2022“几何与物理”小型研讨会

 

会议日期：2022年7月25日至28日

会议地点：腾讯会议435-3987-7606

组织单位：中国科学院数学与系统科学研究院

复旦大学数学科学学院

联系人：吴小宁 (wuxn@amss.ac.cn) 谢纳庆 (nqxie@fudan.edu.cn)

 

会议日程

 

报告摘要

 

报告人：黎俊彬

报告题目：Perturbations of naked singularities of dust in general relativity

摘　　要：It is well known that naked singularities will form in the collapse of spherical dust, which is also a stable phenomenon in spherical symmetry. Our goal is to study its perturbations outside spherical symmetry and we will report some progress in this talk.

 

报告人：曹周键

报告题目：Gravitational Wave Memory and its estimation in LIGO data

摘　　要：Gravitational wave memory is an outstanding theoretical prediction of general relativity. It may give an insight to fundamental physics such as quantum gravity. Alongwith the development of gravitational wave astronomy, the gravitational wave memory may be detected in the near future. In this talk I will introduce the physical picture of gravitational wave memory and its relation to fundamental physics. Also I will talk about the possible detection methods of gravitational wave memory.

 

报告人：杨诗武

报告题目：On a class of Yang-Mills-Higgs equations with infinite energy

摘　　要：In this talk, I will talk about the global dynamics for a class of Yang-Mills-Higgs fields with infinite energy, which is equivalent, after conformal transfermation, to some weighted energy space larger than the conformal energy space. As application, for the abelian case of Maxwell-Klein-Gordon system, we extend the small data result of Lindblad-Sterbenz to general large data. This is based on jointed work with D. Wei and P. Yu.

 

报告人：马  跃

报告题目：Nonlinear stability of the rank-one totally geodesic wave maps in non-isotropic manifolds

摘　　要：In this presentation I will talk about some recent progress on the global stability problem of totally geodesic wave maps defined in $\mathbb{R}^{1+2}$. We firstly prove the factorization property of the rank-one totally geodesic maps, which was taken as an a priori hypothesis in previous works. Then we reformulate the problem when the target space is an non-isotropic Riemannian manifold. With some symmetry along the target geodesic, we have found that the evolution system of the perturbation still enjoys sufficiently nice structure such that the global stability can be established via a global analysis on a type of wave-like systems defined in $\mathbb{R}^{1+2}$. For our purpose, two additional technical tools are developed: the conformal energy estimate on the glued hyper-surfaces and a variation of the algebraic normal form transform. This is a joint work with S.-H. Duan and W.-D. Zhang.

 

报告人：李  昕

报告题目：Probing Finslerian Schwarzschild black hole with the orbital precession of Sagittarius A*

摘　　要：Finsler geometry is a natural generalization of Riemannian geometry with the latter as a special case. In this talk, I will introduce basic concepts of Finsler geometry and the derived Finslerian Schwarzschild black hole solution. Then, I will discuss the orbital motions of Finslerian Schwarzschild black hole. Observations of orbits of several stars around Sagittarius A* by GRAVITY collaboration provide an approach to falsify Finslerian Schwarzschild black hole. I will discuss the constraint on Finslerian Schwarzschild black hole by the observation of orbital precession of the star S2. At last, prediction of orbital precession of other stars around Sagittarius A* will be given.

 

报告人：况小梅

报告题目：Instability, scalar hair and scalarization of de Sitter black holes

摘　　要：In this talk, I will analyze the (in)stability of massive scalar field perturbation on Schwarzschild dS (SdS) black hole in EsGB theory and figure out the unstable/stable parameters regions. Then by solving the static perturbation equation, I will show that the bifurcation points, at which the SdS black hole supports spherical scalar clouds, match well with the border of unstable/stable region. Finally, I will discuss the possible existence of scalarized black hole solutions and explicitly construct a typical solution.

 

报告人：张承勇

报告题目：Black hole scalarization and dynamical critical behaviors

摘　　要：We present the fully nonlinear study on the accretion of scalar fields onto a seed black hole in Einstein-Maxwell-scalar and Einstein-scalar-Gauss-Bonnet theories. Intrinsic critical phenomena in the dynamical transition between the bald and scalarized black holes are disclosed. In scalarization, the transition is discontinuous and a metastable black hole acts as an attractor at the threshold. The descalarization can be either discontinuous or continuous at the threshold, distinguished by whether or not an attractor appears.

