
Explore advanced concepts in 4-manifold symmetries, building on previous knowledge and delving into complex mathematical theories.

Explore new upper bounds on geometric and spectral invariants of closed hyperbolic surfaces using the Selberg trace formula and linear programming techniques.

Explore linear programming bounds for hyperbolic surfaces, examining closed geodesics and Laplace eigenvalues. Gain insights into quantitative behavior and predominance in Riemannian metrics.

Explore the essential spectrum of 3D Dirac operators with critical shell interactions, examining how surface geometry influences spectral properties in quantum mechanics.

Explore the algebraic and topological structures of homeomorphism groups, their relation to manifold topology, and dynamics of group actions.

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.

Explorez les systèmes locaux rigides, leurs propriétés et applications en géométrie et théorie des nombres. Découvrez les avancées récentes et la conjecture de Simpson sur leur origine géométrique.

Explore the intriguing world of Kakeya sets and delve into the sticky Kakeya conjecture. Uncover groundbreaking insights on this fundamental problem in harmonic analysis and Fourier transform behavior.

Explore Poisson structures on character varieties, examining maps between oriented surfaces and their impact on conjugacy classes of fundamental group representations into Lie groups.

Explore fractal Weyl bounds in spectral geometry with Anke Pohl, delving into advanced mathematical concepts and their applications.

Explore Twisted Ruelle zeta functions, Fried's conjecture, and applications in locally symmetric spaces. Gain insights into spectral geometry and refined analytic torsion.

Explore the Cheeger constant of hyperbolic surfaces, its relation to spectral gaps, and recent findings on its upper bound for large genus surfaces. Gain insights into cutting Riemannian manifolds efficiently.

Explorez la fonction zêta de Ruelle pour les variétés presque hyperboliques en 3D, en examinant ses propriétés spectrales et géométriques.

Explore connections between matrix spaces and graphs, uncovering surprising equivalences and their applications in theoretical computer science, quantum information theory, and algebra.

Explore mean curvature flow's regularity theory, focusing on distinctions between one-dimensional and higher-dimensional flows in this geometric analysis lecture.

Explore Colding-Minicozzi entropy's role in analyzing submanifold complexity and its applications to mean curvature flow singularities and hypersurface simplicity.

Explore K-tilings of the Aztec diamond, a fascinating mathematical concept in integrable systems and exactly solvable models.

Explore the application of cluster algebra to 2D and 3D hyperbolic geometry, examining ideal triangulations, Teichmuller spaces, and knot volumes through mutations and cluster variables.

Explore finite point configurations across Euclidean, discrete, and arithmetic spaces. Discover size requirements for subsets containing congruent copies of given configurations, with connections to learning theory.

Explore orderability of 3-manifold groups, focusing on the L-space conjecture and its connections to group orderability, taut foliations, and Heegaard Floer homology in hyperbolic 3-manifolds.

Explore minimal-volume cusped hyperbolic 3-manifolds and their fundamental groups' orderability. Investigate order-preserving braids and their impact on Artin actions.