An Introduction to Super Critical Singularities - Lecture 1: Energy Super Critical Singularity Formation
Explore energy super critical singularity formation in non-linear PDEs, focusing on recent discoveries in defocusing problems and their connection to fluid mechanics.
Global Solutions to Quadratic Systems of Stochastic Reaction-Diffusion
Explorez les solutions globales des systèmes quadratiques de réaction-diffusion stochastique en dimension deux, avec un accent sur les perturbations à quatre espèces.
Particle Approximation of the Doubly Parabolic Keller-Segel Equation in the Plane
Explore particle approximation of the parabolic-parabolic Keller-Segel system in the plane, focusing on stochastic particle systems, tightness, and weak solutions for small sensitivity parameters.
Random Models on Regularity-Integrability Structures
Explore a simplified proof of the BPHZ theorem using extended regularity structures with integrability exponents, advancing the study of singular stochastic partial differential equations.
Outliers of Perturbations of Banded Toeplitz Matrices
Explore outlier eigenvalues of perturbed banded Toeplitz matrices, focusing on their behavior in regions outside the limiting spectral distribution's support as matrix size increases.
Zeros of Random Power Series with Stationary Gaussian Coefficients
Explore zeros of random power series with stationary Gaussian coefficients, comparing to i.i.d. case and analyzing expected zero count in disks as radius approaches convergence.
Mathematical Foundation of Various MCMC Methods
Explore advanced MCMC methods for combinatorial optimization, including multi-spin flip techniques. Compare mathematical and numerical results to evaluate efficiency in different contexts.
Formalization of Infinity Category Theory
Explore ∞-category theory's formalization, unifying mathematics, computer science, and physics. Learn synthetic reasoning and the Yoneda Lemma in this advanced mathematical seminar.
Logarithmic Sobolev Inequalities on Homogeneous Spaces
Explore logarithmic Sobolev inequalities on homogeneous spaces with sub-Riemannian structures. Discover how constants depend on Lie group geometry and remain independent of dimension in certain cases.
Quantum Periods for Complements
Explore quantum periods for complements, focusing on polynomial-defined spectral curves and quantization of polynomial algebras. Gain insights into cohomological descriptions of WKB series.
Topological Recursion: A Recursive Way of Counting Surfaces
Explore topological recursion for enumerating surfaces in combinatorics, geometry, and physics. Learn how this universal method links to integrable systems and random matrices.
Waists Measured via Urysohn Width in Riemannian Manifolds
Explore Urysohn width's role in measuring approximate dimension of Riemannian manifolds and its connection to positive scalar curvature, with insights on slicing manifolds.
Inequalities Defining Polyhedral Realizations of Affine Types and Extended Young Diagrams
Explore crystal bases in Lie algebra representation theory, focusing on polyhedral realizations and explicit inequalities for classical affine types using extended Young diagrams.
Combinatorics and Quantum Invariant Differential Operators on Reflection Equation Algebras
Explore quantum analogs of symmetric functions and differential operators in Reflection Equation Algebras, examining their properties and combinatorial applications.
Spectra of Laplace and Dirac Operators on Noncompact Manifolds
Explore spectra of Laplace and Dirac operators on complete manifolds, including types of spectra, results for special behaviors at infinity, and effects of additional potentials.
Another Aspect of Gromov's Conjectures on Scalar Curvature
Explore Gromov's scalar curvature conjectures through general relativity, examining partial solutions via the positive mass theorem.
Positive Mass Theorem for Asymptotically Flat Manifolds with Isolated Conical Singularities
Explore recent advancements in positive mass theorem for asymptotically flat manifolds with isolated conical singularities, covering spin and non-spin settings, analysis techniques, and Geroch-type results.
Beauty of Life Seen Through Keyhole of Mathematics - Lecture 3
Explore the intersection of mathematics and biology, from molecular structures to ecological impact, with insights on Life's nature and future bioengineering applications.
Stable Homotopy Groups, Higher Algebra, and the Telescope Conjecture
Explore stable homotopy groups, spectra, and their applications in topology and geometry. Gain insights into fundamental concepts shaping modern algebraic topology and related fields.
Global Effects of Positive Scalar Curvature in Geometry
Explorez les effets globaux de la courbure scalaire positive, y compris le problème de remplissage de Gromov et les théorèmes de type Llarull sur les variétés complètes.
Index Theory and Applications to Scalar Curvature
Explore index theorems for compact manifolds with boundary and their applications to scalar curvature geometry, focusing on Dirac operators and boundary value problems.