Mathematics Courses and Certifications

ICTP Mathematics

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
• 54 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Symbolic Powers of Ideals - Part 2

Explore advanced concepts in tight closure theory, focusing on symbolic powers of ideals and their applications in algebraic geometry and commutative algebra.

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

ICTP Mathematics

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
• Self-Paced
• Free Video

ICTP Mathematics

Geometry and Algebra of Pseudoholomorphic Curves

Explore advanced concepts in geometry and topology, focusing on pseudoholomorphic curves and their applications in mathematical research and analysis.

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

ICTP Mathematics

Standard and Less Standard Asymptotic Methods - Lecture 12

Explore advanced techniques for evaluating infinite sums and recognizing asymptotic patterns in numerical sequences, with practical examples and applications in various mathematical fields.

• YouTube
• 1 hour 29 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Standard and Less Standard Asymptotic Methods - Lecture 11

Explore advanced techniques for evaluating infinite sums and recognizing asymptotic patterns in numerical sequences, with practical examples and applications in mathematical analysis.

• YouTube
• 1 hour 24 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Standard and Less Standard Asymptotic Methods - Lecture 10

Explore advanced techniques for evaluating infinite sums and recognizing asymptotic patterns in numerical sequences, with applications to complex mathematical problems.

• YouTube
• 1 hour 32 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Standard and Less Standard Asymptotic Methods - Lecture 7

Explore advanced techniques for evaluating infinite sums and recognizing asymptotic patterns in numerical sequences, with practical examples and applications in various mathematical fields.

• YouTube
• 1 hour 33 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Dynamics of Smooth Surface Diffeomorphisms: Strong Positive Recurrence - ICTP 2021

Explore advanced concepts in smooth surface diffeomorphisms, focusing on strong positive recurrence and its implications for dynamical systems theory.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Dynamics of Smooth Surface Diffeomorphisms: Entropy Continuity of Exponents - ICTP 2021

Explore entropy continuity and exponents in smooth surface diffeomorphisms with Jerome Buzzi, delving into advanced mathematical concepts and their applications in dynamical systems.

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

ICTP Mathematics

Probability Invariant Measure, Dynamical Partition and Hitting Times of Circle Map with Singularities

Explore circle dynamics and recent findings in circle maps with break or critical points, focusing on probability invariant measures, dynamical partitions, and hitting times.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Hyperkähler Manifolds, an Introduction I

Explore the fundamental concepts and properties of hyperkähler manifolds in this introductory lecture by Elham Izadi, delving into complex geometry and algebraic topology.

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

ICTP Mathematics

Generalities About Abelian Varieties - Part 2

Explore advanced concepts of abelian varieties, including complex tori, polarizations, and isogenies, building on fundamental algebraic geometry principles.

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

ICTP Mathematics

Generalities About Abelian Varieties - Part 1

Explore fundamental concepts and properties of abelian varieties in algebraic geometry, laying the groundwork for advanced study in this mathematical field.

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

ICTP Mathematics

Sampling, Tilings, and Quasicrystals

Explore connections between sampling theorem, tiling properties, and model sets. Discover links to Fuglede's theorem and quasicrystals, bridging mathematics and materials science.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video