Teoría de Números

One of the features of number theory is the interplay of a great variety of mathematical techniques, including combinatorics, representation theory, harmonic analysis, probability theory, algebraic geometry, motives, p-adic and complex analytic geometry or ergodic theory, all of them applied to solve arithmetic problems.

The Number Theory group works on several problems in analytic, combinatorial and algebraic number theory and in arithmetic geometry. Namely, on applications of harmonic analysis to additive combinatorics; equivariant versions of the Birch and Swinerton-Dyer and the Tamagawa number conjectures; Diophantine equations via modular Galois representations; Riemann-Roch type theorems through motives; and applications of complex and p-adic analysis to number theory through Arakelov theory. The group is also interested in applications of number theory to other areas like theoretical physics.