ICTP Mathematics Courses

Applications of Homogeneous Dynamics - Lecture 1

Explore homogeneous dynamics and its applications in number theory and statistical mechanics, covering key concepts, theorems, and real-world implications.

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

Building Thermodynamics for Non-Uniformly Hyperbolic Maps - Yakov Pesin

Explore advanced concepts in dynamical systems, focusing on non-uniformly hyperbolic maps, symbolic models, and equilibrium measures in thermodynamics.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

On the Equality of Test Ideals

Explore the mathematical concept of test ideals and their equality, delving into advanced algebraic theory with insights from a renowned expert.

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

F-rationality of Rees Algebras

Explore F-rationality in Rees Algebras with M. Kummini, delving into advanced algebraic concepts and their applications in mathematical research.

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

Castelnuovo-Mumford Regularity of Powers of an Idea

Explore the mathematical concept of Castelnuovo-Mumford regularity and its application to powers of ideals in algebraic geometry, presented by expert L.T. HOA from Vietnam's Institute of Mathematics.

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

Tight Closure

Explore prime characteristic algebraic geometry and commutative algebra, focusing on tight closure theory and its applications in mathematics research.

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

Hilbert-Samuel Coefficients of Frobenius Powers of an Ideal

Explore Hilbert-Samuel coefficients and their relationship to Frobenius powers of ideals in this advanced mathematical lecture by A. Banerjee from IIT Kharagpur.

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

F-Signature of Some Hypersurfaces

Explore F-signature of hypersurfaces with A. Caminata, delving into advanced mathematical concepts and their applications in algebraic geometry.

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

Categorical Approaches to Local Singularities

Explore categorical approaches to local singularities, delving into advanced mathematical concepts and their applications in algebraic geometry and commutative algebra.

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

Remarks on Macaulayfications of Noetherian Schemes

Explore advanced algebraic geometry concepts, focusing on Macaulayfications of Noetherian schemes. Gain insights from expert D.T. CUONG on this specialized mathematical topic.

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

Bounds on the Number of Generators of Prime Ideals

Explore prime ideals and their generators, focusing on mathematical bounds and theoretical implications in algebraic geometry and commutative algebra.

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

The 3 Differents

Explore the concept of "The 3 Differents" in mathematics with expert insights from C. POLINI of the University of Notre Dame, offering a deep dive into this intriguing topic.

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

Infinite Free Resolutions

Explore infinite free resolutions in algebra with insights from D. Eisenbud, delving into advanced mathematical concepts and their applications in algebraic geometry.

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

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

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