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Analysis and Mathematical Physics

Institute for Advanced Study via YouTube

Overview

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Explore advanced mathematical physics through this comprehensive 3-day conference featuring cutting-edge research presentations from leading experts at the Institute for Advanced Study. Delve into diverse topics spanning quantum mechanics, statistical physics, differential geometry, and fluid dynamics through lectures covering free dynamics of tracer particles in Fermi seas, spectral gaps in SL2(ℝ), many-body localization, and reinforced random walks. Examine sophisticated mathematical frameworks including discrete harmonic analysis applications to ergodic theory, functional inequalities for quantum evolution, and singularity formation in incompressible fluids. Investigate geometric and topological concepts through discussions of canonical coordinates for Calabi-Yau manifolds, hyperuniformity in many-particle systems, and the amplituhedron unwinding. Study advanced analytical techniques including Liouville theory, extreme eigenvalue distributions of sparse random graphs, Cardy embedding of random planar maps, and the nonlinear stability of the Schwarzschild metric. Explore specialized areas such as inverse problems for quantum graphs, Lipschitz rigidity for scalar curvature, geometric measure theory on non-smooth spaces with lower Ricci curvature bounds, and branched regularity theorems for stable minimal hypersurfaces. Learn about classical turbulence as quantum geometry, vortex and SQG patch regularity, co-dimension one stability of solitons, and degenerate dispersion for generalized SQG equations. Discover connections between diffusion and mixing in Hamiltonian flows, generalized entropy methods, optimization problems over function spaces, and quantitative regularity theory for axisymmetric Navier-Stokes equations.

