Centre de recherches mathématiques - CRM Courses

Critical Metrics of Eigenvalue Functionals via Subdifferential

Explore critical metrics of eigenvalue functionals using subdifferential, covering Laplace and Steklov eigenvalues and offering new perspectives on Riemannian geometry.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Large Steklov Eigenvalues Under Geometric Constraints

Explore large Steklov eigenvalues in compact Riemannian manifolds, examining geometric constraints and constructing metrics with fixed volume and boundary conditions.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Extremely Amenable Automorphism Groups of Countable Structures

Explore extreme amenability in topological groups, focusing on automorphism groups of countable structures. Discover the abundance of non-isomorphic extremely amenable Polish groups.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

On the Critical Points of Steklov Eigenfunctions

Explore critical points of Steklov eigenfunctions on Riemannian manifolds, examining relationships between eigenfunction indexes, boundary behavior, and Euler characteristics.

• YouTube
• 46 minutes
• On-Demand
• Free Video

An Overdetermined Eigenvalue Problem and the Critical Catenoid Conjecture

Explore an overdetermined eigenvalue problem on the two-sphere and its implications for characterizing the critical catenoid as a unique embedded free boundary minimal annulus.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

A Weighted Reilly Formula for Differential Forms and Sharp Steklov Eigenvalue Estimates - Lecture

Explore weighted Reilly formula for differential forms and its applications in sharp Steklov eigenvalue estimates. Gain insights into spectral geometry and related open problems.

• YouTube
• 52 minutes
• On-Demand
• Free Video

New Minimal Surfaces via Equivariant Eigenvalue Optimization - Part II

Explore equivariant optimization of Laplace and Steklov eigenvalues on surfaces to construct embedded minimal surfaces in 3-sphere and 3-ball. Discover new insights into geometric analysis and topology.

• YouTube
• 58 minutes
• On-Demand
• Free Video

New Minimal Surfaces via Equivariant Eigenvalue Optimization - Part I

Explore new embedded minimal surfaces in S³ and free boundary minimal surfaces in B³ through intrinsic shape optimization of Laplace and Steklov eigenvalues, considering symmetries and analytical challenges.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Polynomial Inequalities and Combinatorial Interpretations

Explore polynomial inequalities and their combinatorial interpretations, focusing on explicit injections and challenges in proving inequalities when naive approaches fail.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Interactions Between Computers and Spectral Geometry

Explorez les avancées récentes en géométrie spectrale, mettant en lumière le rôle crucial de l'assistance informatique dans les découvertes et les défis futurs.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

What is an L-function? - An Introduction to Zeta and L-functions in Number Theory

Explore the evolution of L-functions from Euler to Langlands, understanding their crucial role in prime number distribution and mathematical research.

• YouTube
• 1 hour
• On-Demand
• Free Video

Mathematics and Machines: Navigating New Frontiers

Explore the intersection of mathematics and machine learning, examining how computers transform mathematical research and their potential future impact on the field.

• YouTube
• 1 hour
• On-Demand
• Free Video

Finite Time Singularities in Fluids

Explorez les singularités en temps fini dans les fluides, en examinant les résultats récents et classiques, les preuves assistées par ordinateur et les applications de l'apprentissage automatique.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Free Resolutions of Powers of Square-Free Monomial Ideals

Explore free resolutions of square-free monomial ideals and their powers, focusing on combinatorial methods and discrete topology. Gain insights into this central problem in commutative algebra.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Minimal Surfaces and the Isoperimetric Inequality

Explore the generalization of the isoperimetric inequality to submanifolds in Euclidean space, focusing on minimal submanifolds and their sharp isoperimetric properties.

• YouTube
• 55 minutes
• On-Demand
• Free Video