Abstract
These are lecture notes for the AGRA II school, which took place in August 2015 at Universidad de San Antonio Abad del Cusco (Perú). They are geared towards graduate students and young researchers. I. Modular forms and Shimura curves (R. J. Miatello, G. Tornaría, A. Pacetti, M. Harris) II. Additive combinatorics (J. Rué, 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)
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