Learning Seminar on Modular Forms, Automorphic Representations, and $L$-functions

This is the page for the Fall 2026 learning seminar on Modular Forms, Automorphic Representations, and $L$-functions at Fordham University.

Updated schedule

The learning seminar has transformed into two weekend workshops: (1) the weekend of 10/31-11/01 on representation theory and (2) the weekend of 11/14-/11/15 on modular forms.

Venue: Fordham University at Lincoln Center, Room: LL914

Weekend 1: 10/31-11/01

Date   Time   Reading   Speaker
10/31   9:30-10:45AM   Irreducible representations of $\text{GL}_2(\mathbb{R})$   Ajmain Yamin
10/31   11:15AM-12:30PM   Intertwining operations and unitary representations   Ethan Bottomley-Mason
10/31   2:00-3:15PM   Local Langlands correspondence for $\text{GL}_2(\mathbb{R})$   Raghuram
10/31   3:45-5:00PM   Representations of $\text{GL}_2(\mathbb{F}_q)$   Sevan Bharathan
11/01   9:30-10:45AM   Representations of $p$-adic groups - generalities   Ajmain Yamin
11/01   11:15AM-12:30PM   Principal series representations of $p$-adic $\text{GL}_2(\mathbb{F})$   Sevan Bharathan
11/01   2:00-3:15PM   Whittaker models and Jacquet modules   Erin Pierce
11/01   3:45-5:00PM   Local Langlands correspondence for $p$-adic $\text{GL}_2(\mathbb{F})$   Raghuram

Weekend 2: 11/14-/11/15

Date   Time   Reading   Speaker
11/14   9:30-10:45AM   $\Gamma\backslash\mathbb{H}^*$ as a Riemann surface   TBD
11/14   11:15AM-12:30PM   Automorphic forms and differentials   TBD
11/14   2:00-3:15PM   Dimensions of $G_k(\Gamma)$ and $S_k(\Gamma)$   TBD
11/14   3:45-5:00PM   Poincaré series and Eisenstein series   TBD
11/15   9:30-10:45AM   Hecke algebras   TBD
11/15   11:15AM-12:30PM   $\text{SL}_2(\mathbb{Z})$, $\Gamma_0(N)$, $\Gamma_1(N)$, $\Gamma(N)$   TBD
11/15   2:00-3:15PM   Modular forms and Dirichlet series   TBD
11/15   3:45-5:00PM   Hecke $L$-functions for modular forms   TBD

Old schedule

Description: This will be an intense learning seminar on the arithmetic theory of automorphic forms and their \(L\)-functions from both the classical and the representation theoretic perspectives. The seminar will be in-person at the Lincoln Center campus, having two sessions with a small break in between with each session lasting for an hour and 15 minutes.

  • Session - I (S-I), Modular Forms, 2:30-3:45PM. This session will be on the theory of modular forms, especially Hecke theory and \(L\)-functions, based on such references: first 4 chapters of Miyake’s Modular Forms and the first 3 chapters of Shimura’s Arithmetic Theory of Automorphic Functions.

  • Session - II (S-II), Automorphic Representations, 4:00-5:15PM. This session will be on Automorphic Representations for GL(2) based on the references: Bump’s Automorphic Forms and Representations, and the first five chapters of Gelbart’s Automorphic forms on Adele Groups. Depending on how the seminar progresses, we may graduate to automorphic forms on GL(n) or a reductive group over a number field based on Goldfeld and Hundley’s book and Getz and Hahn’s book.

Venue: Fordham University at Lincoln Center, Room: LL902

Day/time: Monday’s at 2:30-5:15PM, starting from August 31, 2026

Learning Seminar on Modular Forms

  • (S-I) Fall 2026, Monday’s at 2:30-3:45PM.
Date   Reading   Speaker
8/31   Invariant metric and measure on $\mathbb{H}$ (notes)   Raghuram
9/7   Labor Day    
9/14   Fuchsian groups (notes)   Sevan Bharathan
9/21   Fundamental domains   Sevan Bharathan

Learning Seminar on Automorphic Representations

  • (S-II) Fall 2026, Monday’s at 4:00-5:15PM.
Date   Reading   Speaker
8/31   Universal enveloping algebra (notes)   Raghuram
9/7   Labor Day    
9/14   Basic representation theory (notes)   Ajmain Yamin
9/21   Irreducible $(\mathfrak{g},K)$-module for $\text{GL}_2(\mathbb{R})$ (notes)   Ajmain Yamin

For any questions, contact ahamakiotes@fordham.edu.