 

报告人：郭俊起

报告题目：Energy and dynamics in critical collapse

摘　　要：We study the energy issue and dynamics in critical collapse of a spherically symmetric scalar field. It is found that in critical collapse, three types of the total energy (Misner-Sharp, Brown-York, and Landau-Lifshitz) take similar values. The material energy dominates over the gravitational energy, which is different from the black hole formation circumstance. Approximate analytic expressions for the metric functions and matter field in the large-radius region are obtained. It is observed that the spacetime in the large-radius region is not effectively flat. The causes to the effective flatness of the spacetime in the small-radius region are discussed.

 

报告人：袁　伟

报告题目：Area comparison of hypersurfaces in space forms

摘　　要：Mean curvature is one of the most fundamental extrinsic curvature in the theory of submanifold. A natural question is that whether mean curvature can control the area of hypersurfaces. In this talk, we discuss the area comparison with respect to mean curvature for hypersurfaces in space forms. This is a joint work with Professor Sun Jun in Wuhan University.

 

报告人：王耀华

报告题目：NNSC fill-ins and asymptotically flat extension

摘　　要：Let (S, g) be a compact n-dimensional manifold with positive scalar curvature which is diffeomorphic to S^n for 3\leq n\leq 6. In this talk we will consider the non-existence of fill-ins of S into (n+1)-dimensional manifolds with nonnegative scalar curvature and positive mean curvature H. Here we give some explicit estimate for the infimum of H if (S, g, H) admits NNSC fill-ins. We also discuss the asymptotically flat extension of the Bartnik data with CMC boundary and provide the upper bound of the Bartnik mass.

 

报告人：王金花

报告题目：Title: Global stability of the open Milne spacetime

摘　　要：The open Milne cosmological spacetime has a 3-dimensional Cauchy surface isometric to a non-compact, hyperbolic manifold. We prove the globally nonlinear stability of the open Milne spacetime for both of the massive Einstein-scalar field equations and show that as $t$ goes to infinity, the spatial metric tends to the hyperbolic metric. We are able to establish the energy decay estimates in geodesic gauge with lower regularity for the trace part of the second fundamental form $\tr k$ than that in the local theory. This allows us to retrieve the top order of $\tr k$ with uniform bound (without decay) when the scalar field is massive. This is joint work with Wei Yuan.

 

报告人：李冏玥

报告题目：On the radiation field of semi-linear Dirac equations with spinor null forms

摘　　要：For a solution of a wave equation, the radiation field is its rescaled restriction to null-infinity. It is always related to the Radon transform and the scattering theory. In this talk, we will talk about how to define the radiation field for the linear and semi-linear Dirac equations. Based on the existence of the Dirac radiation field, we can prove a rigidity theorem and study the inverse problem of the radiation field.

 

报告人：赖宁安

报告题目：Schwarzschild黑洞时空中半线波动方程的有限时间破裂

摘　　要：We study the semilinear wave equation with power type nonlinearity and small initial data in Schwarzschild spacetime. If the nonlinear exponent $p$ satisfies $2\le p\le1+\sqrt 2$, we establish the blow-up result and lifespan estimate. The key novelty is that the compact support of the initial data can be close to the event horizon. By combining the global existence result for $p>1+\sqrt 2$ obtained by Lindblad et al.(Math. Ann. 2014), we then give a positive answer to the interesting question posed by Dafermos and Rodnianski(J. Math. Pures Appl. 2005, the end of the first paragraph in page $1151$): $p=1+\sqrt 2$ is exactly the critical power of $p$ separating stability and blow-up. This is a joint work with Prof. Yi Zhou.

 

报告人：张华丽

报告题目：Rough solutions of 2D compressible Euler equations

 

摘　　要：For the Cauchy problem of irrotational Euler equations and incompressible Euler equations, the sharp regularity has been obtained for controlling the local existence of solutions . However, the sharp regularity problem for 2D compressible Euler equations with non-trvial vorticity remains open. In this talk, we will discuss some recent progress on this topic.