Seminars Sorted by Series

From Romyar's AWS notes:

• Sections 4.1 and 4.2.

Regarding the proof of Ohta's comparison isomorphism:

• Discuss Fukaya-Kato Section 1.7, which explains some p-adic Hodge theory background.
• Discuss some elements of Ohta's proof, from Sections 3...

Introduce the L-function, and then the p-adic L-function, of a cusp form, and the of a Hida family of cups forms. What we need is in Fukaya-Kato Sections 4.4-4.5. See also: Mazur-Tate-Teitelbaum and Mazur's "Anomalous eigenforms" note.

State the main theorems of Fukaya-Kato and outline the proofs.

Give the details of the proof of "Theorem A" from week ten. Fukaya-Kato sections 6.3, 9.1-9.5.

We will talk about the categorification of the positive half of the quantum group $\mathbb{U}_q(\mathfrak{sl}_2)$ using the module categories over NilHecke algebras. We hope to explain the idea of categorification using this example.

It is well known that representations of open compact subgroups (called types) play a fundamental role in studying representations of $p$-adic groups. We give an overview of the theory (after Bernstein, Moy-Prasad, Bushnell-Kutzko) in connection...

It is an old question in representation theory whether any finitely-generated smooth representation of a $p$-adic group has a resolution by representations induced from (finite-dimensional representations of) compact subgroups. We construct such a...

A result of Gelfand and Graev shows that the supercuspidal representations of $\mathrm{SL}_2$ are neatly parameterized by characters of elliptic tori, and that the stable character data for all such representations may be collected into a single...

A quantum symmetric pair consists of a quantum group and its coideal subalgebra. The coideal subalgebra is a quantum analog of the fixed point subalgebra of the enveloping algebra with respect to certain involution. In this talk, we shall describe...

It is known that the number of conjugacy classes of a finite group equals the number of irreducible representations (over complex numbers). The conjugacy classes of a finite group give a natural basis of the cocenter of its group algebra. Thus the...