Seminar of Number Theory

Seminar of Number Theory (2024-2)

Organizers Héctor Pastén and Rocío Sepúlveda Manzo

Description This seminar covered various topics in number theory, including fundamental conjectures and theorems. The first talks introduced Mordell’s Conjecture, followed by discussions on Chabauty’s Theorem and its implications. Later sessions explored the Manin-Dem’janenko theorem, integer representations as sums of squares, and singularity resolution. The seminar featured invited talks by Siddhi Pathak (Chennai) and Dino Lorenzini (University of Georgia), enriching the discussions with insights on Ramanujan polynomials, integer representations, and wild quotient singularities.

Schedule 2024-2 The seminar was held on Fridays at 14:00 pm in Room 2 of the Faculty of Mathematics, Pontificia Universidad Católica de Chile.

Talks

Talk 1 (10/11) Rodrigo Galaz: Introducción a la Conjetura de Mordell I
Talk 2 (10/18) Héctor Pastén: Introducción a la Conjetura de Mordell II
Talk 3 (10/25) Matías Alvarado: Hacia el teorema de Chabauty (pdf)
Talk 4 (11/08) Siddhi Pathak (invited speaker, Chennai): On the zeros of variants of Ramanujan polynomials
Talk 5 (11/15) Rocío Sepúlveda-Manzo: Teorema de Chabauty (pdf)
Talk 6 (11/22) Héctor Pastén: Preliminares para Manin-Dem’janenko
Talk 7 (11/29) José Cuevas-Barrientos: Demostración de Manin-Dem’janenko y aplicaciones (pdf)
Talk 8 (12/06) Matías Bruna (invited speaker, UofT): Sobre la representación de enteros como suma de cuadrados.
Talk 9 (12/19) Dino Lorenzini (invited speaker, UGA): Resolution of wild $\mathbb{Z} / p \mathbb{Z}$-quotient singularities