Mathematical Physics Courses and Certifications

The Royal Institution

Black Holes, Symmetries and Impossible Triangles - A Conversation with Roger Penrose

Explore black holes, symmetries, and impossible triangles with Nobel Laureate Roger Penrose in this engaging conversation covering his groundbreaking work in mathematical physics and cosmology.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

ICTP Mathematics

Regularity of the Boltzmann Equation in Bounded Domains - II

Explore advanced mathematical concepts in nonlocal PDEs, focusing on the Boltzmann equation's regularity in bounded domains. Gain insights from expert Tonon, D. in this in-depth lecture.

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

ICTP Mathematics

On the Zakharov-L'vov Stochastic Model for Wave Turbulence

Explore the Zakharov-L'vov stochastic model for wave turbulence, examining its mathematical foundations and applications in understanding complex wave systems.

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

ICTP Mathematics

Families of Dirac Operators and Applications

Explore Dirac operators and their applications in geometry and topology, focusing on families and their mathematical significance in advanced theoretical frameworks.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

ICTP Mathematics

P=W via H_2 - Part 2

Exploration of H_2 Lie algebra action on cohomology of stable twisted Higgs bundles moduli space, connecting tautological classes and Hecke operators to filtrations P and W.

• YouTube
• 1 hour 40 minutes
• On-Demand
• Free Video

ICTP Mathematics

Introduction to P=W and Mirror Symmetry

Explore topological mirror symmetry, character varieties, and the P=W conjecture in relation to Higgs bundle moduli spaces and Hitchin systems in this advanced mathematics lecture.

• YouTube
• 1 hour 40 minutes
• On-Demand
• Free Video

IMSA

Almost Schur Lemma and Positivity Conditions in Quaternionic Contact Geometry

Explore quaternionic contact geometry, focusing on the Almost Schur Lemma and its implications for estimating qc scalar curvature under specific conditions.

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

Hausdorff Center for Mathematics

Swarming Models with Local Alignment Effects

Explores phase transitions in kinetic equations for swarming models, focusing on noise-driven transitions and their applications in mathematical physics and interacting particle systems.

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

Hausdorff Center for Mathematics

6j-Symbols for SL(2,C) Group and Feynman Diagrams

Explore 6j-symbols for SL(2,C) group using Feynman diagrams, deriving Racah coefficients for infinite-dimensional unitary principal series representations and expressing results as complex integrals or Mellin-Barnes type sums.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Kavli Institute for Theoretical Physics

The Power of Random Quantum Circuits - Bill Fefferman

Explores the computational power of random quantum circuits, discussing classical intractability, simulation algorithms, and the quantum supremacy conjecture. Examines average-case hardness and noise effects in quantum systems.

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

World Science Festival

Noether's Amazing Theorem - Symmetry and Conservation

Explore Emmy Noether's groundbreaking theorem linking symmetry and conservation in physics, explained by Brian Greene through accessible mathematics and engaging storytelling.

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

International Centre for Theoretical Sciences

A Lieb-Schultz-Mattis Type Theorem Without Continuous Symmetry by Hal Tasaki

Explores a Lieb-Schultz-Mattis type theorem for quantum spin chains without continuous symmetry, covering proof techniques, matrix product states, and operator algebraic approaches in infinite quantum systems.

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

Hausdorff Center for Mathematics

Martin Hairer: Stochastic Quantisation of Non-Abelian Yang-Mills

Explore stochastic quantisation of Yang-Mills theory, covering key concepts like canonical sections, connections, and covariant derivatives in non-Abelian gauge theories.

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

ICTP Mathematics

Soliton Quantization and Random Partitions

Explore soliton quantization and random partitions in Benjamin Ono equations, focusing on one-phase solutions, simulations, and Hamiltonian structures in dispersive wave theory.

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

ICTP Mathematics

Collisions in Plasmas - The Landau Equation - Part IV

Explore plasma collisions through the Landau equation, covering entropy structure, factorization theorems, and computational aspects of this advanced mathematical topic.

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