Chen Zhao

activity

20202026

collaborators

6 papers

math.DG2026

A proof of the Willmore-type conjecture in $C P^{2}$

Peng Wang, Zhenxiao Xie, Chen Zhao

In 2002, Montiel and Urbano conjectured that the Clifford torus in $C P^{2}$ minimizes the Willmore-type functional $W^{-} = \int_{T^{2}} (2 + ∣ H ∣^{2}) d A,$ either among all…

quant-ph2025

2D Quon Language: Unifying Framework for Cliffords, Matchgates, and Beyond

Byungmin Kang, Chen Zhao, Zhengwei Liu +2

Simulating generic quantum states and dynamics is practically intractable using classical computers. However, certain special classes -- namely Clifford and matchgate circuits -- p…

math.CV2023

An $L^{2}$ Dolbeault lemma on higher direct images and its application

Chen Zhao

Given a proper holomorphic surjective morphism $f : X \to Y$ from a compact Kähler manifold to a compact Kähler manifold, and a Nakano semipositive holomorphic vector bundle $…

math.AG2022

$L^{2}$ representation of Simpson-Mochizuki's prolongation of Higgs bundles and the Kawamata-Viehweg vanishing theorem for semistable parabolic Higgs bundles

Chen Zhao

In this paper, we provide an $L^{2}$ fine resolution of the prolongation of a nilpotent harmonic bundle in the sense of Simpson-Mochizuki (an analytic analogue of the Kashiwara-Malgr…

math.AG2021

$L^{2}$ -representation of Hodge Modules

Junchao Shentu, Chen Zhao

Over an arbitrary compact complex space or an arbitrary germ of complex space $X$ , we provide fine resolutions of pure Hodge modules with strict supports $I C_{X} (V)$ via dif…

math.CV2020

MacPherson's Conjecture via Hörmander Estimate

Junchao Shentu, Chen Zhao

In this notes we reprove MacPherson's conjecture on $L^{2} - (n, q)$ -cohomology through Demailly's formulation of Hörmander's Estimate. This approach allows us to weaken the condition o…

A proof of the Willmore-type conjecture in CP2

2D Quon Language: Unifying Framework for Cliffords, Matchgates, and Beyond

An L2 Dolbeault lemma on higher direct images and its application

L2 representation of Simpson-Mochizuki's prolongation of Higgs bundles and the Kawamata-Viehweg vanishing theorem for semistable parabolic Higgs bundles

L2-representation of Hodge Modules

MacPherson's Conjecture via Hörmander Estimate

A proof of the Willmore-type conjecture in $C P^{2}$

An $L^{2}$ Dolbeault lemma on higher direct images and its application

$L^{2}$ representation of Simpson-Mochizuki's prolongation of Higgs bundles and the Kawamata-Viehweg vanishing theorem for semistable parabolic Higgs bundles

$L^{2}$ -representation of Hodge Modules