Graph Theory Courses

Hausdorff Center for Mathematics

Tropical Solutions to Hard Problems in Auction Theory and Neural Networks - Lecture I

Explore tropical mathematics and its applications in neural networks, auction theory, and more. Learn about min-plus algebra, tropical objects, and polyhedral geometry to solve complex problems.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Representation Theory for Groups of Lie Type I

Explore representation theory for finite groups of Lie type, covering structural properties, Harish-Chandra theory, and Deligne-Lusztig theory for classifying irreducible complex representations.

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

Hausdorff Center for Mathematics

Peter Dybjer - Intuitionistic Type Theory

Explore intuitionistic type theory, inductive definitions, and finite axiomatizations in this advanced lecture on mathematical foundations and type systems.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Peter Dybjer - Intuitionistic Type Theory - Lecture I

Explore intuitionistic type theory's foundations, historical context, and applications in mathematics and computer science with Prof. Peter Dybjer's comprehensive lecture.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

The Transfer in Algebraic K-Theory and THH

Explore algebraic K-theory transfers, their applications in A-theory, and connections to THH. Gain insights into fundamental questions and trace methods in this advanced mathematics lecture.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

The Slices of Hermitian K-Theory

Explore Hermitian K-theory's slices, their construction, and applications in algebraic geometry. Gain insights into Milnor's conjecture on quadratic forms through this advanced mathematical lecture.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Drinfeld Center, Tube Algebra, and Representation Theory of Monoidal Categories

Explore connections between category theory, subfactor theory, and quantum groups. Learn about Drinfeld center, tube algebra, and representation theory of monoidal categories.

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

Hausdorff Center for Mathematics

On Element Connectivity Preserving Graph Simplification

Explores element-connectivity in graph simplification, focusing on reduction techniques, algorithmic results, and applications in network design. Highlights open problems and submodularity properties for faster algorithms.

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

Hausdorff Center for Mathematics

Real Reductive Groups, K-Theory and the Oka Principle

Explore real reductive groups, K-theory, and the Oka principle in this advanced mathematics lecture, delving into representation theory and complex analysis concepts.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

ICTP Mathematics

From Knots to Number Theory II

Explore connections between quantum knot invariants and number theory, covering topics like hyperbolic topology, Kashaev invariant, and quantum modularity. No prior knowledge required.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Control Theory and Large Deviation Principles for PDEs

Explore control theory and large deviation principles for PDEs, covering IID cases, contraction principles, rate functions, and applications to random forces and controllability.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

ICTP Mathematics

New Complex Analytic Methods in the Theory of Minimal Surfaces - Franc Forstnerič

Explore recent developments in minimal surface theory using complex analytic methods, covering global theory, Calabi-Yau problem, and complex Gauss map applications.

• YouTube
• 1 hour
• Self-Paced
• Free Video

ICTP Mathematics

Introduction to Ergodic Theory 1

Explore measure theory fundamentals, sigma algebras, and Lebesgue measure construction in this comprehensive introduction to ergodic theory.

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

ICTP Mathematics

Regularity Theory for Area-Minimizing Currents

Explore advanced concepts in geometric measure theory, including zero forms, currents, and rectifiability theorems, with applications to area-minimizing problems in mathematics.

• YouTube
• 1 hour 40 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Regularity Theory for Area-Minimizing Currents

Explore advanced concepts in geometric measure theory, including currents, boundaries, and regularity theory for area-minimizing surfaces, with applications to optimal transport problems.

• YouTube
• 1 hour 53 minutes
• Self-Paced
• Free Video