Topological Invariants Courses and Certifications

IMSA

Topological Invariants of Compact Singular Varieties

Explore topological invariants of compact singular varieties with José Seade from UNAM. Gain insights into advanced mathematical concepts and their applications in algebraic geometry.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Topological Invariants Arising in Geometry by Jaya N Iyer

Explore topological invariants in geometry with Jaya N Iyer. This talk delves into advanced mathematical concepts, offering insights for researchers and enthusiasts in the field.

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

International Centre for Theoretical Sciences

Chern-Simons Field Theory Invariants by Pichai Ramadevi

Explore knots, links, and three-manifolds through Chern-Simons field theory. Discover recent developments in knot-quiver correspondence and new Zhat invariants for three-manifolds.

• YouTube
• 1 hour 34 minutes
• On-Demand
• Free Video

Global Noncommutative Geometry Seminar

Axion Insulators and Their Topological Invariants

Explore axion insulators and their topological invariants with Bernardo Uribe, delving into advanced concepts in noncommutative geometry and condensed matter physics.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

ICTP-SAIFR

Unification of Topological Invariants and Topological Markers

Explore topological invariants and markers in quantum materials, unifying concepts through wrapping numbers and quantum metrics. Apply to 1D and 2D systems.

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

Institut des Hautes Etudes Scientifiques (IHES)

Topological Invariants of Gapped States and 't Hooft Anomalies

Explore topological invariants of gapped ground-states in lattice systems, their interpretation as obstructions to gauging, and the role of locality in infinite-volume systems with rapidly decaying interactions.

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

Institute for Advanced Study

The Shapes of Spaces and the Nuclear Force - Gregory Moore

Explores the interplay between physics and mathematics, focusing on topological concepts and their applications in understanding fundamental forces and the structure of space.

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

IMSA

Extensions in MHM and Hain's Biextension Line Bundle - Part 1

Explore complex manifolds, biextension line bundles, and normal functions in algebraic geometry. Discover formulas for Q-line bundle extensions and their topological invariants.

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

Applied Algebraic Topology Network

Persistent Stiefel-Whitney Classes

Explore persistent Stiefel-Whitney classes in topological data analysis, extending beyond homology groups to estimate vector bundle structures from finite samples using a persistent approach.

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

Hausdorff Center for Mathematics

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
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Topological and Combinatorial Models of Directed Path Spaces

Explore topological and combinatorial models for directed path spaces in concurrency theory, focusing on methods to analyze execution paths and state spaces in computer science.

• YouTube
• 1 hour 25 minutes
• On-Demand
• Free Video

Joint Mathematics Meetings

Smooth Invariants of Four-dimensional Manifolds and Quantum Field Theory

Explore the intersection of smooth 4D manifold invariants and quantum field theory, focusing on Yang-Mills theory, instantons, and topological invariants in this advanced mathematics lecture.

• YouTube
• 48 minutes
• On-Demand
• Conference Talk

International Centre for Theoretical Sciences

Topology and the Electromagnetic Responses of Quantum Materials

Explore electromagnetic responses in quantum materials, focusing on topological insulators, Weyl semimetals, and quantized effects. Gain insights into Berry phases, anomalous Hall effect, and circular photogalvanic effect.

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

Applied Algebraic Topology Network

Tomoo Yokoyama - Generalizations of Morse Graph of Flows and Reeb Graph of Hamiltonian Flows

Generalizations of Morse and Reeb graphs for flows, exploring connections between dynamical systems, topological structures, and abstract orbit spaces. Insights into Conley theory and topological invariants.

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

Applied Algebraic Topology Network

Takashi Owada - Limit Theorems for Topological Invariants of the Dynamic Multi-Parameter Simplicial Complex

Explore topological invariants in dynamic multi-parameter simplicial complexes, covering connectivity, probability, and limiting processes in applied algebraic topology.

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