ICTP Mathematics Courses

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

Knotted 3-Balls in S^4 and Knotted 3-Spheres in S^1 Times S^3

Explore advanced topological concepts: knotted 3-balls in S^4 and knotted 3-spheres in S^1×S^3. Delve into cutting-edge research in geometry and topology with Princeton University expert David Gabai.

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

The Degree of a Map and Its Lipschitz Constant

Explore the relationship between a map's degree and its Lipschitz constant in this advanced topology lecture, delving into fundamental concepts and recent research developments.

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

Satellite Operations That Are Not Homomorphisms

Explore non-homomorphic satellite operations in knot theory, examining their properties and implications for geometric topology research.

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

Computations of Vafa-Witten Invariants in Algebraic Geometry

Explore advanced algebraic geometry concepts, focusing on Vafa-Witten invariants and their computational methods in modern mathematical research.

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

A Representability Theorem for Moduli Spaces of Pseudo-Holomorphic Curves

Explore a theorem on representability for moduli spaces of pseudo-holomorphic curves, delving into advanced concepts in geometry and topology.

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

Horizontal Handlebody Decompositions

Explore horizontal handlebody decompositions in topology with Paolo Lisca. Gain insights into cutting-edge research in geometry and its applications.

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

Monopole Floer Homology and Invariant Theta-Characteristics

Explore advanced concepts in geometry and topology, focusing on monopole Floer homology and invariant theta-characteristics in this Princeton University lecture.

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

Skein Lasagna Modules

Explore advanced concepts in geometry and topology with Stanford's Ciprian Manolescu, focusing on Skein Lasagna modules and their applications in mathematical research.

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