Functional Analysis Courses and Certifications

BIMSA

Filling Radius, Positive Scalar Curvature and Quantitative Operator K-Theory

Explore techniques in quantitative operator theory to estimate filling radius, connecting positive scalar curvature and asymptotic dimension in large-scale geometry.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

BIMSA

Optimal Estimates for Neumann Eigenvalues

Explore optimal estimates for Neumann eigenvalues, including award-winning research on maximizing second eigenvalues and recent findings on convex set bounds.

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

BIMSA

Crossed Product Splitting of Intermediate Operator Algebras via 2-Cocycles

Explore intermediate operator algebras through a unified theorem, combining Galois correspondence and crossed product splitting with 2-cocycles. Apply to Bisch-Haagerup inclusions.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

BIMSA

Stability of Sobolev Inequalities - ICBS 2024

Explore quantitative stability of Sobolev inequalities, focusing on Struwe's decomposition and recent advancements in dimensional-dependent estimates for multiple bubbles in various dimensions.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

BIMSA

Eisenstein Series - An Overview

Explore Eisenstein series in a concise, self-contained overview, gaining insights into this mathematical concept and its applications.

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

BIMSA

The David-Semmes Problem, Rectifiability, and Harmonic Measure - ICBS 2024

Explore the David-Semmes problem, its solution in codimension one, and its impact on harmonic measure problems. Gain insights into Riesz transforms and n-rectifiability.

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

BIMSA

Quantum Fourier Analysis

Explore quantum Fourier analysis and its applications in quantum information with Professor Jinsong Wu, delving into functional analysis and operator algebra concepts.

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

BIMSA

Operator Algebras, Bi-Unitary Connections and Tensor Networks - Lecture 4

Explore tensor categories as quantum symmetries, using Jones subfactor theory and bi-unitary connections to study 2D topological order and tensor networks.

• YouTube
• 1 hour 43 minutes
• Self-Paced
• Free Video

BIMSA

Operator Algebras, Bi-Unitary Connections and Tensor Networks - Lecture 2

Explore tensor categories as quantum symmetries, using Jones subfactor theory and bi-unitary connections to study 2D topological order and tensor networks.

• YouTube
• 1 hour 42 minutes
• Self-Paced
• Free Video

BIMSA

Operator Algebras, Bi-Unitary Connections and Tensor Networks - Lecture 1

Explore tensor categories as quantum symmetries, using Jones subfactor theory and bi-unitary connections to study 2D topological order and tensor networks.

• YouTube
• 1 hour 36 minutes
• Self-Paced
• Free Video

Centre de recherches mathématiques - CRM

Corona Rigidity in Operator Theory and C*-Algebras

Explore corona rigidity in operator theory, examining extensions of Weyl-von Neumann theorem and its implications for C*-algebras, Calkin algebra, and isomorphisms of quotients.

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

Centre de recherches mathématiques - CRM

Spectral Minimal Partitions of Metric Graphs: What and Why

Explorez les partitions minimales spectrales des graphes métriques, leurs liens avec la théorie spectrale et les coupures de Cheeger, et découvrez de nouveaux résultats sur les graphes non bornés et les conditions de Robin.

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

Centre de recherches mathématiques - CRM

The Dry Ten Martini Problem for Sturmian Schrodinger Operators

Explore the Dry Ten Martini Problem for Sturmian Schrodinger operators, examining spectral gaps and integrated density of states. Delve into recent solutions and advancements in this mathematical challenge.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Centre de recherches mathématiques - CRM

The Method of Gauge Transform II

Explorez la méthode de transformation de jauge et son application aux problèmes spectraux périodiques et ergodiques avec Jeffrey Galkowski.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Centre de recherches mathématiques - CRM

The Method of Gauge Transform - Periodic and Ergodic Spectral Problems

Explorez la méthode de transformation de jauge et ses applications dans les problèmes spectraux, en mettant l'accent sur les aspects mathématiques avancés et les techniques analytiques.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video