ICTP Mathematics Courses

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Blowup Algebras of Determinantal Ideals in Prime Characteristic

Explore determinantal ideals in prime characteristic, focusing on blowup algebras and their properties. Gain insights into advanced algebraic concepts and techniques.

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

Analytic Spread of Filtrations

Explore the mathematical concept of analytic spread in filtrations, delving into its properties and applications in algebraic geometry and commutative algebra.

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

Singularities via BCM Algebras

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

• YouTube
• 1 hour 12 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
• 52 minutes
• Self-Paced
• Free Video

Basic Notions Seminar on Fourier Optimization and Number Theory

Explore the intersection of harmonic analysis and analytic number theory, including problems related to the Riemann hypothesis, in this advanced mathematics seminar.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

The V-Number of Monomial Ideals

Explore the concept of v-Number in monomial ideals, delving into its mathematical properties and applications in algebraic geometry.

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

Bounds for the Reduction Number of Primary Ideals in Dimension Three

Explore bounds for reduction numbers of primary ideals in 3D, presented by S. Kumari from IIT Patna, offering insights into advanced algebraic geometry concepts.

• YouTube
• 22 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 implications for algebraic geometry and commutative algebra.

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

Vector Bundles and Tight Closure

Explore vector bundles and tight closure in algebraic geometry, delving into their properties, applications, and connections to other mathematical concepts.

• YouTube
• 50 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

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 implications in algebraic geometry and commutative algebra.

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