José María Martell - Layer Potentials, Extrapolation and Boundary Value Problems in Unbounded Domains
Explore layer potentials, extrapolation, and boundary value problems in unbounded domains. Learn about elliptic systems, Neumann series, and weighted Banach function spaces in this advanced mathematics lecture.
Discrete Minimizers of Energy Integrals
Explore the intriguing phenomenon of discrete minimizers in energy integral optimization, its counterintuitive nature, and applications in various fields of mathematics and signal processing.
Moving Currents - On the Lie Transport Equation and a Rademacher Type Theorem
Explore the Lie transport equation for k-currents, extending classical transport theory to generalized surfaces. Insights on challenges and recent developments in modeling defects in plastic materials.
Distance Sets Spanned by Sets of Dimension D/2
Explores distance sets in R^d, proving theorems on Hausdorff and packing dimensions. Analyzes relationships between set dimensions and their distance sets, with focus on d/2 dimension cases.
Guido De Philippis - PDE Constrained Measures III
Explore advanced concepts in PDE-constrained measures with Guido De Philippis, delving into complex mathematical theories and applications in this advanced lecture.
Steve Hofmann - Quantitative Rectiability, and Harmonic and Caloric Measure III
Explore advanced mathematical concepts in quantitative rectifiability and measure theory, focusing on harmonic and caloric measures in complex analytical settings.
Frequency Function Methods in PDE I
Explore frequency function methods in partial differential equations, focusing on applications and theoretical foundations for solving complex mathematical problems.
PDE Constrained Measures I
Explore PDE constrained measures with Guido De Philippis in this advanced mathematical lecture, delving into complex analytical concepts and their applications.
Osama Khalil- Diophantine Approximation on Fractals and Homogeneous Flows
Explore Diophantine approximation on fractals and homogeneous flows, examining exceptional sets and their connections to recurrence behavior. Discover new results on Hausdorff dimension of divergent orbits and self-similar measure projections.
Equidistribution of Linear Random Walks on the Torus
Explores quantitative equidistribution for linear random walks on the torus, presenting recent progress relaxing the proximality assumption in Bourgain et al.'s work. Joint research with Nicolas de Saxcé.
Equidistribution of Expanding Translates of Curves in Homogeneous Spaces
Explores equidistribution of expanding translates of non-degenerate real-analytic curves in semisimple group spaces, extending previous work and applying to Diophantine approximation on matrices.
Don Zagier: Holomorphic Quantum Modular Forms
Explore holomorphic quantum modular forms, their connections to number theory and quantum knot invariants, and applications in odd weight Eisenstein series and Maass cusp forms.
Thermodynamical Formalism and Markoff-Hurwitz Equations
Explore connections between Diophantine geometry and fractals through Markoff-Hurwitz equations, transfer operators, and thermodynamical formalism. Discover links to various mathematical areas.
Horocycle Flow on Moduli Spaces of Translation Surfaces
Explore the intricate dynamics of horocycle flow on moduli spaces of translation surfaces in this advanced mathematics lecture by Jon Chaika.
The Transfer Operator Method
Explore the Transfer Operator Method in dynamical systems, focusing on its applications in topology and number theory within the context of advanced mathematical research.
How to Estimate P Variation
Explore efficient methods for estimating p-variation in metric spaces, with applications to martingales and enhanced paths. Learn techniques for quick computation and moment estimation.
Solvability and Ill Posedness of the Isentropic Euler System
Explore puzzling results on solvability and ill-posedness of the isentropic Euler system, including wild solutions, approximation results, and the selection of physically reasonable solutions.
A Geometric View on Stochastic Euler Equations
Explore geometric approaches to stochastic Euler equations, combining infinite-dimensional geometry and stochastic analysis to establish local well-posedness of non-linear PDEs.
Long Time Behaviour of 2D Spherical Ideal Hydrodynamics
Explore 2D spherical ideal hydrodynamics, focusing on new discretization schemes, geometric preservation, and long-time behavior linked to point vortex dynamics.
Regularization by Noise for the Stochastic Transport Equation
Explore regularization by noise for stochastic transport equations, focusing on uniqueness and regularity of solutions under different drift conditions and the impact of Brownian motion.
Stochastic Ricci Flow on Surfaces
Explores stochastic Ricci flow in 2D, introducing its formulation, symmetry properties, and construction of weak solutions. Discusses implications for compact surfaces and open questions.