ICTP Mathematics Courses

Briancon-Skoda Theorems - Part 1

Explore the Briancon-Skoda Theorems in this graduate-level mathematics lecture, delving into tight closure of ideals and their applications in algebraic geometry.

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

Introduction to Hilbert-Kunz Multiplicity - Part 2

Explore advanced concepts in algebraic geometry, focusing on Hilbert-Kunz multiplicity theory and its applications in tight closure of ideals.

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

F-rational Rings and Rational Singularities - Part 2

Explore F-rational rings and rational singularities in depth, building on previous concepts and advancing understanding of tight closure theory in algebraic geometry.

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

F-rational Rings and Rational Singularities - Part 3

Explore F-rational rings and rational singularities in this advanced mathematics lecture, delving into tight closure theory and its applications in algebraic geometry.

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

F-Rational Rings and Rational Singularities - Part 1

Explore F-rational rings and rational singularities in this advanced mathematics lecture, delving into tight closure theory and its applications in algebraic geometry.

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

An Overview of Tight Closure of Ideals - Part 1

Explore the fundamental concepts and applications of tight closure theory in commutative algebra, focusing on ideals and their properties in ring theory.

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

Direct Summands of Regular Rings - Part 2

Explore advanced concepts in tight closure theory, focusing on direct summands of regular rings and their applications in algebraic geometry and commutative algebra.

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

Direct Summands of Regular Rings - Part 3

Explore advanced concepts in tight closure theory, focusing on direct summands of regular rings and their applications in algebraic geometry and commutative algebra.

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

Where Does Tight Closure Come From?

Explore the origins and fundamental concepts of tight closure in algebraic geometry, delving into its mathematical foundations and significance in ideal theory.

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

Classification of Link Floer and Khovanov Multicurve Invariants

Explore the classification of link Floer and Khovanov multicurve invariants in topology, presented by Claudius Zibrowius from the University of Regensburg.

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

Four-Manifolds with Boundary and Fundamental Group Z

Explore advanced concepts in geometry and topology, focusing on four-manifolds with boundary and fundamental group Z, presented by MIT expert Lisa Piccirillo.

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

Diffeomorphism Groups of 4-Manifolds and Embedding Spaces

Explore the intricate relationship between diffeomorphism groups of 4-manifolds and embedding spaces in this advanced topology lecture by Daniel Ruberman.

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

Toroidal 3-Manifolds, Curves, and Sutures

Explore toroidal 3-manifolds, curves, and sutures in this advanced mathematics lecture by Jake Rasmussen from the University of Cambridge, delving into cutting-edge research in geometry and topology.

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

Inscribed Squares and Linear Relation Avoiding Paths

Explore geometric concepts of inscribed squares and linear relation avoiding paths in this advanced mathematics lecture from Princeton University researcher Cole Hugelmeyer.

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

Algebraic Curves Defined by Singular Instanton Homology

Explore singular instanton homology's role in defining algebraic curves, delving into advanced mathematical concepts at the intersection of geometry and topology.

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