The Rogers-Ramanujan Identities and the Icosahedron - Lecture 2
Explore connections between Rogers-Ramanujan identities and icosahedron, linking number theory, modular forms, combinatorics, and conformal field theory in an accessible survey for mathematicians.
The Rogers-Ramanujan Identities and the Icosahedron - Lecture 1
Explore the deep connections between the Rogers-Ramanujan identities and the icosahedron, spanning number theory, modular forms, combinatorics, and more in this accessible mathematical lecture.
Invariants of Manifolds from 6 Dimensions
Explore advanced mathematical concepts in gauge theories and differential invariants, focusing on invariants of manifolds from 6 dimensions and their applications in theoretical physics.
Asymptotics of the Averaged Characteristic Polynomial for Ginibre Ensemble
Explore asymptotics of averaged characteristic polynomials in Ginibre Ensemble, covering Coulomb gas, Szego curves, orthogonal polynomials, and partition functions in random matrix theory.
Entropy Method for Hypocoercive BGK and Fokker-Planck Equations
Explore entropy methods for hypocoercive equations, focusing on BGK and Fokker-Planck models. Learn about decay rates, auxiliary functionals, and regularization techniques in non-symmetric systems.
Phase-Field Models for Motion by Mean Curvature - Lecture 2
Explore phase-field models for motion by mean curvature, covering topics like skew symmetry, levelsets, distance functions, and classical statements with expert Panagiotis Souganidis.
Spectral Approximation of Transfer Operators
Explore spectral approximation of transfer operators using Galerkin methods and Lagrange-Chebyshev interpolation, with applications in number theory and quantum chaos.
Manfred Denker: Toral Automorphisms Driven by Continued Fractions
Explore toral automorphisms driven by continued fractions, discussing Poisson limits, homoclinic groups, and Steiner's theorem in dynamical systems and number theory.
Regularity of Free Boundaries in Obstacle Problems - Lecture III
Explore free boundary problems in PDE, focusing on regularity of solutions and interfaces. Learn about Stefan and obstacle problems, key results, and current research challenges.
Regularity of Free Boundaries in Obstacle Problems Lecture I
Explore regularity of free boundaries in obstacle problems, covering key concepts, proofs, and current research in this mathematical field of PDE and Geometric Measure Theory.
The Restriction Problem and the Polynomial Method - Lecture I
Explore Stein's restriction conjecture, the Kakeya conjecture, and the polynomial method in harmonic analysis. Learn about wave packet decomposition and its applications in studying hypersurface-supported functions.
Erik Broman- Higher Dimensional Stick Percolation
Explore higher dimensional stick percolation, its applications in physics and chemistry, and the scaling of critical parameters as stick length increases in arbitrary dimensions.
Percolation on Hyperbolic Poisson-Voronoi Tessellations
Explore percolation on hyperbolic Poisson-Voronoi tessellations, resolving conjectures about critical probability behavior and its dependence on Poisson process intensity.
Virtual Invariants of Moduli Spaces of Sheaves on Surfaces and Vafa-Witten Invariants I
Explore virtual invariants of moduli spaces, Vafa-Witten invariants, and related mathematical concepts in this advanced seminar on algebraic geometry and theoretical physics.
Random Matrix Theory and Its Applications - Lecture 3
Explore advanced random matrix theory concepts, including complex quaternionic matrices, rotationally invariant ensembles, and applications to disordered systems in this in-depth lecture.
Random Matrix Theory and Its Applications - Lecture 5
Explore advanced random matrix theory concepts, including Gaussian ensembles, coarse-graining techniques, and the Wigner semi-circular law in this comprehensive lecture.
Random Matrix Theory and its Applications - Lecture 2
Explore advanced concepts in random matrix theory, including linear algebra basics, operators, transformations, eigenvectors, and various matrix ensembles, with applications in statistical physics.
Dynamical Phase Transitions in Markov Processes by Hugo Touchette
Explore dynamical phase transitions in Markov processes, contrasting with equilibrium transitions and examining a Brownian motion model showcasing localization-delocalization phenomena.
Truth and the Scientific Method by David Gross
Explore the nature of scientific truth, the scientific method's strengths and limitations, and its role in society. Gain insights into reductionism and the challenges facing modern science.
The Science of the Man from the 9 Dimensions
Explore the universe's origins, from the Big Bang to cosmic inflation, and delve into superstring theory's quest for a unified understanding of physics across nine dimensions.
Spacetime, Quantum Mechanics and Positive Geometry by Nima Arkani Hamed
Explore the intersection of spacetime, quantum mechanics, and positive geometry, delving into scattering amplitudes, the mystery of time, and emergent phenomena in theoretical physics.