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XXI SCHOOL OF MATHEMATICS ‹LLUIS SANTALӛ. RANDOM AND DETERMINISTIC POINT CONFIGURATIONS

Información General

Información

Información solicitudInformación solicitud

PROGRAMA DEL CURSO

Grants

Código
6547
Horas
30
Fecha
11 Jul 2022
15 Jul 2022
Precio
140 € Tarifa C
Tipo
Escuela
Temática
Ciencia y Tecnología
ECTS
1

Sede donde se gestiona

Santander

Lugar de impartición

Santander - Península de la Magdalena (Biblioteca)

Dirección

Carlos Beltrán Álvarez
Universidad de Cantabria

Secretaría

Jordi Marzo Sánchez
Universidad de Barcelona

ORGANIZADO EN COLABORACIÓN CON


ORGANIZADO EN COLABORACIÓN CON

COLABORACIÓN


COLABORACIÓN

Descripción de la actividad

Which is the “best” way to distribute a given number of points in the surface of a sphere or another geometrical object? For example, how can we choose points that are well-separated, or that provide good choices for integration or interpolation processes? Or that, thinking on the points as negatively charged particles, have a small value of the electrostatic potential?

 

These questions have given rise to a series of deep and fruitful problems in mathematics, ranging from the classical Thomson problem, proposed by Sir Joseph John Thomson in 1903, to “Smale’s 7th problem” proposed by Stephen Smale in his celebrated list of Problems for the XXI Century. From Tammes problem, proposed by Pieter Merkus Lambertus Tammes (a Dutch botanist studying the distribution of exit places in pollen grains) in the 1930’s to Maryna Viazovska’s breakthrough in the generalization of Kepler's conjecture, to name just a few.

 

These and other related problems have attracted the attention of mathematicians and physicists coming from very different areas, ranging from Potential Theory to Approximation Theory, Complexity Theory, Numerical Analysis, Random Matrix Theory, Statistical Physics and more. Moreover, choosing a finite collection of points which are in some sense well distributed in some object is a basic building block in many applications, ranging from numerical integration to the design of optimal communication networks and the description of physical processes such as those governed by gases made of charged particles.

 

This school will provide students with the tools to understand the history, the applications, the state of the art and the beauty of some of these challenging mathematical problems. It will be accessible to general mathematicians and also show some of the last developments in the field by young researchers.

Participantes

DIRECCIÓN

Carlos Beltrán Álvarez
Universidad de Cantabria

SECRETARÍA

Jordi Marzo Sánchez
Universidad de Barcelona

PARTICIPANTES

Dmytro Bilyk
Minnesota University, USA

Alexander Bufetov
Centre National de la Recherche Scientifique, France

Maria Dostert

Ujué Etayo Rodríguez
Universidad de Cantabria, Spain

Damir Ferizovic
KU Leuven, Belgium

Ernesto García Ciganda

Bianca Maria Gariboldi

Khazhgali Kozhasov

Fátima Lizarte López

Pedro R. López Gómez

Mylene Maida
Université de Lille, France

Michelle Mastrianni

Alon Nishry
Tel Aviv University, Israel

Joaquim Ortega Cerdà
Universitat de Barcelona, Spain

Maurizia Rossi
Università degli Studi di Milano, Italy

Andreas Spomer

Josué Tonelli Cueto

Oren Yakir

Programa

Lunes, 11 Julio 2022

09:30
Inauguración
Carlos Beltrán Álvarez
10:00
Points on spheres: discrepancy, energy, and beyond
Dmytro Bilyk
11:00
Introduction to determinantal point processes
Mylene Maida
12:30
Fekete points, an overview
Joaquim Ortega Cerdà
13:30
Debate
Khazhgali Kozhasov
Josué Tonelli Cueto
Fátima Lizarte López
Pedro R. López Gómez
15:30
Exact semidefinite programming bounds for packing problems
Maria Dostert
16:30
Debate 2
Michelle Mastrianni
Ernesto García Ciganda

Martes, 12 Julio 2022

09:30
Points on spheres: discrepancy, energy, and beyond
Dmytro Bilyk
10:30
Introduction to determinantal point processes
Mylene Maida
12:00
Non-universal fluctuations of the empirical measure for time dependent spherical random fields
Maurizia Rossi
13:00
Fekete points, an overview
Joaquim Ortega Cerdà
15:30
The Spherical Cap Discrepancy of HEALPix Points
Damir Ferizovic
17:00
Reproducing kernels and determinantal point processes: completeness and minimality
Alexander Bufetov

Miércoles, 13 Julio 2022

09:30
Points on spheres: discrepancy, energy, and beyond
Dmytro Bilyk
10:30
Introduction to determinantal point processes
Mylene Maida
12:00
Reproducing kernels and determinantal point processes: completeness and minimality
Alexander Bufetov
13:00
Fekete points, an overview
Joaquim Ortega Cerdà
15:30
Riesz Energies on Projective Spaces
16:30
Debate
Oren Yakir

Jueves, 14 Julio 2022

09:30
Points on spheres: discrepancy, energy, and beyond
Dmytro Bilyk
10:30
Introduction to determinantal point processes
Mylene Maida
12:00
Reproducing kernels and determinantal point processes: completeness and minimality
Alexander Bufetov
13:00
Fekete points, an overview
Joaquim Ortega Cerdà
14:00
Debate
Bianca Maria Gariboldi
Andreas Spomer
15:30
t-desings and cubature formulas: asymptotic bounds on the number of points
Ujué Etayo Rodríguez
16:30
Outliers in weakly confined Coulomb-type systems
Alon Nishry

Viernes, 15 Julio 2022

09:30
Introduction to determinantal point processes
Mylene Maida
10:30
Points on spheres: discrepancy, energy and beyond
Dmytro Bilyk
12:00
Fekete points an overview
Joaquim Ortega Cerdà
13:00
Reproducing kernels and determinantal point processes: completeness and minimality
Alexander Bufetov