A Gradient Flow Approach to Kinetic Equations
Gradient flow approach to linear kinetic equations, exploring entropy dissipation inequality and large deviation principles. Discusses potential extensions to non-linear cases and connections to Markov chains.
A New Approach to Study Strong Advection Problems
Explores a novel weak convergence approach for analyzing multiscale advection-diffusion models in turbulent diffusion, introducing "convergence along mean flows" and addressing Lagrangian stretching effects on vanishing microscopic lengthscales.
Numerical Homogenization Based Fast Solver for Multiscale PDEs
Explore numerical homogenization for multiscale PDEs, covering Bayesian approaches, exponential decaying bases, and efficient solvers. Learn about applications in geophysics, materials science, and biology.
Nonlocal Theories for Free Crack Propagation in Brittle Materials
Explora la teoría y modelado de la fractura dinámica en sólidos frágiles, desde enfoques clásicos hasta modelos no locales multiescala, abordando desafíos computacionales y simulaciones peridinámica.
Panorama of Mathematics - Clusters, Loops and Trees in the Ising Model
Explore clusters, loops, and trees in the Ising model with Fields Medalist Stanislav Smirnov, covering topics from conformal field theory to discrete complex analysis and random cost representation.
Quantum Toric Geometry I
Explore quantum toric geometry, a generalization of classical toric geometry using quantum tori, allowing for irrational fans. Learn foundations and motivations behind this advanced mathematical concept.
An Introductory Mini Course into Quantum Toric Geometry Lecture I - Day 1
Explore quantum toric geometry, a non-commutative generalization of toric geometry. Learn about stacks, quantum tori, and quantum toric varieties, building on foundations of traditional toric geometry.
On the Spectral Problem of a Three Term Difference Operator
Explore the spectral problem of quantum mechanical operators in complex Planck's constant scenarios, focusing on toric Calabi-Yau threefolds and their implications.
Microbial Communities - From Modelling to Understanding Ecological Organization
Explore microbial communities' complexity, diversity, and ecological significance. Discover insights into early life, species coexistence, and community assembly through interdisciplinary research and advanced modeling techniques.
Lambda-Coalescents Arising in a Population With Dormancy
Explore Lambda-coalescents in populations with dormancy, examining genealogy and multiple ancestral line mergers through a three-season model of spring awakening, summer reproduction, and winter dormancy.
Dormancy Phenomena in Cancer Progression
Explore dormancy mechanisms in cancer progression, their role in therapy resistance and metastasis, and mathematical models used to study these phenomena. Gain insights into open questions and potential research directions.
The Cosmic Censorship Conjectures in General Relativity - Lecture 4
Explore cosmic censorship conjectures in general relativity, covering singularities, wave equations, and Penrose diagrams. Gain insights from expert Mihalis Dafermos on this advanced topic in theoretical physics.
Static Black Hole Uniqueness Theorems - Lecture 3
Explore asymptotic flatness, positive mass theorem, and scalar curvature in static black hole uniqueness theorems with expert Carla Cederbaum.
The Cosmic Censorship Conjectures in General Relativity - Lecture 3
Explore cosmic censorship conjectures in general relativity, focusing on global high publicity, null infinity, and the Hawking pass, with expert Mihalis Dafermos.
Static Black Hole Uniqueness Theorems - Lecture 2
Explore uniqueness theorems for static black holes, covering classical extensions, spacetime cross-sections, and proof techniques in this advanced mathematics lecture.
Introduction to the AdS-CFT Conjecture from a General Relativity Perspective - Lecture 3
Explore the AdS-CFT conjecture from a general relativity perspective, covering supergravity, universal sectors, and Hawking temperature in this advanced physics lecture.
The Cosmic Censorship Conjectures in General Relativity - Lecture 2
Explore strong and weak cosmic censorship conjectures in general relativity, examining singular behavior, spacelike singularities, and spherical symmetry through Penrose diagrams.
Black Hole Thermodynamics - Lecture 3
Explore black hole thermodynamics, focusing on stationary black holes, their laws, and stability, with insights from General Relativity and expert Robert Wald.
Some Geometric Properties of Spacetime - Lecture 3
Explore geometric properties of spacetime, including minimal hypersurfaces, stability, and boundary integrals. Gain insights into linear and nonlinear models in this advanced mathematics lecture.
Black Holes, Binary Systems, and Gravitational Waves - Comparable-Mass Binaries
Explore comparable-mass binary systems, post-Newtonian theory, and relaxed Einstein equations in the context of gravitational waves and black hole physics.
Some Geometric Properties of Spacetime - Lecture 2
Explore geometric properties of spacetime, including theorems on topology, dihedral angles, and scalar curvature, with insights on the positive mass theorem and Gauss-Bonnet theorem.