Mathematical Analysis - Stable and Unstable Spectral Inequalities, Geometric Analysis, and Differential Equations

Centre de recherches mathématiques - CRM via YouTube

Start learning Write review

Explore advanced mathematical analysis through this comprehensive collection of videoconferences and lectures covering spectral theory, differential equations, and geometric analysis. Delve into cutting-edge research topics including stable and unstable spectral inequalities, scattering theory for differential forms, and singularity formation in black hole interiors. Study the Navier-Stokes equations through Liouville theorems, examine spectral gaps of random hyperbolic surfaces, and investigate restriction of eigenfunctions to sparse sets on manifolds. Learn about uniform rectifiability and elliptic operators, controllability of waves using geometric Carleman estimates, and optimal domains for curl eigenvalues. Discover entropy production in nondegenerate diffusions, ergodic theorems along trees, and locally dissipative solutions of Euler equations. Analyze multi-scale properties of Jordan curves, ergodic properties of eigenfunctions, and control of eigenfunctions on negatively curved surfaces. Explore convex geometry from a Funk perspective, integrated density of states for periodic operators, and stationary solutions to stochastic heat equations. Investigate BV functions on nested fractals, measure theoretic projection bodies, and harmonic maps with free boundary conditions. Examine conformal surface embeddings, extremal length systems, and the two-point Weyl law on manifolds without conjugate points. Study zeros of random polynomial mappings, nodal sets of monochromatic waves, and critical well-posedness for derivative nonlinear Schrödinger equations.

Syllabus

Videoconference: Stable and unstable spectral inequalities
Videoconference: Lambdas, bubbles, and spheres
Videoconference: L^P Norms Via Geodesic Beams
Videoconference: Viscosity limits for 0th order operators
Videoconference: Spectral asymptotics for stationary spacetimes
Videoconference: Homogenization of Steklov problems with applications to sharp isoperimetric bounds
Videoconference: Holomorphic motions, conformal welding and capacity
Videoconference: A quantification of the Besicovitch projection theorem and its generalizations
Videoconference: Bourgain-Brezis inequalities, applications and more
Scattering theory for differential forms and its relation to cohomology (videoconference)
Singularity formation in Black Hole interiors (videoconference)
Liouville theorems for the Navier-Stokes equations
The spectral gap of a random hyperbolic surface
Perturbed Haar function expansions
Restriction of eigenfunctions to sparse sets on manifolds
Uniform rectifiability and elliptic operators satisfying a Carleson measure condition
On Controllability of Waves and Geometric Carleman Estimates
Strangling of the fundamental gap in hyperbolic space
Optimal domains for the first curl eigenvalue
On the stable rank of algebras of bounded holomorphic functions
Boundedness and continuity for rearrangements on spaces defined by mean oscillation
Entropy production in nondegenerate diffusions: large times and small noises
Ergodic theorems along trees
Locally dissipative solutions of the Euler equations
Various formulations and approximations of incompressible fluid motion in porous media
Multi-scale analysis of Jordan curves
Ergodic properties of eigenfunctions
Failure of approximation of odd functions by odd polynomials
Control of eigenfunctions on negatively curved surfaces
A Funk perspective on convex geometry
Integrated density of states of the periodic Airy-Schrödinger operator
On Stationary Solutions to the Stochastic Heat Equation
Towards optimal spectral gaps in large genus
Prime ends for domains in metric measure spaces and their use in potential theory and QC theory
BV functions and some functional inequalities on nested fractals
On measure theoretic projection bodies
Some results on harmonic maps with free boundary and beyond
The extremal length systole of the Bolza surface
Kevin Pilgrim: Conformal surface embeddings and extremal length
Blake Keeler: The Two-Point Weyl Law on Manifoods without Conjugate points
Norm Levenberg: Zeros of Random Polynomial Mappings in several complex variables
Stefano Decio: Zeros of sums of eigenfucntions
Alvaro Romaniega: Nodal Sets of Monochromatic waves from a deterministic and random point of view
Maria Ntekoume: Critical well-posedness for the derivative nonlinear Schrödinger equation onthe line