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.
Maxim Kirsebom - On a Limiting Distribution for Maximal Cusp Excursions of the Unipotent Flow
Exploring the unipotent flow on modular surfaces, focusing on cusp excursions and their probabilistic behavior using geometry of numbers and extreme value statistics.
Michael Baake - A Cocycle Approach to the Fourier Transform of Rauzy Fractals
Explore Fourier transforms of Rauzy fractals and their role in analyzing spectra of Pisot inflation tilings, with applications to diffraction theory and dynamical systems.
Manfred Einsiedler- Effective Homogenous Dynamics 1
Explore homogeneous dynamics, focusing on transformations, orbits, and effective statements in topology and number theory.
Sylvie Paycha: Re-Expansion Maps as Direct Connections
Explore re-expansion maps in groupoids, their connection to regularity structures, and interpretation as "gaugeoid fields" in gauge groupoids. Generalization to jet bundles in polynomial regularity structures.
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.
A Stationary Set Method for Estimating Oscillatory Integrals
Explore a stationary set method for estimating oscillatory integrals, with applications in number theory and Fourier analysis. Learn about o-minimal structures and geometric interpretations of upper bounds.
On Some Tight Convexity Inequalities for Symmetric Convex Sets
Explores tight convexity inequalities for symmetric convex sets, focusing on Gaussian measure, isoperimetric problems, and Dirichlet-Poincare inequality. Discusses progress using L2 methods and energy minimization.
Emanuel Milman: Functional Inequalities on Sub-Riemannian Manifolds via QCD
Explores functional inequalities on sub-Riemannian manifolds using QCD, offering novel quantitative estimates for Poincaré and log-Sobolev inequalities with applications to Heisenberg groups.
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.
Omer Bobrowski - Random Simplicial Complexes
Explore higher-dimensional generalizations of random graphs, focusing on random d-complexes and Cech complexes. Learn about connectivity, cycle formation, and giant components in these structures.
Omer Bobrowski - Random Simplicial Complexes, Lecture I
Explore random simplicial complexes, their applications in data analysis, and key phenomena like connectivity and cycle formation. Includes introduction to algebraic topology and homology theory.
On Yuansi Chen's Work on the KLS Conjecture I
Explore the KLS conjecture in high-dimensional geometry, its implications for Bourgain's slicing problem, and recent progress using Eldan's Stochastic Localization technique.
Introduction to Fukaya Categories - James Pascaleff
Explore symplectic geometry fundamentals for Fukaya categories, covering symplectic manifolds, Lagrangian submanifolds, exactness conditions, and more in this comprehensive lecture.
Curvature of the Determinant Line Bundle for Noncommutative Tori
Explore differential geometry of curved noncommutative tori, including spectral invariants and curvature of determinant line bundle for Dirac operators on noncommutative two tori.
Mirror Symmetry and Big Algebras
Explore mirror symmetry in Hitchin systems, Kirillov algebras, and equivariant cohomology. Delve into conjectures on non-very stable flows and big commutative subalgebras in affine Schubert varieties.
On the Cohomology of Quot Schemes Parametrizing Torsion Quotients on a Smooth Curve
Explore cohomology of Quot schemes on smooth curves, focusing on torsion quotients. Delve into additive basis, natural maps, and geometric interpretations with expert insights.
The Discrete Charm of Geometry by Alexander Bobenko
Explore the fascinating world of discrete geometry and its applications in architecture, computer graphics, and physics. Discover structure-preserving discretizations through simple examples and stunning visuals.
Introduction to Higgs Bundles - Lecture 1
Explore complex geometric concepts in Higgs bundles, including Riemann surfaces, theorems, and constructions. Gain insights into advanced mathematical topics through examples, exercises, and proofs.