ICTP Mathematics Courses

Math Associates Seminar- Bubbling of Q-Curvature Equation on 4-Manifolds in the Null Case

Explore the Q-curvature equation on 4-manifolds, focusing on solution behavior as ε approaches zero. Gain insights into the Paneitz operator and sign-changing functions in mathematical analysis.

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

Reaction Diffusion Equations on Evolving Domains: Regularity and Global Existence

Explore regularity and global existence of reaction diffusion equations on evolving domains, focusing on mathematical analysis and advanced theoretical concepts.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Exotic Spheres and Singularities - Math Associates Seminar

Explore the fascinating journey from exotic spheres to Milnor's Fibration Theorem, a cornerstone in singularity theory, and its impact on complex hypersurface geometry and topology.

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

Dynamics of the Geodesic Flow on Surfaces Without Conjugate Points - Lecture 4

Explore geodesic flow dynamics on surfaces without conjugate points, focusing on uniqueness and ergodicity of maximal entropy measure and mixing properties of the flow.

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

Dynamics of the Geodesic Flow on Surfaces Without Conjugate Points - Lecture 2

Explore geodesic flow dynamics, maximal entropy measures, and Patterson-Sullivan measures on ideal boundaries in surfaces without conjugate points.

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

Mating Quadratic Maps with the Modular Group

Explore holomorphic correspondences and their dynamics, focusing on a specific family of (2:2) correspondences and their relationship to the modular group and rational maps.

• YouTube
• 1 hour 22 minutes
• Self-Paced
• Free Video

Basic Notions Seminar on Tropical Geometry

Introduction to tropical geometry, focusing on plane tropical curves as piecewise linear graphs and their applications in enumerative geometry. Explores the combinatorial aspects that reflect properties of algebraic varieties.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Sampling, Tilings, and Quasicrystals

Explore connections between sampling theorem, tiling properties, and model sets. Discover links to Fuglede's theorem and quasicrystals, bridging mathematics and materials science.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Characterization of Free Boundary CMC Surfaces in the Ball

Exploration of compact stable CMC surfaces with free boundary in convex domains, focusing on classification in the unit Euclidean three-ball and characterization of equatorial disk and critical catenoid.

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

Joint ICTP-Rio de Janeiro Webinar on Analysis and PDEs - Certainty vs. Uncertainty

Explore the uncertainty principle in Fourier transforms, from classical results to new territories, with connections to number theory and surprising insights.

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

Basic Notions Seminar on Mean Curvature Flow of Closed Hypersurfaces

Explore mean curvature flow of closed hypersurfaces, from basic definitions to advanced topics, including variational aspects and key theorems like Grayson's and Huisken's.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 4

Exploración profunda de las identidades Rogers-Ramanujan, su conexión con el icosaedro y sus implicaciones en teoría de números, formas modulares, combinatoria y teoría de campos conformes.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Some Classical Invariants of Links and Their Higher-Dimensional Analogues

Explore geometric invariants of links and knots, including higher-dimensional analogues, with examples of non-trivial cases in ambient isotopy.

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

Chiral Algebras from Three Dimensions

Explore the fascinating connection between chiral algebras and three-dimensional physics in this advanced mathematical lecture by renowned physicist Sergei Gukov.

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

Invariants of Manifolds from Non-Gauge Theories

Explore topological invariants of manifolds derived from non-gauge theories, focusing on innovative approaches and recent developments in theoretical physics and mathematics.

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