ICTP Mathematics Courses

Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 4

Explore advanced techniques in nonuniformly hyperbolic dynamics, focusing on symbolic coding and statistical properties of complex systems using Markov Partitions and Young Towers.

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

Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 3 of 5

Explores advanced techniques in nonuniformly hyperbolic systems, focusing on symbolic dynamics and Markov partitions. Covers key concepts, challenges, and recent developments in the field of dynamical systems.

• YouTube
• 2 hours 13 minutes
• Self-Paced
• Free Video

Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 2 of 5

Explores advanced techniques in symbolic dynamics for nonuniformly hyperbolic systems, focusing on graph transforms, recurrence properties, and Markov partitions to analyze complex dynamical behaviors.

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

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

Ecuaciones Diofantinas con Pocas Soluciones - Lecture 4

Explora teoremas y aplicaciones en ecuaciones diofantinas, incluyendo el teorema de Faltings para curvas y ejemplos prácticos, profundizando en la teoría de números.

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

Involutions of a Cubic Fourfold

Explore involutions of cubic fourfolds, covering hyperkähler manifolds, period domains, and evolution types. Delve into geometry, rationality, and related mathematical concepts.

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

Kirchhoff’s Theorem and Semi-Canonical Representatives for the Tropical Prym Variety

Explore Kirchhoff's theorem, metric graphs, and tropical Prym varieties. Delve into divisors, Jacobians, and double covers, gaining insights into advanced algebraic geometry concepts.

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

Tropical Prym Varieties

Explore tropical geometry, divisors, chip firing, and Jacobians. Learn about double covers, induced maps, and generic curves in relation to Prym varieties.

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

Modularity of Some Geometric Objects - Definitions, Reasons and State of the Art

Explore zeta functions, L-functions, and Galois representations in geometric objects, focusing on plane projective curves and their conjectured relationships with analytic functions.

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

Closed Geodesics on Surfaces without Conjugate Points

Explore asymptotic estimates for closed geodesics on surfaces without conjugate points, covering compact surfaces of genus ≥2. Delve into counting methods, uniform hyperbolicity, and proof techniques.

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

Finding Solitons in Differential Geometry

Explore solitons in differential geometry, their role in discovering distinguished geometric structures, and applications in various mathematical contexts including Lie groups and algebras.

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

Singular Chains on Lie Groups and the Cartan Relations

Explore the connection between Lie group representations and infinitesimal descriptions using Cartan relations, with applications to Chern-Weil theory and higher local systems on classifying spaces.

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

Symmetries in Algebraic Geometry and the Cremona Group

Explore symmetries in algebraic geometry, focusing on automorphisms and birational self-maps of projective varieties. Delve into the Cremona group and its subgroups, with insights from recent research.

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

Phase Transitions - From Physics to Computer Science

Explore phase transitions across physics and computer science, from water states to combinatorial optimization and information theory, revealing their universal nature in complex systems.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 3

Explore the deep connections between Rogers-Ramanujan identities and the icosahedron, spanning number theory, modular forms, combinatorics, and more. Uncover the beauty and complexity of these mathematical gems.

• YouTube
• 1 hour 24 minutes
• Self-Paced
• Free Video