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Operator Algebra Seminar - Advanced Topics in C*-Algebras and Groupoids

Fields Institute via YouTube

Overview

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Attend a comprehensive operator algebra seminar series featuring advanced research presentations on C*-algebras, groupoid theory, and related mathematical structures. Explore cutting-edge topics including Cuntz semigroups and their rank ratio bounds, nuclear dimension of twisted groupoid C*-algebras, and classification problems for simple AH-algebras with Elliott invariants. Delve into specialized areas such as Cuntz-Pimsner algebras of twisted partial Z-actions, graph products with strong 1-boundedness properties, and cohomological obstructions to group stability. Examine dynamical systems through the lens of non-commutative factors, finite dimensional approximations of groups, and Fraïssé theory applications to Cuntz semigroups. Study advanced concepts in K-theory and homology for étale groupoids, correspondences theory, and the symmetry properties of L1(G) for group extensions. Investigate the zero-product structure of C*-algebras, tensor category equivariant Z-stability, and exotic circle actions on classifiable C*-algebras. Learn about uniformly super McDuff II1 factors, abstract harmonic analysis fundamentals, and functional analysis theorems. Discover transformation group C*-algebras, Haar measure theory, and the Pontryagin Duality Theorem through detailed proofs. Explore geometric properties of topological groupoids and their applications to structural problems, covering dimension for Cuntz semigroups, and the Global Glimm Problem. Examine Jung-Hayes free entropy and its applications to von Neumann algebras, optimal transport theory in free probability, and soft C*-algebras. Study Z-stability through classification of Villadsen algebras and generalized BDF-Kasparov and Voiculescu theorems.

Syllabus

The rank ratio bound and the radius of comparison of the Cuntz semigroups.
Nuclear dimension of twisted groupoid C*-algebras
Nonisomorphic simple AH-algebras with the same Elliott invariant and radius of comparison
Cuntz-Pimsner algebras of twisted partial Z-actions
Graph products and strong 1-boundedness
Cohomological obstructions to group stability
On the Existence, or lack, of non-commutative factors of a dynamical system
Finite dimensional approximations of groups
Fraïssé Theory for Cuntz semigroup
Large finite values of Rokhlin dimension with commuting towers
Traces on ultrapowers of C*-algebras
Correspondences, K-theory and homology for étale groupoids
On the symmetry of L1(G) for certain group extensions
The zero-product structure of C*-algebras
Tensor category equivariant Z-stability
Infinitesimal Operators, Part II
Infinitesimal Operators
Long thin covers and nuclear dimension
Exotic circle actions on classifiable C*-algebras
Uniformly Super McDuff II1 Factors
Abstract harmonic analysis: an overview
Some functional analysis theorems
Structure of transformation group C*-algebras
Reading Course Summary
Discussing the Haar measure
Unveiling the Pontryagin Duality Theorem: A Proof in 4 Steps
Classification of Cuntz-Pimsner algebras associated to vector bundles, Part II
Classification of Cuntz-Pimsner algebras associated to vector bundles, Part I
Geometric properties on topological groupoids and applications to the structures... IV
Geometric properties on topological groupoids and applications to the structures... III
Geometric properties on topological groupoids and applications to the structures... II
Geometric properties on topological groupoids and applications to the structures... I
Covering dimension for Cuntz semigroups
The Global Glimm Problem
Jung-Hayes free entropy and its applications to von Neumann algebras, Part II
Jung-Hayes free entropy and its applications to von Neumann algebras, Part I
Optimal Transport Theory in Free Probability, Part II
Optimal Transport Theory in Free Probability, Part I
Soft C*-algebras
An introduction to the Cuntz semigroup
Around Z-stability: a classification of Villadsen algebras [...], Part II
Around Z-stability: a classification of Villadsen algebras [...], Part I
A generalized BDF-Kasparov theorem and Voiculescu theorem, Part II
A generalized BDF-Kasparov theorem and Voiculescu theorem, Part I

Taught by

Fields Institute

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