Aritm\'etica, Grupos y An\'alisis (AGRA II, Cusco, Per\'u)

TL;DR

This collection of lecture notes from the AGRA II school in Cusco covers advanced topics in mathematics including modular forms, additive combinatorics, elliptic curves, group growth, and Diophantine analysis, aimed at graduate students and researchers.

Contribution

It compiles comprehensive lecture notes on diverse modern mathematical topics, providing educational material for advanced learners in the field.

Findings

Introduces foundational concepts in modular forms and Shimura curves.

Provides an overview of additive combinatorics techniques.

Includes introductory material on elliptic curves and their applications.

Abstract

These are lecture notes for the AGRA II school, which took place in August 2015 at Universidad de San Antonio Abad del Cusco (Per\'u). They are geared towards graduate students and young researchers. I. Modular forms and Shimura curves (R. J. Miatello, G. Tornar\'ia, A. Pacetti, M. Harris) II. Additive combinatorics (J. Ru\'e, J. Wolf, J. Cilleruelo, P. Candela) III. Introduction to elliptic curves (M. Rebolledo and M. Hindry) IV. Growth in groups and expanders (H. A. Helfgott, M. Belolipetsky) V. Analysis and geometry in groups (A. Zuk) VI. Equidistribution and Diophantine analysis (R. Menares)