Functional Analysis Courses and Certifications

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Simpliciality of Vector-Valued Function Spaces

Explore the generalizations of Choquet theory for vector-valued function spaces, focusing on weak simpliciality and vector simpliciality concepts, their comparisons, and recent developments in representing measures.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Continuous Functions on Fedorchuk Compacta

Explore the characterization of continuous functions on limits of inverse systems with fully closed bonding mappings, including Fedorchuk compacta, and their connection to functions on trees.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

ICTP-SAIFR

Infinite Dimensional Vector Spaces - Class 6

Delve into infinite dimensional vector spaces with Oscar Reula in this sixth class of the Partial Differential Equations minicourse, exploring analytical and numerical tools.

• YouTube
• 2 hours 19 minutes
• Self-Paced
• Free Video

ICTP-SAIFR

Infinite Dimensional Vector Spaces - Class 5 - Part 2

Delve into analytical and numerical tools for partial differential equations with Oscar Reula, focusing on infinite dimensional vector spaces in this advanced minicourse session.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

ICTP-SAIFR

Infinite Dimensional Vector Spaces - Class 5 - Part 1

Dive into infinite dimensional vector spaces with Oscar Reula in this analytical exploration of partial differential equations, part of ICTP-SAIFR's minicourse on PDEs.

• YouTube
• 40 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Subspaces With or Without a Common Complement in Hilbert Spaces

Delve into the mathematical exploration of subspace pairs in Hilbert spaces, examining their common complements through Grassmann manifolds and operator theory in infinite-dimensional geometry.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Rademacher Projection in Non-Symmetric Convex Bodies - Alexander Litvak

Explores the Rademacher projection in non-symmetric convex bodies, proving sharpness of bounds and discussing implications for Banach-Mazur distances and mean zero functions.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

The Functional Volume Product Under Heat Flow

Explores monotonicity of functional volume product along Fokker-Planck heat flow, leading to improved Borell's hypercontractivity and Laplace transform quasi-norm lower bound.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Composition Semigroups on Analytic Spaces of the Upper Half Plane

Explore continuous semigroups of composition operators on analytic spaces, examining generators, spectra, and resolvents. Gain insights into norm and spectral properties of integral operators.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Connections Between Minimal Norm Interpolation and Local Theory of Banach Spaces

Explores statistical performance of minimum norm interpolators in non-linear regression, focusing on 2-uniformly convex norms and cotype 2 property. Analyzes bias and variance using tools from Banach space theory.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

Centre International de Rencontres Mathématiques

H-Infinity Calculus and Square Functions on Banach Spaces

Explore $H^{\infty}$-calculus and square functions on Banach spaces in this advanced mathematical conference talk, delving into harmonic analysis techniques for elliptic operators.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

BIMSA

Function Spaces on Quantum Tori and Their Applications

Explore Sobolev, Besov, and Triebel-Lizorkin spaces on quantum tori, examining their properties and applications in pseudo-differential theory and noncommutative geometry.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

Centre de recherches mathématiques - CRM

Weyl Asymptotics for Poincare-Steklov Eigenvalues in Domains with Lipschitz Boundaries

Explorez les asymptotiques de Weyl pour les valeurs propres de Poincaré-Steklov dans un domaine à frontière lipschitzienne, avec une approche basée sur l'approximation par des problèmes réguliers.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Modern Trends in Gagliardo-Nirenberg Inequality

Explore modern trends in Gagliardo-Nirenberg inequality, including generalizations, refinements, and applications in functional analysis and partial differential equations.

• YouTube
• 26 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Schatten Properties for Noncommutative Martingale Paraproduct

Explore Schatten class memberships of d-adic martingale paraproducts in semi-commutative settings and characterize Sp-norms using transference methods.

• YouTube
• 32 minutes
• Self-Paced
• Free Video