ICTP Mathematics Courses

The Hilbert Functions of Artinian Local Complete Intersections

Explore Hilbert functions in Artinian local complete intersections, examining their properties and applications in commutative algebra and algebraic geometry.

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

Singularities via BCM Algebras

Explore singularities through BCM algebras, delving into advanced mathematical concepts with expert K. Tucker from the University of Illinois at Chicago.

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

Singularity Invariants in Positive Characteristic

Explore singularity invariants in positive characteristic mathematics, focusing on advanced concepts and their applications in algebraic geometry and related fields.

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

Vector Bundles and Tight Closure

Explore vector bundles and tight closure in algebraic geometry, delving into advanced mathematical concepts and their applications.

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

Singularities via BCM Algebras

Explore singularities through BCM algebras in this advanced mathematics lecture, delving into commutative algebra and algebraic geometry in prime characteristics.

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

Singularity Invariants in Positive Characteristic

Explore singularity invariants in positive characteristic, focusing on their applications in commutative algebra and algebraic geometry in prime characteristics.

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

F-Singularities — Applications of Characteristic P Methods to Singularity Theory

Explore applications of characteristic p methods in singularity theory, focusing on F-singularities and their role in commutative algebra and algebraic geometry.

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

Vector Bundles and Tight Closure

Explore vector bundles and tight closure in commutative algebra and algebraic geometry, focusing on prime characteristics and their applications in modern mathematics.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

P=W via H_2 - Part 2

Exploration of H_2 Lie algebra action on cohomology of stable twisted Higgs bundles moduli space, connecting tautological classes and Hecke operators to filtrations P and W.

• YouTube
• 1 hour 40 minutes
• Self-Paced
• Free Video

P=W via H_2

Exploration of Lie algebra H_2 and its action on cohomology of moduli spaces, connecting natural filtrations and tautological operations to unify mathematical concepts.

• YouTube
• 1 hour 41 minutes
• Self-Paced
• Free Video

Introduction to P=W and Mirror Symmetry

Explore topological mirror symmetry, character varieties, and the P=W conjecture in relation to Higgs bundle moduli spaces and Hitchin systems in this advanced mathematics lecture.

• YouTube
• 1 hour 40 minutes
• Self-Paced
• Free Video

Lipschitz Learning and the Infinity-Laplacian

Explore Lipschitz learning, infinity-harmonic functions, and their applications in Semi-Supervised Learning. Dive into the Lipschitz extension problem and AMLE, with insights on regularity and open challenges.

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

Geometric and Multilinear Problems in Analysis

Explore key geometric problems in analysis, their multilinear approaches, and interdisciplinary connections. Gain insights into harmonic, nonlinear, functional, and discrete analysis.

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

On the Geometry of Hyperkähler Manifolds

Explore hyperkähler manifolds, their properties, and examples. Delve into deformation types, moduli spaces of stable sheaves, and the birational geometry of K3-type manifolds with symplectic actions.

• YouTube
• 1 hour 43 minutes
• Self-Paced
• Free Video

Symbolic Powers of Ideals - Part 2

Explore advanced concepts in tight closure theory, focusing on symbolic powers of ideals and their applications in algebraic geometry and commutative algebra.

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