ICTP Mathematics Courses

Reduced Type in One Dimensional Analytic Algebras

Explore the concept of reduced type in one-dimensional analytic algebras, delving into mathematical intricacies and theoretical foundations.

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

50 Years of Mathematics - The Work of Melvin Hochster

Explore the profound impact of Melvin Hochster's contributions to mathematics over five decades, highlighting key breakthroughs and their significance in the field.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Symbolic Rees Algebras and Set-Theoretic Complete Intersections

Explore symbolic Rees algebras and set-theoretic complete intersections in commutative algebra and algebraic geometry, focusing on prime characteristics.

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

Hilbert-Kunz Density Function and Its Applications to Some Hilbert-Kunz Multiplicity Conjectures

Explore the Hilbert-Kunz density function and its applications to multiplicity conjectures in this advanced mathematics lecture by V. Trivedi from the Tata Institute.

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

Algebraic and Homological Properties of Polyominoes

Explore algebraic and homological aspects of polyominoes, uncovering mathematical properties and structures within these geometric shapes.

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

Gorenstein Property of Normalized Tangent Cones of Integrally Closed Ideals of 2-Dimensional Normal

Explore the Gorenstein property in normalized tangent cones of integrally closed ideals within 2-dimensional normal local rings, presented by K. Watanabe from Nihon University, Japan.

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

Lattices in Low-Dimensional Topology

Explore the fascinating intersection of lattice theory and low-dimensional topology, delving into fundamental concepts and their applications in geometric and topological structures.

• YouTube
• 1 hour 32 minutes
• On-Demand
• Free Video

Families of Dirac Operators and Applications

Explore advanced concepts in geometry and topology, focusing on families of Dirac operators and their applications in mathematical physics and differential geometry.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Geometry and Algebra of Pseudoholomorphic Curves

Explore the intricate world of pseudoholomorphic curves, delving into their geometric properties and algebraic structures. Gain insights from Princeton University expert John Pardon in this advanced mathematics lecture.

• YouTube
• 1 hour 34 minutes
• On-Demand
• Free Video

Families of Dirac Operators and Applications

Explore Dirac operators and their applications in geometry and topology, focusing on families and their mathematical significance in advanced theoretical frameworks.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

Heegaard Floer Homology and Topology in Dimensions 3.5 - 1

Explore Heegaard Floer homology and its applications in low-dimensional topology, focusing on dimensions 3.5 to 1 in this advanced mathematics lecture.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video

More Deformations of the Cohomology Ring of the Moduli Space of Representations

Explore deformations of cohomology rings in representation spaces of Riemann surfaces, examining algebraic, geometric, and physical perspectives on this rich mathematical topic.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Theory of Weights in Rooted K-Trees

Explore the mathematical concept of weights in rooted k-trees, delving into their properties, applications, and theoretical foundations.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Computation of the Vertical Vafa-Witten Invariants II

Explore advanced algebraic geometry concepts, focusing on vertical Vafa-Witten invariants computation using localization on Hilbert schemes of points for toric surfaces.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Computation of Vertical Vafa-Witten Invariants

Explore vertical Vafa-Witten invariants, nested Hilbert schemes, and Laarakker's structure theorem. Learn to compute generating functions using toric surfaces and localization techniques.

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