Random Graphs and Nonlinear Spectral Gaps
Explore discrete Poincaré inequalities in regular expander graphs, long-range expansion properties, and their implications for Banach space-valued functions, with improved estimates for Poincaré constants.
Continuity Properties of Lyapunov Exponents - Lecture 5
Explore the control of Lyapunov exponents using entropy in smooth surface diffeomorphisms. Gain insights into recent research on expansion of smooth unstable curves and their relation to homoclinic tangencies.
Continuity Properties of Lyapunov Exponents - Lecture 7
Explore the control of Lyapunov exponents using entropy in smooth surface diffeomorphisms. Gain insights into recent research on expansion of smooth unstable curves and their relation to homoclinic tangencies.
A Spectral Gap for the Transfer Operator on Complex Projective Spaces - Lecture 4
Explore the transfer operator on complex projective spaces, focusing on spectral gaps, equilibrium states, and statistical properties in holomorphic dynamics. Gain insights into pluripotential theory applications.
Continuity Properties of Lyapunov Exponents - Lectures 3 and 4
Delve into the continuity properties of Lyapunov exponents in smooth surface diffeomorphisms, exploring entropy control and the impact of near homoclinic tangencies on unstable curve expansion.
Dynamics of Smooth Surface Diffeomorphisms - Spectral Gap and Stochastic Properties
Explore surface diffeomorphisms, spectral gaps, and stochastic properties in smooth dynamics. Gain insights into symbolic models, entropy continuity, and hyperbolic systems.
Heights on Character Varieties, Free Subgroups and Spectral Gaps by Emmanuel Breuillard
Explore heights on character varieties, free subgroups, and spectral gaps in this advanced mathematics lecture, delving into Zariski dense subgroups and their applications in geometry and number theory.
Spectral Gap of the Laplacian for Random Hyperbolic Surfaces
Explore spectral gap of Laplacian for random hyperbolic surfaces in large genus limit. Delve into Weil-Petersson measure, Mirzakhani's work, and trace method applications.
On the Spectral Gap of the Laplacian for Random Hyperbolic Surfaces
Explorez le comportement spectral du laplacien sur des surfaces hyperboliques aléatoires, en mettant l'accent sur l'écart spectral dans la limite des grands genres.
Geodesic Levy Flight and Foraging Hypothesis - Analytic Techniques in Dynamics and Geometry
Explore analytic techniques in dynamics and geometry, focusing on geodesic Levy flight and the foraging hypothesis. Gain insights into Brownian motion and geometric operators.
Spectral Gap of the Laplacian for Random Hyperbolic Surfaces - Part 2
Explore spectral gap of Laplacian for random hyperbolic surfaces using trace method and asymptotic expansions in large genus limit. Analyze Weil-Petersson measure and Friedman-Ramanujan property.
Spectral Gaps vs the Baum-Connes Conjecture
Explore the relationship between spectral gaps and the Baum-Connes conjecture in mathematics, delving into advanced concepts in functional analysis and topology.
Towards an Optimal Spectral Gap Result for Random Compact Hyperbolic Surfaces
Explore recent progress in proving near-optimal spectral gaps for hyperbolic surfaces. Delve into trace methods, challenges, and new tools developed to improve bounds in spectral geometry.
Thermodynamic Formalism for Dispersing Billiards
Explores mathematical billiards in statistical mechanics, focusing on dispersing billiards. Discusses equilibrium states, geometric potentials, and spectral analysis, with insights into SRB measures and maximal entropy.
Spectral Gaps of Random Covers of Hyperbolic Surfaces
Explore spectral gaps in random hyperbolic surfaces, including Laplacian resonances and a probabilistic version of Selberg's 3/16 theorem, using transfer operators and zeta functions.
Spectral Gap Estimates for the Random Field Ising Model - Lecture
Spectral gap estimates for random field Ising model: convergence rates, Glauber dynamics, Griffiths phase. Combines stochastic localization and percolation-theoretic coarse-graining techniques.
Metaplex Networks: Influence of Exo-Endo Structure on Diffusion in Complex Systems
Explore super diffusion in complex systems, focusing on metaplex networks and their impact on diffusion processes through fractional modeling and real-world examples.
Thermalization of Quantum Memories - A Tensor Networks Approach
Explore thermalization of quantum memories using tensor networks, focusing on 2D Kitaev's quantum double models and their Gibbs state representation as PEPS.