Del 25 al 27 de noviembre de 2025 se realizarán dos mini-cursos introductorios en áreas de mucho desarrollo reciente en la interacción entre optimización, probabilidad y álgebra. Estos estarán a cargo de investigadores internacionales destacados que buscan fortalecer sus lazos científicos con el país.
Requisitos previos: Cursos básicos de cálculo en una y varias variables, probabilidad y estadística y álgebra.
Cursos
Curso 1: The Moment-SOS Hierarchy for Polynomial Optimization
- Speaker: Didier Henrion (LAAS-CNRS Toulouse, France & Czech Technical University, Prague)
- Lecture notes
- Abstract:
Polynomial optimization consists of minimizing a polynomial of many real variables subject to polynomial equality and inequality constraints. It includes many difficult problem classes such as e.g. combinatorial optimization.
The moment-sum-of-squares (moment-SOS) hierarchy is an approach to polynomial optimization that solves it globally at the price of solving a family of convex optimization problems of increasing size.
In these lectures we describe the main technical ingredients of the moment-SOS hierarchy:
- The moment cone and its dual,
- Semidefinite relaxations of the moment cone and polynomial SOS approximations,
- Polynomial optimization and moment relaxations,
- Solution recovery with flat extension and with the Christoffel-Darboux polynomial.
Curso 2: Introduction to Random Matrix Theory
- Speaker: Reda Chhaibi (Université Côte d’Azur, France)
- Abstract:
This mini-course provides a concise introduction to Random Matrix Theory and its core universal phenomena:
- The semi-circle law: The eigenvalue distribution of large random Hermitian matrices converges to a semi-circle.
- The Tracy–Widom law: Universal fluctuations at the spectral edge.
Proofs will proceed via (random) orthogonal polynomials on the real line and tri-diagonal matrix models.
If time permits, we will cover Free Probability, the framework for studying interactions between independent large random matrices.
Fecha y Lugar
Fechas: Martes 25, Miercoles 26 y Jueves 27 de noviembre de 2025
Horario: 13:00 – 17:00
Lugar: Facultad de Ingeniería (FING)
Salón: 102
Agenda Provisional
- Martes 25/11: Curso 1 (parte 1): 13:00–14:30 — Curso 2 (parte 1): 15:00–16:30
- Miércoles 26/11: Curso 1 (parte 2): 13:00–14:30 — Curso 2 (parte 2): 15:00–16:30
- Jueves 27/11: Curso 1 (parte 3): 13:00–14:30 — Curso 2 (parte 3): 15:00–16:30
Inscripción
La participación es libre y gratuita, pero se requiere registro previo por cuestiones organizativas.
Registro
Organizadores
Marcelo Fiori — (IMERL, FING)
Mauricio Velasco — (CMAT, FCIEN)
Agradecemos el apoyo financiero del Instituto Franco Uruguayo de Matemáticas e Interacciones IFUMI.