Metric SYZ Conjecture for Calabi-Yau Manifolds - ICBS 2024
Explore special Lagrangian torus fibrations on Calabi-Yau manifolds, focusing on recent progress and the Fermat family of hypersurfaces.
Generic and Random Behavior of Minimal Surfaces
Explore minimal surfaces in Differential Geometry, focusing on recent quantitative findings under genericity and randomness conditions. Discover spatial equidistribution and hyperbolic properties.
Tightness and Legendrian Surgery in Contact Structures
Explore contact structures, open book decompositions, and tightness characterization in 3-manifolds. Investigate preservation of tightness under Legendrian surgery.
Complex Brunn-Minkowski Theory and Uniqueness Theorems in Kähler Geometry
Explore complex Brunn-Minkowski theory and its applications in Kähler geometry, focusing on uniqueness theorems and generalizations of Bando-Mabuchi's work on Kähler-Einstein metrics.
Categorification of Lagrangian Floer Theory and Its Relation to Various Mathematics
Explore categorification of Lagrangian Floer theory and its connections to diverse mathematical fields with renowned mathematician Kenji Fukaya.
Ricci Limit Spaces are Semi-Locally Simply Connected
Explore Ricci limit spaces and their semi-local simple connectivity, delving into fundamental groups and Gromov-Hausdorff convergence of Riemannian manifolds.
Locally Symmetric Varieties with Moduli Interpretation
Explore complex algebraic geometry, focusing on realizing moduli spaces as locally symmetric varieties through Hodge theory. Survey existing results and examine Calabi-Yau manifolds with complex hyperbolic ball periods.
The Singular Set of Stable Minimal Hypersurfaces
Explore stable minimal hypersurfaces, their singularities, and recent findings on constructing metrics with specific singular sets in higher dimensions.
Generic Dynamics of the Mean Curvature Flows
Explore generic dynamics of mean curvature flows, including perturbation of shrinkers and isolatedness of cylindrical singularities in hypersurface evolution.
On the Enclosed Volume of Constant Mean Curvature Surfaces in the 3-Sphere and Euclidean 3-Space
Explore constant mean curvature surfaces in 3D spaces, computing area and enclosed volume using flat connection invariants. Joint work insights included.
Recent Progress on Self-Expanders of Mean Curvature Flow and Applications
Explore recent advancements in self-expanders of mean curvature flow, their role in modeling singularities, and applications in geometric analysis.
Symplectic Singularities Arising from Algebras of Symmetric Tensors
Explore symplectic singularities from symmetric tensor algebras, their construction, and relation to existing methods in algebraic geometry and representation theory.
Recent Progress on Gamma Conjectures - ICBS 2024
Explore recent advancements in Gamma conjectures, including modifications to Gamma conjecture I and its application over Kähler moduli space.
Hermitian Yang-Mills Connections on Log Terminal Kahler Spaces
Explore Hermitian Yang-Mills theory on mildly singular spaces, focusing on recent results for sheaves and log terminal Kähler spaces.
Filling Radius, Positive Scalar Curvature and Quantitative Operator K-Theory
Explore techniques in quantitative operator theory to estimate filling radius, connecting positive scalar curvature and asymptotic dimension in large-scale geometry.
New Minimal Surfaces in S^3 and B^3 via Eigenvalue Optimization
Explore new methods for producing minimal surfaces in $S^3$ and $B^3$ through spectral geometry optimization, addressing topological realization and low-area surface growth.
A Beautiful World Beyond Hyperbolic Geometry - Anosov Representations and Higher Teichmüller Spaces
Explore advanced geometric concepts beyond hyperbolic geometry, delving into Anosov representations and higher Teichmüller spaces.
Rigidity of Convex Surfaces in Space-Forms
Explore rigidity properties of convex surfaces in space-forms, focusing on mathematical concepts and geometric analysis techniques.
The Mandelbrot Set and Its Satellite Copies
Explore the fascinating world of the Mandelbrot set and its satellite copies, delving into complex mathematical concepts and intricate geometric patterns.
Thurston's Asymmetric Metric on Teichmüller Space Revisited
Explore Thurston's asymmetric metric on Teichmüller space and its generalizations to higher-rank Lie groups, examining geometric and dynamical invariants of hyperbolic structures.
Knot Invariants and Hyperbolic Flows
Explore knot invariants and hyperbolic flows in this advanced mathematics talk by Northwestern researcher Solly Coles.