Recent Developments in Constant Mean Curvature Hypersurfaces - Part I
Explore recent developments in constant mean curvature hypersurfaces, focusing on existence theory using min-max methods and discussing open problems in the field.
Spherical Plateau Problem and Applications in Geometric Analysis
Explore area minimization in Hilbert sphere quotients, entropy inequality, and stability results for Riemannian surfaces, with applications to hyperbolic geometry and eigenvalue bounds.
Currents on Metric Spaces and Intrinsic Flat Convergence
Explore Ambrosio-Kirchheim's Theory of Currents on Metric Spaces and delve into integral current spaces and intrinsic flat convergence, providing essential background for Antoine Song's talk.
Self-Similar Solutions to Extension and Approximation Problems - Lecture
Explore self-similar solutions in extension and approximation problems, focusing on Lipschitz and Hölder maps with unique properties in higher dimensions.
Lipschitz Constant and Degree of Mappings in Riemannian Manifolds
Explore the relationship between Lipschitz constant and degree of mappings in Riemannian manifolds, focusing on recent developments and clever mapping techniques.
Schatten Properties of Commutators on Quantum Tori
Explore Schatten properties of commutators on quantum tori, characterizing them through Besov spaces and extending to Calderon-Zygmund operators in noncommutative settings.
Cluster Duality and Non-Holomorphic Spectral Curves
Explore cluster duality, geometric interpretations of tropical points, and their connections to local systems on curves through graphs, Lagrangian coverings, and affine group-valued local systems.
Kontsevich's Star-Product up to Order Seven for Affine Poisson Brackets
Explore Kontsevich's star-product formula for affine Poisson brackets, examining its expansion up to seventh order and investigating the mechanism of associativity in higher orders.
Reddening Sequences for Cluster Algebras
Explore reddening sequences in cluster algebras, their implications, and known cases, delving into finite dimensionality, invariants, and canonical bases.
Random Lattices as Sphere Packings
Explore lattice-sum functions and their applications in sphere packing density, including Siegel's mean value theorem and recent advancements in optimal packing bounds.
Multiscale Basis Dictionaries and Scattering Networks on Simplicial Complexes
Explore multiscale basis dictionaries and scattering networks on simplicial complexes, focusing on HGLET and GHWT. Learn applications in coauthorship/citation complex and article classification.
Interplay Between Notions of Convexity in Complex, Symplectic and Contact Geometries
Explore the interplay between convexity notions in complex, symplectic, and contact geometries. Gain insights into pseudo-convexity, rational convexity, and their geometric counterparts.
Stein and Weinstein Manifolds - An Introduction to Topological and Symplectic Aspects
Explore topological and symplectic aspects of Stein manifolds, including handlebody construction, Weinstein manifolds, and flexibility versus rigidity in complex variables theory.
Recent Developments in Constant Mean Curvature Hypersurfaces - Part II
Explore recent developments in constant mean curvature hypersurfaces, focusing on min-max theorems and the half-volume spectrum. Gain insights into advanced geometric analysis concepts.
Scalar Curvature Rigidity in Manifolds
Explore scalar curvature rigidity in manifolds, examining known solutions and current research questions using spinorial techniques.
Scalar Curvature Rigidity and Extremality in Dimension 4
Explore scalar curvature rigidity in 4D using Finsler-Thorpe trick and twisted spinor methods. Discover area-extremal properties of 4-manifolds with nonnegative sectional curvature.
Recent Inequalities on the Mass-to-Capacity Ratio
Explore new inequalities for mass-to-capacity ratio on manifolds with nonnegative scalar curvature, revealing proofs of positive mass theorem and applications in geometry.
A Gift for Louis: The New Aperiodic Monotile
Explore the groundbreaking discovery of a new aperiodic monotile, unraveling its mathematical significance and implications for tiling theory.
Positive Mass Theorem for Asymptotically Hyperbolic Manifolds
Explore the positive mass theorem for asymptotically hyperbolic manifolds and its implications in AdS/CFT correspondence and global invariants at conformal infinity.
Intrinsic Flat Stability of the Positive Mass Theorem for Graphical Manifolds
Explore intrinsic flat stability of positive mass theorem for graphical manifolds, focusing on asymptotically flat and hyperbolic cases. Gain insights into rigidity, stability, and ongoing research.
Continuous Time Bubbling for the Harmonic Map Heat Flow in Two Dimensions
Explore continuous time bubbling in harmonic map heat flow, focusing on finite energy maps from plane to two-sphere without symmetry assumptions.