Cursos

Sede donde se gestiona

Santander

Lugar de impartición

Santander - Península de la Magdalena

Dirección

Secretaría

COLABORACIÓN

Descripción de la actividad

Convex Geometry is the geometry of convex sets in Euclidean space. It plays a central role in several fields in Mathematics, pure and applied. This summer School aims to showcase cutting-edge results in Convex Geometry that have been obtained using techniques from Harmonic Analysis and PDEs, within the framework of Differential Geometry. The courses will be aimed at starting researchers by providing a comprehensive introduction to the topics,  and also to established researchers from one of the areas who want to learn techniques from a different area.

The summer school will consist of three mini-courses.  The main speakers are key players in the most important recent developments in modern convex geometry:

-Semyon Alesker (Tel Aviv University, Israel): Valuations and convex geometry.

-Alina Stancu (Concordia University, Montreal, Canada): Applications of partial differential equations to convex geometry.

-Vladyslav Yaskin (University of Alberta, Edmonton, Canada):  Harmonic Analysis Methods in Geometric Tomography.

Additional 1 hour lectures will be delivered by experts on the topic, both Spanish and international. We aim to enhance and promote the research activity in these topics, by facilitating discussions and joint work among the participants.

The School «Lluís Santaló» is organized yearly as part of the summer courses at the Universidad Internacional Menéndez Pelayo, in Santander, by the Real Sociedad Matemática Española. This School is aimed mainly to master and Ph.D students.

The 2024 School is titled “Convex Geometry, Diffential Geometry and Harmonic Analysis: Building Synergies". Its goal is to emphasize and promote the connections among three main areas of mathematics: convex geometry, differential geometry, and harmonic analysis. Its program consists of three mini courses delivered by Alina Stancu (Concordia University, Montreal), Semyon Alesker (Universidad de Tel Aviv) and Vladyslav Yaskin (University of Alberta).

Yaskin’s course will showcase how classical operators in harmonic analysis (such as the Hilbert, Radon and cosine transforms) can be instrumental in proving uniqueness results for convex bodies if certain information about their sections and projections is known. The topic of Stancu’s course is the determination of convex bodies with a prescribed Gauss curvature, using elliptic equations of Monge-Ampère type, and curvature flows for parabolic equations. Finally, Alesker’s course will focus on the study of the space of valuations (finitely additive measures) defined on the set of convex bodies, and on the application of the convolution and Fourier type transforms to solve problems such as Kotrbat’s conjecture, and to prove new geometric inequalities.

In addition, several 40 and 50 minute talks will complement the main topics of the School, and there will be an opportunity for younger participants to showcase their work during the poster session.