Langlands Duality for the Affine Hecke Category
Explore Langlands duality for affine Hecke category, its applications in representation theory, and potential generalizations to symplectic singularities. Gain insights into geometric local Langlands duality.
Triangulations of Manifolds and the Triangulation Conjecture
Explore the triangulation conjecture in topology, its validity in low dimensions, and its disproval in higher dimensions using advanced mathematical techniques.
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.
Optimal Estimates for Neumann Eigenvalues
Explore optimal estimates for Neumann eigenvalues, including award-winning research on maximizing second eigenvalues and recent findings on convex set bounds.
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.
Distribution on Achiral Manifolds
Explore distribution of commensurable classes in geometric models, focusing on Sol and hyperbolic 3-manifolds. Delve into related number theory concepts and recent research findings.
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.
The Global Unramified Geometric Langlands Equivalence
Explore the global unramified geometric Langlands conjecture, its history, motivation, and recent proof, along with remaining open questions in the field.
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.
Generalized Spin-Statistics Theorem for Loop Excitations
Explore an extended spin-statistics theorem for loops using Klein bottle representation. Examine new solvable lattice models for topological phases and fermionic loop excitations in higher dimensions.
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.
Summation for Two Sets in Hyperbolic Space - ICBS 2024
Explore hyperbolic summation and its application in developing Brunn-Minkowski theory for hyperbolic space geometry, extending classical Euclidean concepts.
Points, Lines, and Subdivisions in Polyhedra - ICBS 2024
Explore polyhedra's role in mathematics, from PL topology to arithmetic, and discover new insights in combinatorics and related fields.
Equiangular Lines and Eigenvalue Multiplicity - ICBS 2024
Explore equiangular lines in high dimensions, solving a longstanding problem using spectral graph theory and discussing future research directions.
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.
A Morse Model for Stable Homotopy - ICBS 2024
Explore stable homotopy groups, framed bordism, and Morse theory in topological spaces. Gain insights into Floer homotopy foundations and the Pontryagin-Thom construction.
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.
Total Positivity: Combinatorics, Geometry and Representation Theory
Explore total positivity theory in matrices, its applications, and recent developments in combinatorics, geometry, and representation theory.
Bourgain's Proof of the Circular Maximal Function Theorem - Part 3
Explore Bourgain's groundbreaking proof of the circular maximal function theorem, delving into advanced mathematical concepts and techniques.