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.
A Mathematical Adventure in Immunology by Carmen Molina-Paris
Explore the immune system's complexity through mathematical modeling, examining cell interactions, disease prevention, and quantifying pathogen infectivity.
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.
How Often Does a Polynomial Take Squarefree Values? by Manjul Bhargava
Explore the frequency of squarefree values in polynomials with Manjul Bhargava. Delve into number theory concepts, heuristic explanations, and recent developments in this fascinating mathematical topic.
Quantum Field Theory as the Language of Physics by Nathan Seiberg
Explore quantum field theory's role as the universal language of physics, its applications, limitations, and potential reformulation in this insightful talk by Nathan Seiberg.
Eisenstein Cocycles and Values of L-Functions
Explore Eisenstein cocycles, equivariant cohomology, and their applications to L-functions. Gain insights into recent constructions and their connections to theta kernels and arithmetic groups.
Numerical Computation of Monodromy Action Over R
Explore numerical computation of monodromy action over real numbers, focusing on a new piece-wise approach for analyzing real solution sets, with applications in kinematics and mechanism calibration.
Chance and Chaos - How to Predict the Unpredictable by Jens Marklof
Explore chaos theory, unpredictability, and mathematical tools for analyzing chaotic systems. Discover applications in weather forecasting, statistical physics, and everyday phenomena like coin tosses and bread kneading.
The Tropical Limit of String Theory and Feynman Integrals
Explore the intersection of string theory, Feynman integrals, and tropical geometry. Discover how tropical limits provide insights into complex physical phenomena and algebraic structures.
Phylogenetic Algebraic Geometry
Explore phylogenetic algebraic geometry, its applications in species history reconstruction, and the use of algebraic and geometric perspectives to solve phylogenetic problems.