ICTP Mathematics Courses

Mirror Symmetry and Big Algebras

Explore mirror symmetry in Hitchin systems, Kirillov algebras, and equivariant cohomology. Delve into conjectures on non-very stable flows and big commutative subalgebras in affine Schubert varieties.

• YouTube
• 1 hour 26 minutes
• On-Demand
• Free Video

On the Riemann Zeta-Function, Fourier Optimization and Quadratic Forms

Explore the Riemann zeta-function, Fourier analysis, and quadratic forms in number theory. Delve into Selberg's theorem, Berry's conjecture, and representation of integers by quadratic forms.

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

On the Cohomology of Quot Schemes Parametrizing Torsion Quotients on a Smooth Curve

Explore cohomology of Quot schemes on smooth curves, focusing on torsion quotients. Delve into additive basis, natural maps, and geometric interpretations with expert insights.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Standard and Less Standard Asymptotic Methods - Lecture 9

Explore advanced asymptotic methods for evaluating infinite sums and recognizing sequence patterns. Learn techniques from standard to unconventional, with practical examples and applications in mathematics.

• YouTube
• 1 hour 36 minutes
• On-Demand
• Free Video

Standard and Less Standard Asymptotic Methods - Lecture 8

Explore advanced asymptotic methods for evaluating infinite sums and recognizing sequence patterns. Learn techniques like Euler-Maclaurin formula and less standard approaches with practical examples.

• YouTube
• 1 hour 36 minutes
• On-Demand
• Free Video

Standard and Less Standard Asymptotic Methods - Lecture 6

Explore advanced asymptotic methods for evaluating infinite sums and recognizing sequence patterns, with practical examples and techniques for high-precision numerical computations.

• YouTube
• 1 hour 31 minutes
• On-Demand
• Free Video

Standard and Less Standard Asymptotic Methods - Lecture 5

Explore advanced asymptotic methods for evaluating infinite sums and sequences, including Euler-Maclaurin formula variants and less conventional techniques, with practical examples and applications.

• YouTube
• 1 hour 40 minutes
• On-Demand
• Free Video

Standard and Less Standard Asymptotic Methods - Lecture 3

Explore advanced asymptotic methods for evaluating infinite sums and recognizing sequence patterns, with practical examples and techniques for high-precision numerical computations.

• YouTube
• 1 hour 41 minutes
• On-Demand
• Free Video

ICTP-IGAP Seminar on Algebraic Geometry - Refined Invariants and Vafa-Witten Invariants

Explore refined invariants and Vafa-Witten invariants in algebraic geometry, covering virtual Euler numbers, moduli spaces of sheaves, and Higgs pairs. Delve into localization techniques for C*-actions.

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

Lectures on Standard and Less Standard Asymptotic Methods - Lecture 1

Explore advanced asymptotic methods for evaluating infinite sums and recognizing sequence patterns. Learn techniques from standard to unconventional, with practical examples and high-precision computations.

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

Virtual Invariants of Moduli Spaces of Sheaves on Surfaces and Vafa-Witten Invariants I

Explore virtual invariants of moduli spaces, Vafa-Witten invariants, and related mathematical concepts in this advanced seminar on algebraic geometry and theoretical physics.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Dynamics of Smooth Surface Diffeomorphisms - Spectral Gap and Stochastic Properties

Explore surface diffeomorphisms, spectral gaps, and stochastic properties in smooth dynamics. Gain insights into symbolic models, entropy continuity, and hyperbolic systems.

• YouTube
• 1 hour 23 minutes
• On-Demand
• Free Video

Markov Partition for Hyperbolic Systems with Singularities - ICTP 2021

Explore Markov partitions in hyperbolic systems with singularities, covering scatters, collision maps, uniform hyperbolicity, and SRB measures. Gain insights into advanced mathematical concepts and their applications.

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

Inducing Schemes and Their Role in Thermodynamics - ICTP 2021

Explore inducing schemes in thermodynamics, focusing on Young diffeomorphisms, symbolic representations, and equilibrium measures. Gain insights into pressure analyticity and phase transitions.

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

Symbolic Dynamics for Orbits with 0 Lyapunov Exponents - ICTP 2021

Explore symbolic dynamics for orbits with zero Lyapunov exponents, covering key concepts like spacing reduction, temperability, and the greedy algorithm.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video