International Centre for Theoretical Sciences Courses

Introduction to Sphere Packing Problems by Abhinav Kumar

Explore sphere packing in geometry, covering its history, applications, and recent advances. Learn about lattices, codes, bounds, and energy minimization in various dimensions.

• YouTube
• 1 hour 39 minutes
• Self-Paced
• Free Video

Quadratic Forms and Hermite Constant, Reduction Theory by Radhika Ganapathy

Explores techniques for computing densest lattice packings, including quadratic forms, Hermite constants, and reduction theory. Covers perfect forms, eutactic lattices, and Voronoi's algorithm for listing perfect forms.

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

GAP Installation and Practical Introduction - Lecture 2

Practical introduction to GAP software for group theory computations, covering installation, basic commands, and exercises on symmetric groups, conjugacy classes, and finite group enumeration.

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

Statistical Physics and Statistical Inference - Lecture 2

Explore statistical physics and inference, covering Bayesian methods, error correction, spin glasses, and advanced algorithms like belief propagation. Gain insights into phase transitions and applications in machine learning.

• YouTube
• 1 hour 43 minutes
• Self-Paced
• Free Video

Artificial Intelligence: Success, Limits, Myths and Threats - Lecture 1

Explore AI's successes, limitations, and societal impact. Delve into machine learning, neural networks, and the future of AI. Gain insights on scientific intelligence and ethical considerations.

• YouTube
• 1 hour 48 minutes
• Self-Paced
• Free Video

Turbulence - Arrow of Time and Equilibrium-Nonequilibrium Behaviour

Explore turbulence, time's arrow, and equilibrium-nonequilibrium behavior. Delve into fundamental physics concepts, Kolmogorov's theory, energy transfer, and connections to kinetic theory and cosmology.

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

Structure of Group Rings and the Group of Units of Integral Group Rings - Lecture 1

Explores group rings, their structure, and units of integral group rings. Covers idempotents, invertible elements, augmentation mapping, and constructions of units including Bass and cyclotomic units.

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

Gamma Convergence - Lecture 2

Explore gamma convergence, minimization problems, and homogenization in this advanced mathematics lecture. Learn about coercivity, lower semicontinuity, and integral functions in the context of multi-scale analysis.

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

From Local to Global Holomorphic Peak Functions - Lecture 1

Explore holomorphic peak functions in complex analysis, from local to global perspectives. Gain insights into Cauchy-Riemann equations, L2-theory, and applications in higher-dimensional complex manifolds.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

The Monge-Ampère Equations and the Bergman Kernel - Lecture 1

Explore complex analysis in higher dimensions, focusing on Cauchy-Riemann equations, L2 theory, and applications to geometry. Learn about Bergman kernels and extension theorems in this advanced mathematics lecture.

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

The Beta to Omega Phase Transition - A Unique Example

Explore the unique beta to omega phase transition in metals, examining its mechanism, pre-transition effects, and recent high-resolution electron microscopy findings.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

Topology, Correlations and Superconductivity in Magic Angle Graphene - Lecture 2

Explore topology, correlations, and superconductivity in magic angle graphene. Dive into band structures, symmetries, and experimental findings. Gain insights on flat bands, Landau levels, and correlated electron paradigms.

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

Approximating Profile Maximum Likelihood Efficiently - New Bounds on the Bethe Permanent by Moses Charikar

Explore symmetric distribution properties and efficient estimation techniques, focusing on profile maximum likelihood and its connections to the Bethe permanent in statistical physics.

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

The Sensitivity Conjecture: A Proof from the Book and Connections to Physics

Explore the elegant proof of the Sensitivity Conjecture, its implications for theoretical computer science, and connections to physics concepts like Majorana fermions.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Entanglement and Topology in Quantum Solids - Lecture 1

Explore quantum entanglement in solids, topological phases, and their applications. Learn about Weyl semimetals, magic angle graphene, and surface topological order from a leading expert.

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