Institut des Hautes Etudes Scientifiques (IHES) Courses

Particle Approximation of the Doubly Parabolic Keller-Segel Equation in the Plane

Explore particle approximation of the parabolic-parabolic Keller-Segel system in the plane, focusing on stochastic particle systems, tightness, and weak solutions for small sensitivity parameters.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Random Models on Regularity-Integrability Structures

Explore a simplified proof of the BPHZ theorem using extended regularity structures with integrability exponents, advancing the study of singular stochastic partial differential equations.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Regularity Structures for Quasilinear Singular SPDEs

Explore regularity structures for analyzing semilinear and quasilinear parabolic singular stochastic PDEs, suitable for beginners and experts alike.

• YouTube
• 45 minutes
• On-Demand
• Free Video

An Exact Solution of the Macroscopic Fluctuation Theory

Explore an exact solution of the Macroscopic Fluctuation Theory for diffusive interacting particle systems using Inverse Scattering Theory, focusing on the simple exclusion process.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Outliers of Perturbations of Banded Toeplitz Matrices

Explore outlier eigenvalues of perturbed banded Toeplitz matrices, focusing on their behavior in regions outside the limiting spectral distribution's support as matrix size increases.

• YouTube
• 54 minutes
• On-Demand
• Free Video

Zeros of Random Power Series with Stationary Gaussian Coefficients

Explore zeros of random power series with stationary Gaussian coefficients, comparing to i.i.d. case and analyzing expected zero count in disks as radius approaches convergence.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Dunkl Operators, Random Matrices and Hurwitz Numbers

Explore probabilistic aspects of Dunkl operators, including radial Dunkl processes, reflected Brownian motion in Weyl chambers, and connections to Hurwitz numbers and generalized Bessel functions.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Dominated Representations, Intersections and Large Deviations

Explore hyperbolic metrics, dominated representations, and counting measures in groups, examining their connections to mean distortions and growth rates.

• YouTube
• 46 minutes
• On-Demand
• Free Video

A Statistical Physics Approach to the Sine Beta Process and Other Random Point Processes

Explore statistical physics approaches to Sine Beta processes and random point systems, focusing on universality properties and applications of DLR tools.

• YouTube
• 54 minutes
• On-Demand
• Free Video

Cutoff for the Transience Time for the SSEP with Traps and the Facilitated Exclusion Process

Explore phase separation in the facilitated exclusion process, examining its mapping to SSEP with traps and analyzing transience time cutoff and mixing time implications.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Fredrickson-Andersen 2-Spin Facilitated Model - Sharp Threshold

Explore sharp threshold results for the Fredrickson-Andersen 2-spin facilitated model, examining relaxation mechanisms and proof techniques for interacting particle systems with kinetic constraints.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Mathematical Foundation of Various MCMC Methods

Explore advanced MCMC methods for combinatorial optimization, including multi-spin flip techniques. Compare mathematical and numerical results to evaluate efficiency in different contexts.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Point-Counting and the Zilber-Pink Conjecture - Lecture 3

Explore the Zilber-Pink conjecture, its relation to classical conjectures, and point-counting strategies for proving cases, focusing on curves in modular curve powers.

• YouTube
• 1 hour 49 minutes
• On-Demand
• Free Video

A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Part 1

Explore Gromov's angle shrinking problem and its role in proving the dihedral extremality/rigidity conjecture through a new index theorem for manifolds with polyhedral boundary.

• YouTube
• 52 minutes
• On-Demand
• Free Video

A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Lecture 2

Explore a stable algebraic version of Gromov's angle shrinking problem and its application to dihedral rigidity conjecture, focusing on Fredholm index computation.

• YouTube
• 51 minutes
• On-Demand
• Free Video