohomology of quaternionic Shimura varieties and level raising
Feb 13 Preston Wake (IAS) Variation of Iwasawa invariants in residually reducible Hida families
Feb 20 Lillian Pierce (Duke) Recent progress on understanding class groups of number fields
Feb 27 Charlotte Chan (Princeton) Affine Deligne--Lusztig varieties at infinite level for GLn
Mar 6 Nicholas Triantafillou (MIT)
Mar 13 Samit Dasgupta (Duke)
Mar 20 No seminar (Spring Recess)
Mar 27 Kai-Wen Lan (U Minnesota, Twin Cities)
Apr 4 (Thurs.) Avner Ash (Boston College)
@ Science Center Hall E in the basement
Apr 10 Naser Talebizadeh Sardari (U Wisconsin-Madison)
Apr 17 Brian Smithling (Johns Hopkins)
Apr 24 Yiannis Sakellaridis (Rutgers)
May 1 Romyar Sharifi (UCLA)

Past seminars

Fall 2018, Academic Year 2017, Academic Year 2016.

Organizers

Chi-Yun Hsu and Alison Miller

Abstracts

Speaker: Rong Zhou (IAS)
Title: Motivic cohomology of quaternionic Shimura varieties and level raising
Abstract: For a smooth scheme of finite type over a field its motivic cohomology groups generalize the usual Chow groups and are an important algebraic invariant. In this talk we will explain how, for the special fibers of certain quaternionic Shimura varieties, its motivic cohomology can encode very rich arithmetic information. More precisely we will show that the cycle class map from motivic cohomology to étale cohomology gives a geometric realization of level raising between Hilbert modular forms. The main ingredient for this construction is a form of Ihara's Lemma for Shimura surfaces which we prove by generalizing a method of Diamond-Taylor.

Speaker: Preston Wake (IAS)
Title: Variation of Iwasawa invariants in residually reducible Hida families
Abstract: We'll discuss a work in progress describing properties of p-adic L-functions of a modular form whose Galois representation is residually reducible. As an application, we prove cases of a conjecture of Greenberg about mu-invariants of Selmer groups of elliptic curves, paying particular attention to the case of X_0(11) with p=5. This is joint work with Rob Pollack.

Speaker: Lillian Pierce (Duke)
Title: Recent progress on understanding class groups of number fields
Abstract: It is natural to think of number fields in families---for example, all number fields of a fixed degree. Correspondingly, we can ask about the distribution of the class number, or of the class group, as the field varies over a family. We will describe a diverse array of recent work that studies for a fixed prime p the size of the p-torsion subgroup of the class group, as the number field varies over a family.

Speaker: Charlotte Chan (Princeton)
Title: Affine Deligne--Lusztig varieties at infinite level for GLn
Abstract: Affine Deligne--Lusztig varieties have been of interest for some time because of their relation to Shimura varieties and the Langlands program. In this talk, we will construct a tower of affine Deligne--Lusztig varieties for GLn and its inner forms. We prove that its limit at infinite level is isomorphic to the semi-infinite Deligne--Lusztig variety of Lusztig and that its cohomology realizes certain cases of automorphic induction and Jacquet--Langlands. This is joint work with A. Ivanov.

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