ICTP Mathematics Courses

Lefschetz Fibrations and Closed Exotic 4-Manifolds

Explore advanced techniques in 4-dimensional topology through Lefschetz fibrations and their role in constructing exotic smooth structures on closed 4-manifolds.

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

Real Seiberg-Witten Theory 4

Explore advanced concepts in Real Seiberg-Witten theory through expert mathematical analysis and theoretical developments in this specialized topology seminar.

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

Skein Lasagna Modules - Part 4

Explore advanced skein lasagna modules through expert mathematical analysis and theoretical frameworks in this specialized topology session.

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

On the Stability and Instability of Elliptic Equilibria and Invariant Quasi-Periodic Tori of Real Analytic Hamiltonians

Explore the stability and instability of elliptic equilibria and invariant quasi-periodic tori in real analytic Hamiltonian systems with expert Bassam Fayad.

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

An Extension of Katok Non-Stationary Normal Coordinate Along One Dimensional Invariant Manifold

Explore advanced mathematical techniques for extending Katok non-stationary normal coordinates along one-dimensional invariant manifolds in dynamical systems theory.

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

Rigidity for Generalized u-Gibbs States - Part IV

Explore advanced rigidity theory for generalized u-Gibbs states in this specialized mathematics lecture from ICTP featuring expert analysis of dynamical systems.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Lefschetz Fibrations and Closed Exotic 4-Manifolds - 5

Explore advanced techniques in 4-dimensional topology through Lefschetz fibrations and their role in constructing exotic smooth structures on closed 4-manifolds.

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

Real Seiberg-Witten Theory - 5

Explore advanced concepts in Real Seiberg-Witten theory through expert mathematical analysis and theoretical developments in this specialized topology seminar.

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

Skein Lasagna Modules - 5

Explore advanced skein lasagna modules through expert mathematical analysis and theoretical frameworks in this specialized topology session.

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

Kontsevich Invariants from Configuration Spaces - 4

Explore advanced mathematical concepts connecting Kontsevich invariants to configuration spaces through expert analysis and theoretical frameworks.

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

Mathematics Seminars - Advanced Topics in Analysis, Algebra, and Geometry

Explore advanced mathematical research through specialized seminars covering algebraic geometry, analysis, number theory, and differential equations from leading experts.

• YouTube
• 2 days 6 hours 55 minutes
• Self-Paced
• Free Video

School on Commutative Algebra and Algebraic Geometry in Prime Characteristics

Explore advanced commutative algebra and algebraic geometry in prime characteristics, covering vector bundles, tight closure, F-singularities, and BCM algebras through four specialized lecture series.

• YouTube
• 21 hours 39 minutes
• Self-Paced
• Free Video

Frontiers in Geometry and Topology Summer School

Explore advanced topics in geometry and topology including Heegaard Floer homology, Dirac operators, pseudoholomorphic curves, and Seiberg-Witten equations through expert lectures.

• YouTube
• 15 hours 34 minutes
• Self-Paced
• Free Video

Standard and Less Standard Asymptotic Methods

Master advanced techniques for evaluating infinite sums and recognizing asymptotic patterns in sequences, from Euler-Maclaurin formulas to cutting-edge methods with practical examples.

• YouTube
• 18 hours 38 minutes
• Self-Paced
• Free Video

Hyperkähler and Prym Varieties - Classical and New Results

Explore advanced algebraic geometry through hyperkähler manifolds and Prym varieties, covering classical theory, recent advances, and open problems in this specialized mathematical field.

• YouTube
• 20 hours 47 minutes
• Self-Paced
• Free Video