Cursos

Sede donde se gestiona

Santander

Lugar de impartición

Santander - Península de la Magdalena (Riancho-Bringas)

Dirección

Secretaría

ORGANIZADO EN COLABORACIÓN CON

Descripción de la actividad

The school aims to provide an introduction to a very dynamic area of research that lies at the intersection of number theory, p-adic analysis, algebraic geometry and singularity theory. In this area, the local zeta functions (p-adic, archimedean, motivic, etc) and certain counterparts known as Poincaré series (usual and motivic) associated with filtrations play a central role. The local zeta functions were introduced in the 50s by I. M. Gel'fand and G. E. Shilov. Later, in the 70s, J.-I. Igusa developed a uniform theory for local zeta functions and oscillatory integrals, with a polynomial phase, on fields of characteristic zero. In the p-adic case the local zeta functions are related to the number of solutions of polynomial congruences and to certain exponential sums. There are many (very difficult) conjectures that connect the poles of the local zeta functions with the topology of complex singularities. Recently J. Denef and F. Loeser introduced zeta motivic functions, which constitute a vast extension of the p-adic Igusa zeta functions. Another important object is the Poincaré motivic series introduced by Campillo, Delgado and Gusein-Zade, also involving the topology of complex singularities. This summer school proposes four courses which give an advanced introduction to these topics, proposing exercise sessions (coordinated) as well as fourtalks that present current related research problems. The school is aimed at doctoral and postdoctoral students working on topics broadly connected to the topics in the school.

Civil dislocation and mathematical roots

Open conferences on the work and figure of Lluís A. Santaló Sors

Tuesday 25th of June

19.00h Magdalena PalaceExile of Spanish science and its consequences.The mathematical influence of Lluís A. Santaló Sors.

Antonio Campillo

Wednesday 26th of June

19.00h Magdalena Palace

Professors of Mathematics in the republican exile.The case of Lluís A. Santaló SorsLuis Español González

Thursday 27th of June

19.00h Magdalena Palace

Lluís A. Santaló Sors: His research dimensionSebastià Xambó-Descamps