# Number Theory Seminar @ University of Melbourne

Alex Ghitza and I are running a working seminar on things number-theoretic.

Time: 13:00--14:00 Tue. (Melbourne local time) for 2024S2.

The theme for 2024S2 is an arithmetic introduction to Shimura varieties. We will mostly follow "Jared Weinstein. Reciprocity laws and Galois representations: recent breakthroughs. Bull. Amer. Math. Soc. (N.S.), 53(1):1β39, 2016."

Time: 13:00--14:00 Mon. (Melbourne local time) for 2024S1.

Venue: Peter Hall 162 (The πNEWπ seminar room)

Please go to the Number Theory Research Group website where you can find a link to join our mailing list. You will receive the Zoom link and announcements of talks.

### 13 Aug. 2024

Class field theory

Riley Moriss

### 6 Aug. 2024

Classical reciprocity laws

Alexander Stratov

### 30 July. 2024

Introduction to the "Reciprocity laws" survey by Jared Weinstein

### 23 July 2024

Modular Forms and Galois Representations

I will begin by recalling the basic facts about Tate modules of elliptic curves. Building on this discussion, I will recall the basic facts about Galois representations attached to modular forms, and sketch the proofs of some of them.

This is the preliminary talk to the talk, From Modular Curves to Categorification, in the representation theory seminar on 25 July, also given by Matt.
More details are on the

representation theory seminar webpage.

Last talk of 2024S1. We will resume in 2024S2.

There may be special talks during the Winter break, in which case, we will send out announcements.

### 27 May 2024

Quasimodular forms with examples

Miles Koumouris

### 20 May 2024

Serre p-adic modular forms with examples

Miles Koumouris

### 13 May 2024

Parabolic Induction and Eisenstein Series II with examples

Chengjing Zhang

### 6 May 2024

Parabolic Induction and Eisenstein Series with examples

Chengjing Zhang

This talk focuses on parabolic induction and Eisenstein series. We will discuss how induction, a powerful tool in the representation theory of finite groups, appears as parabolic induction in the theory of automorphic representations. Although parabolically induced representations are not automorphic themselves, they can be associated with automorphic representations through Eisenstein series.

### 29 Apr. 2024

Automorphic forms on GL_{n} with examples

Qizheng Han

### 22 Apr. 2024

Automorphic forms with examples

Riley Moriss

### 15 Apr. 2024

Eisenstein series (GL_{2} and Siegel cases) with examples

Bowan Hafey

### 8 Apr. 2024

Parabolic subgroups with examples

Bowan Hafey

### 1 Apr. 2024

Easter Break. No Talk. April Fool's Day. It is true, no talk.

### 25 Mar. 2024

Reductive groups with examples

Riley Moriss

### 18 Mar. 2024

Elliptic curves and Tate modules with examples

Kwan Sheng Ong

### 11 Mar. 2024

Group schemes with examples

Riley Moriss

### 4 Mar. 2024

A grand overview of the universe of Number Theory