ICTP Mathematics Courses

Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 5

Explore advanced techniques in symbolic dynamics for complex hyperbolic systems. Gain insights into infinite Markov partitions and their applications in studying statistical properties of dynamical systems.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video

SRB Measures and Young Towers - Lecture 2 of 4

Explore SRB measures and Young Towers in nonuniformly hyperbolic systems. Learn advanced techniques for studying statistical properties of complex dynamical systems.

• YouTube
• 1 hour 51 minutes
• On-Demand
• Free Video

SRB Measures and Young Towers - Lecture 1

Explore groundbreaking techniques in Ergodic Theory applied to differentiable dynamical systems. Learn about SRB measures, Markov Partitions, and Young Towers in nonuniformly hyperbolic systems.

• YouTube
• 2 hours 7 minutes
• On-Demand
• Free Video

Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 1 of 5

Explore symbolic dynamics for nonuniformly hyperbolic systems, focusing on Markov Partitions and Young Towers. Learn advanced techniques to analyze complex dynamical systems and their statistical properties.

• YouTube
• 2 hours 6 minutes
• On-Demand
• Free Video

From Knots to Number Theory I

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

• YouTube
• 1 hour 33 minutes
• On-Demand
• Free Video

Reversible D-Dimensional CA Over the Ring ZM and Some Applications in Ergodic Theory

Explore cellular automata on $\mathbf{Z}_p$ and $\mathbf{Z}_m$, covering invertibility, ergodic properties, and entropy concepts. Delve into measure-theoretic and topological entropy for 1D linear CA and $\mathbb{Z}^2$-actions.

• YouTube
• 59 minutes
• On-Demand
• Free Video

Basic Notions Seminar - Orientations in the Plane as Quantum States

Explore fundamental quantum physics concepts through plane orientations and light polarization. Gain insights into quantum states, dynamics, and measurement using real-world examples and mathematical formalism.

• YouTube
• 59 minutes
• On-Demand
• Free Video

Conditional Measures for the Zero Set of the Gaussian Analytic Function

Explore conditional distributions of zero sets in Gaussian analytic functions, focusing on fixed configurations outside compact sets. Gain insights into determinantal formulas and Lobachevskian isometries.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Probability Invariant Measure, Dynamical Partition and Hitting Times of Circle Map with Singularities

Explore circle dynamics and recent findings in circle maps with break or critical points, focusing on probability invariant measures, dynamical partitions, and hitting times.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Combinatoria de Superficies Quadriculadas e Geometria de Espacos de Modulos - Lecture 5

Combinatoria de superficies quadriculadas e geometria de espacos de modulos: explorando conexões entre topologia, geometria e teoria dos números em espaços de módulos.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

AGRA IV - Diophantine Equations with Few Solutions - Lecture 5

Exploración avanzada de ecuaciones diofantinas con énfasis en casos con soluciones limitadas, presentada por el experto Hector Pasten de la PUC, Chile.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Superficies Racionales sobre un Cuerpo - AGRA IV Minicourse 2 - Lecture 5

Explora superficies racionales sobre cuerpos en esta conferencia avanzada de matemáticas, examinando conceptos clave y resultados recientes en geometría algebraica aritmética.

• YouTube
• 53 minutes
• On-Demand
• Free Video

Combinatoria de Superficies Quadriculadas e Geometria de Espacos de Modulos - Lecture 4

Exploración avanzada de combinatoria en superficies cuadriculadas y geometría de espacios de módulos, con énfasis en aplicaciones a la teoría de grupos y análisis.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Superficies Racionales sobre un Cuerpo - AGRA IV Minicourse 2 - Lecture 4

Explora superficies racionales sobre cuerpos en esta conferencia avanzada de matemáticas, abordando conceptos de geometría algebraica y teoría de números.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Ecuaciones Diofantinas con Pocas Soluciones - Lecture 3

Explora ecuaciones diofantinas con pocas soluciones, profundizando en conceptos avanzados de teoría de números y álgebra abstracta.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video