ICTP Mathematics Courses

Standard and Less Standard Asymptotic Methods - Lecture 10

Explore advanced techniques for evaluating infinite sums and recognizing asymptotic patterns in numerical sequences, with applications to complex mathematical problems.

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

Standard and Less Standard Asymptotic Methods - Lecture 7

Explore advanced techniques for evaluating infinite sums and recognizing asymptotic patterns in numerical sequences, with practical examples and applications in various mathematical fields.

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

Moduli Spaces of Sheaves and Vafa-Witten Formula in Algebraic Geometry

Explore moduli spaces of sheaves, Hilbert schemes, and the Vafa-Witten formula. Learn about perfect obstruction theories, virtual fundamental classes, and their role in defining enumerative invariants for singular spaces.

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

Standard and Less Standard Asymptotic Methods - Lecture 4

Explore advanced techniques for evaluating infinite sums and recognizing asymptotic patterns in numerical sequences, with practical examples and applications in various mathematical fields.

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

Standard and Less Standard Asymptotic Methods - Lecture 2

Explore advanced asymptotic methods in mathematics, delving into both standard and unconventional approaches to enhance problem-solving skills and theoretical understanding.

• YouTube
• 1 hour 35 minutes
• Self-Paced
• Free Video

ICTP-IGAP Seminar on Algebraic Geometry - Representations of the Diagonal for Moduli Spaces of Sheaves

Explore representations of the diagonal for moduli spaces of sheaves, focusing on cohomology, Chow rings, and Lie algebra actions. Gain insights into algebraic geometry and holomorphic symplectic geometry.

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

Moduli Spaces of Sheaves, Vafa-Witten Formula and Virtual Invariants

Explore moduli spaces of sheaves, Vafa-Witten formula, and virtual invariants in algebraic geometry. Learn about Hilbert schemes, stable sheaves, and perfect obstruction theories.

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

ICTP-IGAP Seminar on Algebraic Geometry - The SL(2) Action on the Chow Ring of an Abelian Variety

Explore the sl(2) action on the Chow ring of an abelian variety in this advanced algebraic geometry seminar by Alina Marian, delving into complex mathematical concepts and theories.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Mixing Rates for Symplectic Almost Anosov Maps - ICTP 2021

Explore mixing rates in symplectic almost Anosov maps with Peyman Eslami. Gain insights into advanced mathematical concepts and their applications in dynamical systems theory.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Dynamics of Smooth Surface Diffeomorphisms: Strong Positive Recurrence - ICTP 2021

Explore advanced concepts in smooth surface diffeomorphisms, focusing on strong positive recurrence and its implications for dynamical systems theory.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

On the Thermodynamical Formalism for Expanding Measures - ICTP 2021

Explore thermodynamical formalism for expanding measures with expert Vilton Pinheiro, delving into advanced mathematical concepts and their applications in dynamical systems.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

Young Towers for Geodesic Flows on Certain Non-Positively Curved Surfaces - ICTP 2021

Explore Young towers for geodesic flows on non-positively curved surfaces with Yakov Pesin. Gain insights into Sinai-Ruelle-Bowen measures and their applications in surface diffeomorphisms.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Dynamics of Smooth Surface Diffeomorphisms: Entropy Continuity of Exponents - ICTP 2021

Explore entropy continuity and exponents in smooth surface diffeomorphisms with Jerome Buzzi, delving into advanced mathematical concepts and their applications in dynamical systems.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

SRB Measures and Young Towers - Lecture 4

Explore advanced techniques in dynamical systems, focusing on SRB measures and Young Towers. Learn about recent developments and applications in nonuniformly hyperbolic systems.

• YouTube
• 2 hours 23 minutes
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video