47 citations · 47 across the 7 of their papers we have counts for
7 papers
Moduli of bundles and semiorthogonal decomposition
Kai Xu
In this paper we construct semiorthogonal decompositions of moduli of principal bundles on a curve into its symmetric powers, for both the moduli stack of all -bundles and the c…
Statistical Mechanics and Categorical Entropy
Haiqi Wu, Kai Xu
This paper investigates the relationship between categorical entropy and von Neumann entropy of quantum lattices. We begin by studying the von Neumann entropy, proving that the ave…
3-Manifolds with positive scalar curvature and bounded geometry
Otis Chodosh, Yi Lai, Kai Xu
We show that a complete contractible 3-manifold with positive scalar curvature and bounded geometry must be . We also show that an open handlebody of genus larger than…
Codimension 2 drawstrings with scalar curvature lower bounds
Demetre Kazaras, Kai Xu
We produce new examples of Riemannian manifolds with scalar curvature lower bounds and collapsing behavior along codimension 2 submanifolds. Applications of this construction are g…
Scalar curvature and volume entropy of hyperbolic 3-manifolds
Demetre Kazaras, Antoine Song, Kai Xu
We show that any closed hyperbolic 3-manifold M admits a Riemannian metric with scalar curvature at least -6, but with volume entropy strictly larger than 2. In particular, this co…
Drawstrings and flexibility in the Geroch conjecture
Demetre Kazaras, Kai Xu
In this paper, we observe new phenomena related to the structure of 3-manifolds satisfying lower scalar curvature bounds. We construct warped-product manifolds of almost nonnegativ…