ICTP Mathematics Courses

Gauge Theories and Differential Invariants - Recent Developments in Mathematics and Physics

Explore advanced gauge theories connecting theoretical physics and mathematics through Donaldson invariants, supersymmetric quantum field theories, and differential geometry applications.

• YouTube
• 20 hours 31 minutes
• Self-Paced
• Free Video

Random Matrix Theory and Point Processes

Explore advanced mathematical concepts in random matrix theory, determinantal point processes, and their applications in dynamical systems through expert lectures and research seminars.

• YouTube
• 1 day 32 minutes
• Self-Paced
• Free Video

Mixing and Control - Mathematical Control Theory for Stochastically Perturbed Dynamical Systems

Explore advanced mathematical control theory and mixing properties of stochastically perturbed dynamical systems through mini courses and research seminars.

• YouTube
• 21 hours 31 minutes
• Self-Paced
• Free Video

Geometry and Gravity School - Black Holes, Spacetime, and Gravitational Waves

Explore advanced topics in general relativity including black holes, gravitational waves, thermodynamics, and the AdS-CFT conjecture through comprehensive lectures.

• YouTube
• 1 day 14 hours 8 minutes
• Self-Paced
• Free Video

Summer School in Dynamics - Introductory and Advanced

Explore fundamental and advanced concepts in dynamical systems through circle maps, ergodic theory, and renormalization techniques with expert-led lectures and hands-on tutorials.

• YouTube
• 1 day 1 hour 23 minutes
• Self-Paced
• Free Video

Nonlocal Partial Differential Equations and Applications to Geometry, Physics and Probability

Explore advanced mathematical techniques in nonlocal partial differential equations with applications spanning plasma physics, geometry, and probability theory.

• YouTube
• 1 day 14 hours 4 minutes
• Self-Paced
• Free Video

Geometry of Moduli Spaces of Curves

Explore advanced algebraic geometry through moduli spaces of stable curves, vector bundles of coinvariants, conformal blocks, and their cohomological properties and relationships.

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

Geometric Measure Theory and Optimal Transport

Explore advanced mathematical concepts connecting geometric measure theory with optimal transport through expert lectures on regularity theory, Monge-Ampère equations, and stability results.

• YouTube
• 1 day 7 hours 45 minutes
• Self-Paced
• Free Video

Extrinsic Curvature Flows - Analysis and Geometry at the Interface

Explore advanced mathematical techniques in extrinsic curvature flows, covering mean curvature flow, singularities, Brakke flow theory, and applications to geometry and physics.

• YouTube
• 1 day 18 hours 51 minutes
• Self-Paced
• Free Video

Advanced School and Workshop on Geometry of Discrete Actions

Explore discrete group actions in geometry through hyperbolic spaces, complex dynamics, Teichmüller theory, and holomorphic dynamics with leading mathematicians.

• YouTube
• 1 day 16 hours 38 minutes
• Self-Paced
• Free Video

School and Conference on Dynamical Systems

Explore advanced dynamical systems theory through expert lectures on chaotic dynamics, conservative systems, ergodic theory, and geometric aspects from leading mathematicians.

• YouTube
• 2 days 9 hours 28 minutes
• Self-Paced
• Free Video

School on Algebraic, Geometric and Probabilistic Aspects of Dynamical Systems and Control Theory

Explore algebraic, geometric and probabilistic aspects of dynamical systems through expert minicourses covering counting techniques, group actions, symbolic dynamics, and Brownian motion.

• YouTube
• 1 day 6 hours 1 minute
• Self-Paced
• Free Video

Moduli Spaces, Mirror Symmetry, and Enumerative Geometry

Explore advanced algebraic geometry through moduli spaces, mirror symmetry, and enumerative geometry with leading experts from top institutions worldwide.

• YouTube
• 1 day 9 hours 46 minutes
• Self-Paced
• Free Video

Advanced School on Geometric Group Theory and Low-Dimensional Topology - Recent Connections and Advances

Explore cutting-edge connections between geometric group theory and low-dimensional topology through advanced lectures on virtually special groups, hyperbolic manifolds, and Teichmuller theory.

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

Algebraic Geometry

Master algebraic geometry fundamentals through comprehensive lectures covering varieties, schemes, and geometric structures in this ICTP diploma program.

• YouTube
• 1 day 6 hours 23 minutes
• Self-Paced
• Free Video