ICTP Mathematics Courses

The Variance of a General Class of Multiplicative Functions in Short Intervals

Explore the variance of multiplicative functions in short intervals, applying Fourier analysis and rational point counting to derive asymptotic estimates for k-free numbers and other functions.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Superlinear Structures and Conformal Geometry

Explore superlinear structures and conformal geometry, from historical roots to modern applications in physics and mathematics, with insights on representation theory and potential links to the standard model.

• YouTube
• 1 hour 27 minutes
• Self-Paced
• Free Video

On the Resurgence and Asymptotic Resurgence of Homogeneous Ideals

Explore the mathematical concepts of resurgence and asymptotic resurgence in homogeneous ideals, delving into advanced algebraic geometry and commutative algebra theories.

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

Nash Blowups in Prime Characteristic

Explore Nash blowups in prime characteristic, delving into advanced algebraic geometry concepts with insights from speaker L. Núñez-Betancourt of CIMAT, Mexico.

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

General Hyperplane Section of Log Canonical Threefolds in Positive Characteristic

Explore log canonical threefolds in positive characteristic, focusing on general hyperplane sections. Gain insights into advanced algebraic geometry concepts and their applications.

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

Frobenius Maps on the Rings of Invariants

Explore Frobenius maps and their applications to invariant theory, focusing on algebraic structures and group actions in characteristic p.

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

Normal and Tight Hilbert Polynomials

Explore normal and tight Hilbert polynomials with P.H. QUY from FPT University, Vietnam. Gain insights into this specialized mathematical topic through an expert presentation.

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

Residual Intersections

Explore residual intersections in mathematics with expert M. CHARDIN, delving into advanced concepts and their applications in algebraic geometry.

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

The Mathematical Contributions of Craig Huneke - A Sampler

Explore the significant mathematical contributions of Craig Huneke, focusing on his influential work in commutative algebra and algebraic geometry.

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

Geometry of the Tight Closure Operation

Explore the geometric aspects of tight closure operations in mathematics, delving into advanced algebraic concepts and their applications.

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

Singularities and Hilbert Functions

Explore the mathematical concepts of singularities and Hilbert functions, delving into their properties, applications, and interconnections in algebraic geometry and commutative algebra.

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

On a Generalization of Two Results of Happel to Commutative Rings

Explore generalizations of Happel's results in commutative ring theory, expanding mathematical understanding and applications in algebraic structures.

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

Finite Presentation for the Tame Fundamental Group in Positive Characteristic

Explore the tame fundamental group in positive characteristic, focusing on finite presentations and their implications for algebraic geometry and number theory.

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

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