ICTP Mathematics Courses

Hopf-Galois Extensions and Applications

Explore Hopf-Galois theory, its applications in field extensions, and arithmetic properties derived from algebraic curves. Gain insights into this generalization of classical Galois theory.

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

Superlinear Structures and Conformal Geometry

Explore superlinear structures and conformal geometry, from historical roots to modern applications in physics and mathematics, with insights on representation theory and potential links to the standard model.

• YouTube
• 1 hour 27 minutes
• Self-Paced
• Free Video

Analysis Seminar - Up to the Boundary Gradient Estimates in Bernoulli Type Free Boundary Problems

Explore recent advances in gradient estimates for viscosity solutions of free boundary problems, featuring new Inhomogeneous Pucci Barriers and innovative proof techniques inspired by Harmonic Analysis.

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

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video