L^2 Homology of Groups and Consequences - Part I
Explore l^2 homology of groups, its definition via simplicial complex actions, and implications for group theory, particularly when these invariants vanish.
L^2 Homology of Groups and Consequences - Lecture 3
Explore l^2 homology of groups, its computation, and implications for group theory, focusing on cases where these invariants vanish.
Hyperbolically Embedded Subgroups of Acylindrically Hyperbolic Groups - Lecture 1
Explore acylindrically hyperbolic groups through hyperbolically embedded subgroups. Investigate geometric properties, connections with random walks, and applications to important results in group theory.
L^2 Homology of Groups and Consequences - Lecture 2
Explore l^2 homology of groups through examples, calculations, and implications for group theory, focusing on vanishing invariants.
The Loop Hecke Algebra and Charge Conserving Yang-Baxter Operators
Explore Loop Braid Group, Loop Hecke Algebras, and charge conserving Yang-Baxter operators. Gain insights into recent mathematical developments in quantum symmetries and topological quantum field theories.
Algebraic Presentations of 4- and 3-Manifolds in Low-Dimensional Topology
Explore algebraic presentations of 4- and 3-manifolds, focusing on categories of n-cobordisms and their relation to low-dimensional topology and combinatorial group theory.
Volume Conjecture for Surface Diffeomorphisms
Explore quantum invariants for surface diffeomorphisms and their connection to mapping torus volume. Examine representation theory, numerical evidence, and a proof for the figure-eight knot complement case.
Algebraization of Low-Dimensional Topology - Part II
Explore algebraic presentations of cobordism categories in 3 and 4 dimensions, focusing on torus-based structures and their implications for Topological Quantum Field Theories.
Smooth 2-Groups and Their Principal Bundles
Explore smooth 2-groups and principal bundles in Lie groupoids. Learn about categorical generalizations of groups and their applications in mathematics.
New Isoperimetric Inequalities and Their Applications to Systolic Geometry and Minimal Surfaces
Explore new isoperimetric inequalities for k-dimensional submanifolds, their applications to systolic geometry, and implications for minimal submanifolds in this mathematical colloquium.
On the Critical Points of Steklov Eigenfunctions
Explore critical points of Steklov eigenfunctions on Riemannian manifolds, examining relationships between eigenfunction indexes, boundary behavior, and Euler characteristics.
An Overdetermined Eigenvalue Problem and the Critical Catenoid Conjecture
Explore an overdetermined eigenvalue problem on the two-sphere and its implications for characterizing the critical catenoid as a unique embedded free boundary minimal annulus.
A Weighted Reilly Formula for Differential Forms and Sharp Steklov Eigenvalue Estimates - Lecture
Explore weighted Reilly formula for differential forms and its applications in sharp Steklov eigenvalue estimates. Gain insights into spectral geometry and related open problems.
New Minimal Surfaces via Equivariant Eigenvalue Optimization - Part II
Explore equivariant optimization of Laplace and Steklov eigenvalues on surfaces to construct embedded minimal surfaces in 3-sphere and 3-ball. Discover new insights into geometric analysis and topology.
Interactions Between Computers and Spectral Geometry
Explorez les avancées récentes en géométrie spectrale, mettant en lumière le rôle crucial de l'assistance informatique dans les découvertes et les défis futurs.
Minimal Surfaces and the Isoperimetric Inequality
Explore the generalization of the isoperimetric inequality to submanifolds in Euclidean space, focusing on minimal submanifolds and their sharp isoperimetric properties.
Scalar Curvature Rigidity of Polytopes
Explore Riemannian metrics and scalar curvature positivity in differential geometry. Delve into Gromov's comparison principle for polytopes and recent advancements in verifying his conjecture.
Singularity Models in 3D Ricci Flow
Explore singularity formation in 3D Ricci flow, examining recent developments leading to a complete classification of singularity models beyond Perelman's breakthrough.
Corona Rigidity in Operator Theory and C*-Algebras
Explore corona rigidity in operator theory, examining extensions of Weyl-von Neumann theorem and its implications for C*-algebras, Calkin algebra, and isomorphisms of quotients.
How to Prove Isoperimetric Inequalities by Random Sampling
Explore isoperimetric inequalities through random sampling. Learn probabilistic approaches to Lp affine isoperimetric inequalities in non-convex ranges, bridging Brunn-Minkowski and dual theories.
Parametric Geometric Inequalities and Weyl Law for the Volume Spectrum
Explore parametric geometric inequalities and their connection to the volume spectrum, examining proofs, applications, and implications for minimal surfaces and stationary geodesic nets.