Hilbert Spaces Courses and Certifications

For the Love of Physics

Introduction to Hilbert Spaces in Quantum Mechanics

Explore the mathematical foundations of quantum mechanics through Hilbert spaces, covering vector operations, inner products, norms, and completeness principles essential for understanding quantum states.

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

Fields Institute

Hilbert Spaces With No Choice

Explore the intriguing concept of Hilbert spaces without the axiom of choice in this advanced mathematical seminar, delving into set theory and functional analysis.

• YouTube
• 1 hour 37 minutes
• On-Demand
• Free Video

Fields Institute

Hilbert Spaces Without Countable AC

Explore advanced mathematical concepts in Hilbert spaces without countable axiom of choice, presented by Bruce Blackadar from the University of Nevada, Reno.

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

Banach Center

The Drunkard's Walk and UHF Algebra - From Hilbert Spaces to Supernatural Numbers

Explore UHF algebra, from Hilbert spaces to supernatural numbers, with a focus on compact operators and inductive limits in this mathematical journey.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Geometry of Reproducing Kernels in Hilbert Spaces of Analytic Functions

Explore geometric properties of reproducing kernels in Hilbert spaces of analytic functions, focusing on their applications and implications in mathematical analysis.

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

Fields Institute

Mini-course on Drury-Arveson Space - Part 1

Explore Drury-Arveson Space: origins, function theory, and connections to noncommutative geometry. Gain insights into this fundamental concept in operator theory and its applications.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Nonmonotone Forward-Backward Splitting Method for Infinite-Dimensional Optimization Problems

Explore nonmonotone forward-backward splitting for nonsmooth composite problems in Hilbert spaces, covering convergence analysis, complexity, and numerical experiments.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Weaving Frames and Riesz Bases in Quantum Harmonic Analysis

Explore woven frames in Hilbert spaces, from finite-dimensional cases to Riesz bases, with applications to vector reconstruction and Fourier matrices.

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

Applied Algebraic Topology Network

Alexander Wagner - Nonembeddability of Persistence Diagrams into Hilbert Spaces

Explore nonembeddability of persistence diagrams in Hilbert spaces, examining stability, metrics, and implications for machine learning applications in topological data analysis.

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

Schmid College, Chapman University

Shift Operators on Harmonic Hilbert Function Spaces on Real Unit Ball

Explore shift operators on harmonic function spaces, their properties, and applications in reproducing kernel Hilbert spaces. Discover new identities and inequalities in harmonic analysis.

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

Stony Brook Mathematics

Hilbert Spaces of Square Integrable Holomorphic Functions

Explore square integrable holomorphic functions, their historical development, and recent advancements in complex analysis and geometry through Bergman spaces.

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

BIMSA

Higher Hilbert Spaces and Their Operator Algebras

Explore higher category theory through 3-Hilbert spaces that categorify 2-Hilbert spaces, featuring unitary constructions and operator algebra condensation techniques.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

ICTP-SAIFR

Onset of Quantum Chaos and Ergodicity in Spin Systems with Highly Degenerate Hilbert Spaces

Explore quantum chaos and ergodicity emergence in spin systems featuring highly degenerate Hilbert spaces through advanced theoretical analysis.

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

Introduction to Quantum Mechanics

This course offers a basic introduction to quantum mechanics, covering both theoretical concepts and practical applications. It aims to equip students with a foundational understanding of quantum phenomena and prepare them for further studies.

• edX
• 4 weeks, 1-3 hours a week
• On-Demand
• Free Online Course (Audit)