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XX SCHOOL OF MATHEMATICS ‹LLUIS SANTALӛ. RESEARCH SUMMER SCHOOL 2019: P-ADIC ANALYSIS, ARITHMETIC AND SINGULARITIES

Información General

Código
64AO
Horas
30
Fecha
24 Jun 2019
28 Jun 2019
Precio
135 € Tarifa C
Tipo
Escuela
Temática
Ciencia y Tecnología
ECTS
1

Sede donde se gestiona

Santander

Lugar de impartición

Santander - Península de la Magdalena (Riancho)

Dirección

Alejandro Melle Hernández
Catedrático de la Universidad Complutense de Madrid

Secretaría

Carlos Galindo Pastor
Profesor Titular de la Universitat Jaume I de Castellón

ORGANIZADO EN COLABORACIÓN CON


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

Participantes

DIRECCIÓN

Alejandro Melle Hernández
Catedrático de la Universidad Complutense de Madrid

SECRETARÍA

Carlos Galindo Pastor
Profesor Titular de la Universitat Jaume I de Castellón

PARTICIPANTES

Juan Manuel Burgos
CONACYT Researcher

Félix Delgado de la Mata
Universidad de Valladolid

Sabir Gusein-Zade
Lomonosov Moscow State University

Edwin León Cardenal
Centro de Investigación en Matemáticas, CONACYT

Francisco José Monserrat Delpalillo
Universidad Politécnica de Valencia

Julio José Moyano Fernández
Universitat Jaume I de Castelló

Christopher Sinclair
University of Oregon

Willem Veys
University of Leuven (KU Leuven)

Wilson Álvaro Zúñiga Galindo
Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional

Programa

Lunes, 24 Junio 2019

10:00
Opening

10:15
Introduction to motivic Poincaré series (I)
Sabir Gusein-Zade

11:30
Coordination-Exercise Session (I)
Julio José Moyano Fernández

12:00
Introduction to the singularities of plane curves (I)
Francisco José Monserrat Delpalillo

15:30
Introduction to p-adic analysis (I)
Wilson Álvaro Zúñiga Galindo

16:30
Introduction to motivic Poincaré series (II)
Sabir Gusein-Zade

Martes, 25 Junio 2019

09:30
Introduction to motivic Poincaré series (III)
Sabir Gusein-Zade

11:00
Coordination-Exercise Session (II)
Julio José Moyano Fernández

11:30
Introduction to p-adic analysis (II)
Wilson Álvaro Zúñiga Galindo

12:30
Introduction to motivic Poincaré series (IV)
Sabir Gusein-Zade

15:30
Introduction to local zeta functions (I)
Willem Veys

16:30
Introduction to the singularities of plane curves (II)
Francisco José Monserrat Delpalillo

Miércoles, 26 Junio 2019

09:30
Introduction to the singularities of plane curves (III)
Francisco José Monserrat Delpalillo

11:00
Coordination-Exercise Session (III)
Julio José Moyano Fernández

11:30
Introduction to p-adic analysis (III)
Wilson Álvaro Zúñiga Galindo

12:30
Introduction to the singularities of plane curves (IV)
Francisco José Monserrat Delpalillo

15:30
Poincaré series and topology
Félix Delgado de la Mata

16:15
On Archimedean zeta functions and Newton polyhedra
Edwin León Cardenal

Jueves, 27 Junio 2019

09:30
Introduction to p-adic analysis (IV)
Wilson Álvaro Zúñiga Galindo

11:00
Coordination-Exercise Session (IV)
Julio José Moyano Fernández

11:30
Introduction to local zeta functions (II)
Willem Veys

15:30
Introduction to local zeta functions (III)
Willem Veys

16:30
A tour on p-adic string theory
Juan Manuel Burgos

17:15
p-adic electrostatics
Christopher Sinclair

Viernes, 28 Junio 2019

09:30
Introduction to p-adic analysis (V)
Wilson Álvaro Zúñiga Galindo

10:30
Coordination-Exercise Session (V)
Julio José Moyano Fernández

11:30
Introduction to local zeta functions (IV)
Willem Veys

13:00
Closing

Sin fecha definida

Opening

Closing

Coordination-Exercise Session (I)

Introduction to the singularities of plane curves (I)

Introduction to p-adic analysis (I)

Introduction to motivic Poincaré series (II)

Introduction to motivic Poincaré series (III)

Coordination-Exercise Session (II)

Introduction to p-adic analysis (II)

Introduction to motivic Poincaré series (IV)

Introduction to local zeta functions (I)

Introduction to the singularities of plane curves (II)

Introduction to the singularities of plane curves (III)

Coordination-Exercise Session (III)

Introduction to p-adic analysis (III)

Introduction to the singularities of plane curves (IV)

Poincaré series and topology

On Archimedean zeta functions and Newton polyhedra

Introduction to p-adic analysis (IV)

Coordination-Exercise Session (IV)

Introduction to local zeta functions (II)

Introduction to local zeta functions (III)

A tour on p-adic string theory

p-adic electrostatics

Introduction to p-adic analysis (V)

Coordination-Exercise Session (V)

Introduction to local zeta functions (IV)

Introduction to motivic Poincaré series (I)