Noncommutative Geometry Courses and Certifications

Fields Institute

How Topological Recursion Organises Quantum Fields on Noncommutative Geometries

Explore how topological recursion structures quantum fields in noncommutative geometries, presented by Alexander Hock from the University of Oxford.

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

Fields Institute

How Topological Recursion Organizes Quantum Fields on Noncommutative Geometries - Part 2

Explore advanced concepts in quantum field theory, focusing on topological recursion and its application to noncommutative geometries in this advanced mathematics lecture.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Index Problem for Elliptic Operators Associated With Group Actions and NCG

Explore noncommutative geometry methods for solving index problems in elliptic operators associated with group actions, including pseudodifferential uniformization and applications to mathematical physics.

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

IMSA

Non-commutative Deformation of Moduli Space of Flat Connections on Riemann Surfaces

Explore the mathematical foundations of quantum mechanics through formal deformations of functions on manifolds, focusing on flat connections on Riemann surfaces and Kontsevich's revolutionary framework.

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

SCI MUNI

Quantum Flag Manifolds and Noncommutative Geometric Representation Theory

Delve into advanced mathematical concepts exploring quantum flag manifolds and their relationship with noncommutative geometric representation theory in modern mathematics.

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

Global Noncommutative Geometry Seminar

Cyclic Cocycles and One-Loop Corrections of the Spectral Action

Explore cyclic cocycles and one-loop corrections in spectral action, delving into advanced concepts of noncommutative geometry and quantum field theory.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Exploring Boundary Conditions of Bicolored Maps: Universal Behaviors and New Structures

Explore boundary conditions of bicolored maps, uncovering universal behaviors and new structures in map enumeration and random map models.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

One-Loop Renormalizability of the Spectral Action Using Cyclic Cocycles

Explore one-loop renormalizability of the spectral action principle using cyclic cocycles, uncovering its cyclic structure and connections to ribbon graphs in non-commutative geometry.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Functional Relations for Higher Order Free Cumulants and Moments

Explore functional relations between generating series of cumulants and moments in higher order free probability. Gain insights into matrix models and topological recursion.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Noncommutative U(1) Gauge Theory in the Semiclassical Limit

Explore U(1) gauge theory on Poisson manifolds as a semiclassical limit of noncommutative spacetimes. Examine gauge potentials, transformations, and symplectic realizations in Poisson electrodynamics.

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

Galileo Galilei Institute

Hopf Algebroids, Atiyah Sequences and Noncommutative Gauge Theories

Explore Hopf algebroids, Atiyah sequences, and their applications in noncommutative gauge theories with expert insights and advanced mathematical concepts.

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

Galileo Galilei Institute

Introduction to Non-Commutative Geometry - Lecture 3

Explore advanced concepts in non-commutative geometry, delving into complex mathematical structures and their applications in theoretical physics and quantum mechanics.

• YouTube
• 1 hour 46 minutes
• Self-Paced
• Free Video

Galileo Galilei Institute

Introduction to Non-Commutative Geometry - Lecture 2

Explore non-commutative geometry concepts and applications in this advanced mathematics lecture, building on foundational principles to deepen understanding of complex algebraic structures.

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

Galileo Galilei Institute

Introduction to Non-Commutative Geometry - Lecture 1

Explore non-commutative geometry with John Barrett, covering algebraic concepts, reconstruction theorems, and differential operators. Gain insights into fuzzy spaces and Hermitian operators.

• YouTube
• 1 hour 41 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Schatten Properties of Commutators on Quantum Tori

Explore Schatten properties of commutators on quantum tori, characterizing them through Besov spaces and extending to Calderon-Zygmund operators in noncommutative settings.

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