## Seminar on Galois Representations and their $L$-functions (2023-2)

**Organizers**
Héctor Pastén and Rocío Sepúlveda Manzo

**Description**
The seminar on Galois Representations and their $L$-functions aims to learn tools from group representation theory with an emphasis on applications to number theory, specifically oriented towards the Tate Conjecture.

**Schedule 2023-2**
The seminar was held on Fridays at 9:40 am in Room 5 of the Faculty of Mathematics, Pontificia Universidad Católica de Chile.

**Talks** (For now, the notes are in Spanish)

- Talk 1 (01/09) Héctor Pastén: Introduction to Galois representations.
- Talk 2 (08/09) Rocío Sepúlveda-Manzo: Galois Theory: Basic Tools.
- Talk 3 (15/09) Rocío Sepúlveda-Manzo: Representations of Finite Groups: Basic Tools.
- Talk 4 (22/09) Benjamín Castillo: Frobenius Element: Basic Constructions from Algebraic Number Theory.
- Talk 5 (29/09) Matías Alvarado: Examples of Frobenius elements.
- Talk 6 (13/10) Rocío Sepúlveda-Manzo: Dirichlet $L$-functions and their Analytical Properties.
- Talk 7 (20/10) Rocío Sepúlveda-Manzo: Artin $L$-functions and their Analytical Properties.
- Talk 8 (03/11) Patricio Pérez: Brauer’s Theorem for Induced Characters.
- Talk 9 (17/11) Rocío Sepúlveda-Manzo: Artin Formalism.
- Talk 10 (24/11) Héctor Pastén: Analytical Properties of Artin $L$-functions.