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

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

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

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

Dublin Institute for Advanced Studies DIAS

ceff as a New Invariant of 3-Manifolds

Explore new invariant ceff for 3-manifolds, connecting low-dimensional topology with supersymmetric gauge theory through numerical analysis of homology spheres.

• YouTube
• 56 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

Applied Algebraic Topology Network

Sheaves as Computable and Stable Topological Invariants for Datasets

Explores sheaf theory in topological data analysis, connecting level-sets persistence with derived sheaves. Presents functorial equivalences, stability theorems, and barcode decompositions for continuous data analysis.

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

Harvard CMSA

Quantum Phase Diagrams - Order Parameters, Topological Invariants, Examples

Explore quantum lattice systems' ground states, phase diagrams, order parameters, and topological invariants through mathematical frameworks and concrete examples.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

ICTP Mathematics

Virtual Topological Invariants of Moduli Spaces of Sheaves on Surfaces

Explore virtual topological invariants of moduli spaces, focusing on multiplicative classes, convergence, and residual formulas in sheaf theory on surfaces.

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

ICTP Mathematics

Virtual Topological Invariants of Moduli Spaces of Sheaves on Surfaces

Explore virtual topological invariants of moduli spaces, focusing on sheaves on surfaces. Learn about ischemic points, Euler numbers, and perfect obstruction theory.

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

Cambridge Materials

Ab Initio Charge Transport of Ionic Fluids: Invariance Principles and Topological Invariants

Explore ab initio charge transport in ionic fluids, combining invariance principles and topological quantization to redefine oxidation numbers and electrical conductivity calculations.

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

Simons Institute

Topological and Algebraic Invariants to Classify Types of Singularities of Maps Relevant to Spacecraft Attitude Control and Robotic Manipulation

Explore topological and algebraic invariants for classifying map singularities in spacecraft attitude control and robotic manipulation, including numerical pseudoinverse challenges.

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

IIT Guwahati;  NPTEL

Topology and Condensed Matter Physics

Explore topological implications in condensed matter physics, covering quantum Hall effect, graphene, and Weyl semi-metals. Gain insights into exotic features and novel viewpoints for advanced research and teaching.

• Swayam
• 8 weeks
• On-Demand
• Free Online Course