Syllabus

Free dynamics of a tracer particle in a Fermi sea - Sören Petrat
A spectral gap in SL2(ℝ)SL2(R) and applications: expansion, Furstenberg measures... - Jean Bourgain
Introduction to many-body localization - David Huse
Reinforced random walks and statistical physics - Pierre Tarres
Large coupling asymptotics for the Lyapunov...with analytic potentials -Christoph Marx
Discrete harmonic analysis and applications to ergodic theory - Mariusz Mirek
Functional inequalities and gradient flow for quantum evolution - Eric Carlen
Singularity formation in incompressible fluids - Tarek Elgindi
Canonical coordinates for Calabi Yau manifolds I - Sean Keel
Hyperuniformity in many-particle systems and its generalizations - Salvatore Torquato
Applications of twisted technology - Christoph Thiele
On structure results for intertwining operators - Wilhelm Schlag
Unwinding the amplituhedron - Nima Arkani-Hamed
Thermodynamical approach to the Markoff-Hurwitz equation - Michael Magee
Billiards and Hodge theory - Simion Filip
Imaging of Small Inhomogeneities, Homogenization and Super Resolution - Yves Capdeboscq
An Introduction to Liouville Theory - Antti Kupiainen
Unitary, Symplectic, and Orthogonal Moments of Moments - Emma Bailey
Extreme eigenvalue distributions of sparse random graphs - Jiaoyang Huang
Cardy embedding of random planar maps - Nina Holden
The nonlinear stability of the Schwarzschild metric without symmetry - Mihalis Dafermos
Inverse problems for quantum graphs - Pavel Kurasov
Lipschitz rigidity for scalar curvature - Bernhard Hanke
On the stability of the fractional Caffarelli-Kohn-Nirenberg inequality - Federico Glaudo
Geometric Measure Theory on non smooth spaces with lower Ricci curvature bounds - Daniele Semola
Branched Regularity Theorems for Stable Minimal Hypersurfaces Near Classical Cones...- Paul Minter
Three things about polynomials - Ruixiang Zhang
Additive Energy of Regular Measures in One and Higher Dimensions, and the Fractal... - Laura Cladek
Classical Turbulence as Quantum Geometry - Alexander Migdal
Regularity of Vortex and SQG Patches - Alexander Kiselev
On Co-dimension One Stability of the Soliton for the 1D Focusing Cubic Klein-Gor... - Wilhelm Schlag
Degenerate Dispersion and Illposedness for Generalized SQG Equations - Dr. In-Jee Jeong
Blume-Capel and the Tricritical Point - Trishen Gunaratnam
The adjoint Brascamp-Lieb inequality - Terence Tao
Diffusion and Mixing for Two-dimensional Hamiltonian Flows - Michele Coti-Zelati
Generalized Entropy Methods and Stability in Sobolev and Related Inequalities - Jean Dolbeault
The Alt-Phillips Functional for Negative Powers - Daniela De Silva
Resonances as a Computational Tool - Katharina Schratz
Lipschitz Graphs in Carnot Groups - Davide Vittone
Frobenius-type Results on Submanifolds and Currents - Annalisa Massaccesi
Optimization Problem Over the Space of Functions with Second Order Bounded Variation - Camillo Brena
Hawking Mass Monotonicity for Initial Data Sets - Sven Hirsch
The Robin Problem in Rough Domains - Stefano Decio
Existence of Four Minimal Spheres in S^3 with a Bumpy Metric - Xin Zhou
Quantitative Regularity Theory for the Axisymmetric Navier-Stokes Equations - Stan Palasek
Chaos in Lattice Spin Glasses and Some Questions for Analysts - Sourav Chatterjee
Arithmetic Study Behind Spectra of Quantum Interactions - Masato Wakayama
Variations on Fefferman's Ball Multiplier Theorem - Mikael De La Salle
Generic Properties of Laplace Eigenfunctions in the Presence of Symmetry - Craig Sutton
Supersymmetric Approach to the Analysis of Random Band Matrices - Mariya Shcherbina
Inertial Manifolds for the Hyperbolic Cahn-Hilliard Equation - Ahmed Bonfoh
Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties - Pavel Kurasov
Serrin’s Overtermined Problem In Rough Domains - Alessio Figalli
Evolution of Coherent Structures in Incompressible Flows - Francisco Gancedo
Duality of Fluid Mechanics and Solution of Decaying Turbulence - Alexander Migdal
Absolute Continuity of the Robin Harmonic Measure On Rough Domains - Guy David
New Estimates for Navier–Stokes and the Inviscid Limit Problem - Jincheng Yang
Spectral Minimal Partitions: Local vs Global Minimality - Gregory Berkolaiko
The 3D Kinetic Couette Flow Via The Boltzmann Equation In The Diffusive Limit - Robert Strain
Restriction Estimates Using Decoupling Theorem and Incidence Estimates For Tubes - Hong Wang
On Minkowski's Monotonicity Problem - Ramon van Handel
Geometry and Topology of Spectral Minimal Partitions - Graham Cox
Manifolds With Curvature Bounded Below In the Spectral Sense - Gioacchino Antonelli
ractional Parabolic Theory as a High-dimensional Limit of Fractional El...- Mariana Smit Vega Garcia
Lower Bounds on Lyapunov Exponents for Linear PDEs Driven by Stochastic Na...- Samuel Punshon-Smith
The Smale conjecture for RP^3 and minimal surfaces - Daniel Ketover
Min-Max Construction of Anisotropic Minimal Hypersurfaces - Guido De Philippis
From Bourgain's Projection Theorem to Kakeya and Khintchine on Fractals: An Impre...- Pablo Shmerkin
Towards a Geometric Theory of Deep Learning - Govind Menon
Quadratic Flatness and Regularity for Codimension-One Varifolds with Bounded...- Sławomir Kolasiński
The Relation Between the Geodesic Flow and Finite-Area Holomorphic Quadratic Diff...- Dragomir Saric
Uniqueness and Convexity in the Calculus of Variations - Bernd Kirchheim
Inviscid Limits From Compressible Navier-Stokes to Small BV Solutions to Euler - Alexis Vasseur
Navier-Stokes Equations at Critical Regularity - Stan Palasek
Highly Irregular Microstructures and TN Configurations - John Ball
Existence of non convex V-states - Javier Gomez Serrano
Estimates for Ricci Solitons in Dimension 4 - Bennett Chow

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