Noncommutative Geometry Courses and Certifications

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

Banach Center

Principal Differential Calculi on Quantum Flag Manifolds

Explore quantum flag manifolds through principal differential calculi, covering key concepts like Schneider Theorem and covariant calculi with Thomas Weber.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Banach Center

Spilt Extensions and KK-Equivalences for Quantum Projective Spaces

Explore quantum projective spaces through split extensions and KK-equivalences, focusing on graph algebras, gauge actions, and complex projective lines.

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

Banach Center

New Equivariant Dimensions

Explore equivariant dimensions with Ludwik Dąbrowski, delving into advanced mathematical concepts and their applications in theoretical physics.

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

Banach Center

Principal Equivariant Spectral Triples

Explore principal equivariant spectral triples with Bram Mesland, delving into advanced mathematical concepts and their applications in noncommutative geometry.

• YouTube
• 46 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

Global Noncommutative Geometry Seminar

Cyclic Structure Behind the Modular Gaussian Curvature

Explore the cyclic structure underlying modular Gaussian curvature in noncommutative geometry, delving into advanced mathematical concepts and their applications.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Global Noncommutative Geometry Seminar

The Helffer-Nourrigat Conjecture - Hypoellipticity and Fredholmness of Polynomials of Vector Fields

Explore hypoellipticity and Fredholmness in vector field polynomials through the Helffer-Nourrigat Conjecture, advancing understanding in noncommutative geometry.

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

Global Noncommutative Geometry Seminar

Equivariant Local Index Theory for Lie Groupoids

Explore equivariant local index theory for Lie groupoids, covering motivation, key concepts, and advanced mathematical techniques in noncommutative geometry.

• YouTube
• 56 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

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