Existence and Regularity Theories of Brakke Flow
Explore theories of Brakke flow, including existence and regularity, with expert Yoshihiro Tonegawa. Delve into key concepts like geometric metatheory, approximate tangent space, and multiplicity functions.
Lorentzian Geometry - T. Drumm
Explore Lorentzian geometry, covering basic definitions, hyperbolic spaces, isometries, and advanced concepts like Margulis space-times and crooked planes.
Slope Detection in 3-Manifolds
Explore key concepts in 3-manifold topology, including slope detection, Lagrangian theory, and foliations. Learn about conjectures, theorems, and algorithms in this advanced mathematical field.
Mirror Symmetry for Fano Orbifolds - Lecture 01
Explore mirror symmetry for Fano orbifolds, covering key concepts like differential operators and torque variety in this advanced mathematics lecture.
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.
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.
Taylor McAdam- Almost-Prime Times in Horospherical Flows
Explore effective results in horospherical flows, their applications to number theory, and connections to Sarnak's Mobius disjointness conjecture in this advanced mathematics lecture.
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.
The Dynamical Systems Approach to Spatially Homogenous Einstein-Vlasov Cosmology
Explore spatially homogenous Einstein-Vlasov cosmology using dynamical systems analysis. Investigate asymptotic solutions near singularities and expanding futures, focusing on Kantowski-Sachs models with Vlasov matter.
Uncertainty Quantification for Kinetic Equations I
Overview of uncertainty quantification for kinetic equations, covering Monte Carlo methods, multi-fidelity techniques, and stochastic Galerkin particle methods. Explores computational challenges and recent advancements in the field.
Variational and Jump Inequalities
Explore variational and jump norms in mathematical analysis, covering applications in rough paths, singular integrals, and ergodic theory. Gain insights into endpoint results and their proofs.
Antonio Esposito: Nonlinear Degenerate Cross Diffusion Systems with Nonlocal Interaction
Explores nonlinear degenerate cross-diffusion systems with nonlocal interaction, proving global existence of weak solutions using a semi-implicit JKO scheme for applications in social sciences, finance, and biology.
Sobolev Regularity for Maximal Operators
Explore recent developments in regularity theory for maximal operators, focusing on Sobolev and BV data. Accessible overview of an active research area with open questions.
Alexander Volberg - Poincaré Inequalities on Hamming Cube - Analysis, Combinatorics, Probability
Explore improved L^1-Poincaré inequality constants on Hamming cube, comparing with Gaussian space. Discuss proofs, estimates, and related mathematical concepts in analysis, combinatorics, and probability theory.
Helmut Abels - Diffuse and Sharp Interface Models for Two Phase Flows
Overview of analytic results for diffuse and sharp interface models in two-phase flow, discussing asymptotic limits as interfacial thickness approaches zero and exploring rigorous analytic results for sharp interface limits.
Non Uniqueness for the Transport Equation with Sobolev Vector Fields
Explore non-uniqueness in transport equations with Sobolev vector fields, challenging established theorems and offering new insights into solution behavior in mathematical physics.
Derek Holt- Algorithms for Finitely Presented Groups III
Explore advanced algorithms for finitely presented groups, including Todd-Coxeter coset enumeration, Reidemeister-Schreier algorithm, and automatic structures. Learn applications in group theory and computational methods.
Neil Olver: On the Integrality Gap of the Prize Collecting Steiner Forest LP
Explores the integrality gap of the prize collecting Steiner forest LP, disproving the belief it was 2 and showing it's at least 9/4, with implications for approximation algorithms in combinatorial optimization.