6 papers
Kobayashi Hyperbolicity of General Surfaces via the Poincaré Problem
Song-Yan Xie, Shengyuan Zhao
We prove that a general surface in of degree at least contains no rational or elliptic curves, strengthening the classical result of Clemens by replacing the or…
Periods of Oka K3 surfaces are dense
Song-Yan Xie, Shengyuan Zhao
We give the first known examples of Oka K3 surfaces: every smooth hypersurface of multidegree \((2,2,2)\) in \((\mathbb{P}^1)^3\) is Oka. Building on this example, we prove that in…
Equidistribution of currents under Anosov group actions
Nguyen-Bac Dang, Michael Kapovich, Mikhail Lyubich +1
We study the behavior of currents on flag-manifolds under actions of Anosov subgroups of complex semisimple Lie groups G. Given a current T of bidimension (k, k) on the full flag-m…
On cube and Cremona rigidity for higher-rank lattices
Shengyuan Zhao
For irreducible lattices in semisimple Lie groups of real rank at least , we prove a cohomological vanishing result implying that any action on a CAT(0) cube complex fixes a ver…
Decay of weighted cusp counts for congruence subgroups of over number fields
Shengyuan Zhao
For congruence subgroups commensurable with over number fields, we study cusp counts with arithmetic multiplicities. We prove that the ratio of the total weig…
Berkovich dynamics of twisted rational maps
Hongming Nie, Shengyuan Zhao
A twisted rational map over a non-archimedean field is the composition of a rational function over and a continuous automorphism of . We explore the dynamics of some twi…