International Centre for Theoretical Sciences Courses

Additive Number Theory - Extremal Problems and the Combinatorics of Sumsets by M. Nathanson

Explore extremal problems and combinatorics of sumsets in additive number theory, covering density, lower bounds, Cauchy-Davenport theorem, and Erdos-Turan conjecture.

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

The Selberg Sieve and Large Sieve - Lecture 1

Explore the Selberg Sieve and Large Sieve in number theory, covering linear algebra, duality principles, and applications like the Bombieri-Vinogradov theorem in this advanced mathematics lecture.

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

The Selberg Sieve - Lecture 1

Explore the Selberg sieve method in number theory, covering heuristics, probability, and applications to twin primes. Learn about sieve techniques for detecting primes in sequences.

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

Light and Beyond - Lecture 2: Optical Phenomena and Wave Propagation

Explore advanced concepts in optics, from electromagnetic waves to quantum physics, through lectures, demonstrations, and simulations. Gain insights into optical phenomena in nature and technology.

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

Light and Beyond - Lecture 1: Introduction to Optics and Geometrical Principles

Explore light as electromagnetic waves, optical phenomena, and underlying concepts through math, experiments, and simulations. Covers geometrical optics, least action principle, and introduces quantum physics.

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

Physics and Astrophysics of Gamma-Ray Bursts - Part 1

Comprehensive exploration of gamma-ray bursts, covering discovery, observational facts, physics, and astrophysical implications. Delves into prompt emission, afterglows, and theoretical models, providing insights for researchers and students.

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

Numerical Relativity - Mathematical Formulation by Harald Pfeiffer

Explore mathematical formulation of numerical relativity, focusing on simulating binary black hole coalescence, gravitational waves, and advanced computational techniques in astrophysics.

• YouTube
• 2 hours 11 minutes
• Self-Paced
• Free Video

Basic Lower Bounds and Kneser's Theorem by David Grynkiewicz

Explore set addition, basic lower bounds, and Kneser's Theorem in additive combinatorics. Learn key proofs, including Cauchy-Davenport theorem, and applications to field extensions.

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

Mirror Symmetry for Character Varieties and Field Theory by Sergey Galkin

Explore mirror symmetry for character varieties, using threespace mirrors to construct SU(2) character variety mirrors on Riemann surfaces, with applications in topological field theory and random walks.

• YouTube
• 3 hours 12 minutes
• Self-Paced
• Free Video

Non-Equilibrium Dynamics of Inhomogeneous Fluids by Sutapa Roy

Explore non-equilibrium dynamics of inhomogeneous fluids, focusing on colloidal particles in binary solvents. Learn about phase transitions, critical points, and phenomena like coalescence, nucleation, and aging.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Surface Critical Dynamics and Casimir Forces in a Binary Fluid by Sutapa Roy

Explore critical dynamics and Casimir forces in binary fluids through molecular dynamics simulations, focusing on surface properties, scaling behavior, and correlation functions in confined fluid systems.

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

Why It Is -Still- Difficult to Be a Woman in Science by Shobhana Narasimhan

Exploring gender imbalance in science: challenges, biases, and success stories of women scientists. Discusses historical context, current statistics, societal pressures, and strategies for promoting equality in scientific fields.

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

Exotic Patterns in Faraday Waves

Explore exotic patterns in Faraday waves through advanced numerical simulations and theoretical analysis. Discover fascinating phenomena like quasipatterns, superlattices, and dynamic pattern evolution in vibrated fluid layers.

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

The Route to Turbulence by Dwight Barkley

Explore the fascinating journey to understanding turbulence in shear flows, from historical observations to modern insights on phase transitions, intermittency, and universal scaling laws.

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

Representations of Fuchsian Groups, Parahoric Group Schemes by Vikraman Balaji

Explore advanced mathematical concepts including Fuchsian groups, parahoric schemes, and root systems. Delve into complex algebraic structures and their representations in this in-depth lecture on geometric group theory.

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