Graph Theory Courses

Applied Algebraic Topology Network

Morse Theory for Group Presentations and the Persistent Fundamental Group

Discrete Morse theory refinement for CW-complexes, with applications in combinatorial group theory and topological data analysis, including persistent fundamental group computation.

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

Applied Algebraic Topology Network

Exemplars of Sheaf Theory in TDA

Exploring sheaf theory applications in topological data analysis through four case studies, covering level set persistence, merge trees, and innovative approaches to persistent homology.

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

Applied Algebraic Topology Network

Claudia Landi - Multi-parameter Persistence from the Viewpoint of Discrete Morse Theory

Explore multi-parameter persistence through discrete Morse theory, connecting combinatorial properties of critical cells to algebraic properties of persistence modules in topological data analysis.

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

Applied Algebraic Topology Network

Discrete Morse Theory Meets Multi-Parameter Persistence

Exploring connections between discrete Morse theory and multiparameter persistence in topological data analysis, focusing on critical cells, fibered rank invariant, and computational efficiency.

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

Applied Algebraic Topology Network

Vietoris-Rips Complexes and Geometric Group Theory

Explore Vietoris-Rips complexes in geometric group theory, focusing on topological finiteness properties, hyperbolic groups, and recent developments in Morse theory and persistent homology.

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

Applied Algebraic Topology Network

An Application of Discrete Morse Theory to Robot Motion Planning

Explore discrete Morse theory and its variants, learning how to apply this mathematical concept to develop continuous motion planning algorithms for autonomous devices.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

On the Lusternik-Schnirelmann Theory of 4-Manifolds

Explore Lusternik-Schnirelmann category in 4-manifolds, focusing on covers, fillings, and Gay-Kirby trisections. Gain insights into decompositions of 4-manifolds into 1-handlebodies.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

A Fiber Bundle Theory for Shapes

Explore fiber bundle applications in probabilistic modeling for shapes and surfaces, focusing on regression, variable selection, and Gaussian processes in evolutionary biology and biomedicine.

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

Applied Algebraic Topology Network

Graph Reconstruction via Discrete Morse Theory

Explore graph reconstruction using discrete Morse theory, focusing on geometric graphs and density data. Learn about theoretical guarantees and applications in road network reconstruction.

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

Applied Algebraic Topology Network

Greg Henselman - Matroids & Canonical Forms Theory and Applications

Explore matroids and canonical forms, their theoretical foundations, and practical applications in algebraic topology and related fields.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

International Mathematical Union

30 Years of Modularity - Number Theory Since the Proof of Fermat's Last Theorem

Explore advancements in number theory since Fermat's Last Theorem, focusing on modularity and its impact on mathematical research over the past three decades.

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

International Mathematical Union

Joel Kamnitzer- Perfect Bases in Representation Theory- Three Mountains and Their Springs

Exploration of perfect bases in representation theory, examining three approaches and their combinatorial implications for tensor product multiplicities in semisimple groups.

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

International Mathematical Union

Mean Curvature and Variational Theory

Explores recent developments in prescribing mean curvature equations, focusing on existence theory, min-max theory for CMC/PMC surfaces, and Morse theory for area functional. Includes solution to Multiplicity One Conjecture.

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

International Mathematical Union

Probability Theory for Random Groups Arising in Number Theory

Explores probability theory for random groups in number theory, topology, and combinatorics. Covers moment problems, universality theorems, and distributions of class groups and Selmer groups.

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

International Mathematical Union

Algebraic-Geometrical Methods in the Theory of Integrable Systems

Explore algebraic-geometrical methods in integrable systems theory with renowned mathematician Igor Krichever, delving into advanced mathematical concepts and their applications.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video