ICTP Mathematics Courses

Existence and Regularity Theories of Brakke Flow

Explore existence and regularity theories of Brakke flow, covering initial configuration, linear and alpha regularity, dispersed irregularity, and the Monotonicity Formula for minimal surfaces.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

Existence and Regularity Theories of Brakke Flow

Explore theories of Brakke flow, including existence and regularity, with expert Yoshihiro Tonegawa. Delve into key concepts like geometric metatheory, approximate tangent space, and multiplicity functions.

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

Introduction to Quantum Computation - Antonello Scardicchio

Learn the basics of quantum computation, its potential for problem-solving, and current technological advancements in this field. Explore algorithms, complexity classes, and real-world applications.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

Quantum Fields, Strings, and Black Holes: A Primer for Non Experts, Part I - Atish Dabholkar

Explore quantum black holes, string theory, and their connections to number theory and geometry. Gain insights into fundamental physics concepts, suitable for mathematicians and physics students.

• YouTube
• 1 hour 58 minutes
• On-Demand
• Free Video

Lorentzian Geometry - T. Drumm

Explore Lorentzian geometry, covering basic definitions, hyperbolic spaces, isometries, and advanced concepts like Margulis space-times and crooked planes.

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

The Liouville Current and Complex Structures for Hitchin Representations - F. Labourie

Explore Hitchin representations, Liouville currents, and complex structures in this advanced mathematics lecture, covering theorems, symplectic manifolds, and modular space vibrations.

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

Veech Groups, Cutting Sequences, and Penetration Spectra - C. Ulcigrai

Explore Veech groups, cutting sequences, and penetration spectra in translation surfaces. Learn about affine automorphisms, Sturmian sequences, and Teichmüller curves in this advanced mathematics lecture.

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

Slope Detection in 3-Manifolds

Explore key concepts in 3-manifold topology, including slope detection, Lagrangian theory, and foliations. Learn about conjectures, theorems, and algorithms in this advanced mathematical field.

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

Brownian Motion, Evolving Geometries and Entropy Formulas - A. Thalmaier

Explore Brownian motion, stochastic processes, and related mathematical concepts in this comprehensive lecture on evolving geometries and entropy formulas.

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

Mirror Symmetry for Fano Orbifolds - Lecture 01

Explore mirror symmetry for Fano orbifolds, covering key concepts like differential operators and torque variety in this advanced mathematics lecture.

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

Applications of Homogeneous Dynamics - Lecture 1

Explore homogeneous dynamics and its applications in number theory and statistical mechanics, covering key concepts, theorems, and real-world implications.

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

Building Thermodynamics for Non-Uniformly Hyperbolic Maps - Yakov Pesin

Explore advanced concepts in dynamical systems, focusing on non-uniformly hyperbolic maps, symbolic models, and equilibrium measures in thermodynamics.

• YouTube
• 1 hour 3 minutes
• On-Demand
• 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
• On-Demand
• Free Video

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
• On-Demand
• 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
• On-Demand
• Free Video