Hausdorff Center for Mathematics Courses

TQFTs From Non-Semisimple Modular Categories and Modified Traces - Marco de Renzi

Explore advanced TQFTs, non-semisimple modular categories, and modified traces in topology. Learn about cutting-edge techniques for studying 3-manifolds and mapping class group representations.

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

Felix Klein Lectures 2020 - Quiver Moduli and Applications

Explore quiver moduli spaces' construction, topology, and geometry, with focus on cohomology and applications to Gromov-Witten and Donaldson-Thomas theories via wall-crossing.

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

Felix Klein Lectures 2020- Quiver Moduli and Applications

Explore quiver moduli spaces: their construction, topology, and applications in representation theory, Gromov-Witten theory, and Donaldson-Thomas theory. Gain insights into these algebraic varieties and their geometric properties.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Homological Mirror Symmetry for Not-So-Simple Singularities - Yanki Lekili

Explore homological mirror symmetry for invertible polynomials' Milnor fibers, focusing on explicit conjectures and proofs for simple and not-so-simple singularities.

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

Perverse Sheaves and Schobers on Riemann Surfaces - Tobias Dyckerhoff

Explore derived constructible categories on stratified Riemann surfaces, t-structures, Verdier duality, and categorified perverse sheaves with applications in algebraic geometry and topology.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

TQFTs from Non-Semisimple Modular Categories and Modified Traces - Marco de Renzi

Explore non-semisimple TQFTs and modified traces in topology, focusing on construction methods, invariants, and mapping class group representations derived from modular categories.

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

From Hall Algebras to Legendrian Skein Algebras

Explore the connection between Hall algebras and skein algebras, delving into legendrian knot theory and Fukaya categories of surfaces. Gain insights into cutting-edge mathematical research.

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

Partially Wrapped Fukaya Categories of Symmetric Products of Marked Disks, Gustavo Jasso

Explore the equivalence between partially wrapped Fukaya categories and perfect derived categories, examining their rich mathematical structures and connections to higher Auslander algebras and Waldhausen S-constructions.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

TQFTs from Non-Semisimple Modular Categories and Modified Traces - Lecture I

Explore advanced topological quantum field theories, focusing on non-semisimple constructions and modified traces for powerful invariants and mapping class group representations.

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

A Geometric Model for the Bounded Derived Category of a Gentle Algebra - Sibylle Schroll Lecture 3

Explore geometric models for bounded derived categories of gentle algebras, their role in cluster algebras and homological mirror symmetry, and connections to partially wrapped Fukaya categories.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Winter School JTP- Plumbings and Flops, Ivan Smith

Explore advanced concepts in symplectic topology, focusing on plumbings and flops. Gain insights into cutting-edge research and techniques in this specialized field of mathematics.

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

A Geometric Model for the Bounded Derived Category of a Gentle Algebra - Sibylle Schroll Lecture 2

Explore geometric models for bounded derived categories of gentle algebras, focusing on their role in cluster algebras and homological mirror symmetry. Learn about line fields and derived invariants.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

An Introduction to Modified Traces - Jonathan Kujawa

Explore fundamental invariants in representation theory, focusing on modified traces as replacement invariants in non-semi-simple settings. Learn basic properties and applications.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

A Geometric Model for the Bounded Derived Category of a Gentle Algebra - Sibylle Schroll

Explore geometric models for gentle algebras' derived categories, connecting algebra to surface topology and line fields. Gain insights into representation theory and homological mirror symmetry.

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

Introduction to Fukaya Categories - James Pascaleff

Explore examples of Fukaya categories, focusing on surfaces and potentially other cases, building upon previous lectures on symplectic geometry and Floer cohomology.

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