Graph Theory Courses

International Centre for Theoretical Sciences

Introduction to Nonlinear Dynamics - The Case of Catastrophe Theory by Vishwesha Guttal

Explore nonlinear dynamics and catastrophe theory in finance and macroeconomics. Learn alternative frameworks for analyzing modern financial systems and their economic impacts.

• YouTube
• 37 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

Topology of Surprisal - Information Theory and Vietoris-Rips Filtrations

Explore the fusion of information theory and Vietoris-Rips filtrations, focusing on Kullback-Leibler divergence and its applications in deep learning, with insights on overcoming non-symmetry challenges.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

The Reeb Graph of a Smooth Function Encodes the Function Class and Manifold Type

Explore how Reeb graphs of smooth functions encode function class and manifold type, examining structures for Morse and Morse-Bott functions and their relationship to manifold properties.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

Recent Advances in Theory and Implementation of Multi-Parameter Persistence

Explores recent developments in multi-parameter persistence, covering stable filtrations and discrete descriptors. Includes interactive clustering software demo and discusses extensions of one-parameter persistence concepts.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

The Topological Complexity of Pure Graph Braid Groups Is Stably Maximal

Explore the topological complexity of configuration spaces in graphs, using group theoretic estimates for higher topological complexity instead of traditional cohomology approaches.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

Krystyna Kuperberg - Shape Theory: Vietoris-Cech Approach to Homotopy

Explore shape theory's geometric approach to homotopy for compact metric spaces, extending Vietoris' work on first homotopy groups to higher dimensions with applications in mind.

• YouTube
• 42 minutes
• Self-Paced
• Free Video

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video