Graph Theory Courses

Applied Algebraic Topology Network

Graph Representation Learning and Its Applications to Biomedicine

Graph representation learning techniques for biomedical applications, focusing on SubGNN for disentangled subgraph embeddings and their use in predicting disease treatments and safe drug combinations.

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

Applied Algebraic Topology Network

Topological Complexity of Pure Graph Braid Groups

Explore topological complexity in graph braid groups, focusing on Farber's conjecture about ordered configuration spaces and its implications for topological robotics.

• YouTube
• 56 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

Hardness Results in Discrete Morse Theory for 2-Complexes

Explore inapproximability and parameterized complexity in discrete Morse theory for 2-complexes, focusing on minimizing critical simplices and presenting new hardness results and an approximation algorithm.

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

Applied Algebraic Topology Network

Conley-Morse-Forman Theory for Generalized Combinatorial Multivector Fields

Generalized combinatorial multivector fields on finite topological spaces: extending Conley-Morse-Forman theory for data science applications, including isolated invariant sets, Conley index, and Morse decompositions.

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

Applied Algebraic Topology Network

Lower Dimensional Topological Information: Theory and Applications

Explore lower dimensional topological features in data analysis, covering detection methods, theoretical foundations, and applications in image segmentation using topological and statistical approaches.

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

Applied Algebraic Topology Network

Catastrophe Theory

Explore catastrophe theory, covering critical points, germs, classification theorems, unfoldings, and elementary catastrophes. Visualize concepts and discover applications in chemistry.

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

Applied Algebraic Topology Network

Henry Adams and Enrique Alvarado - An Introduction to Morse Theory

Explore Morse theory's applications in topology, including CW complexes, key theorems, and simplification techniques, with real-world examples in material science.

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

Applied Algebraic Topology Network

Vidit Nanda - Morse Theory for Local Coefficients

Explore Morse theory with local coefficients, covering cohomogeneous complexes, wave graphs, and isomorphisms. Delve into advanced topics and theorems in algebraic topology.

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

Applied Algebraic Topology Network

Bala Krishnamoorthy: Linear Programming in Geometric Measure Theory

Explore geometric measure theory through linear programming, examining integral currents, simplicial flat norm, and polyhedral approximation. Discover applications in median shape analysis.

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

International Mathematical Union

Hodge Theory, Between Algebraicity and Transcendence

Explore recent advances in Hodge theory, comparing algebraic structures and bounding transcendence using o-minimal geometry. Gain insights into complex algebraic varieties and their applications.

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

International Mathematical Union

Stable Homotopy Groups of Spheres and Motivic Homotopy Theory

Survey of stable homotopy groups of spheres computation, covering classical methods, Mahowald's Uncertainty Principles, and new techniques using motivic homotopy theory. Includes recent computations and future research directions.

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

International Mathematical Union

Real Gromov-Witten Theory

Survey of recent developments in real Gromov-Witten theory, covering construction challenges, structural results, and connections to physics. Explores moduli spaces, invariants, and enumerative geometry.

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

International Mathematical Union

Alexander Efimov: On the K-Theory of Large Triangulated Categories

Explore Grothendieck groups, categorical localization, and continuous K-theory in large triangulated categories. Delve into higher algebraic K-theory, negative K-theory, and dualizable DG categories.

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

International Mathematical Union

Julia Boettcher- Graph and Hypergraph Packing

Explore graph and hypergraph packing, Latin squares, and randomness in mathematics with Julia Boettcher's insightful lecture on combinatorial structures.

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