夏波

教育背景与访学经历:

 

2005——2009.09,于中国矿业大学数学与应用数学系获学士学位。

 

2009.09——2011.09,在中国科学技术大学,数学系进行硕士学习主要学习关于椭圆方程和抛物方程的一些经典理论,以及它们在微分几何中的应用,比如极小曲面,平均曲率流和Ricci流等。指导者麻希南和庆杰。

 

2011.09——2012.09,在中国科学技术大学,数学科学学院进行博士学习,主要学习广义相对论中的发展问题,其中包括“Minkowski空间在初值小扰动下的稳定性”这一经典结论和新近的关于“黑洞的形成”的结果。指导者麻希南和庆杰。

 

2012.09——2013.09,在巴黎十一大数学系进行硕士学习,通过了Nicolas Burq开的课《波方程》和Patrick Gerard开的课《有限维和无限维Hamilton系统》.并且通过文章《超临界波方程的局部的概率适定性》拿到硕士学位。

 

2013.09——2016.09,在巴黎十一大数学系,进行博士学习,主要关注超临界色散方程,所用到的工具为对初值进行随机化,和考虑给定方程在一些不变测度的支集上的演化。此过程所用到的不变测度主要有Gibbs测度,Gauss测度等。指导者Nicolas Burq。

 

2016.10——2017.1,访问中国科学技术大学数学科学学院麻希南教授。

 

联系方式:

办公电话     0756-3668373

邮箱      xiabo7@mail.sysu.edu.cn

 

2017.03——present,于中山大学数学学院(珠海)任特聘副研究员。

 

学位及授予单位: 
巴黎第十一大学(巴黎南大学) 数学系博士学位。
学术活动: 

1. Advanced course: Topics in Conformal Geometry and Geometry Analysis, June25-18, 2013 and Conference: Geometrical Analysis July 1-5, 2013 at CRM, Barcelona.

2. Journées EDP 2014, Roscoff; June 2-6, 2014.

3. Microlocal Analysis and Applications, in honour of Gille Lebeau, Université de NiceSophia Antipolis; June 23-27, 2014.

4. Summer school: 99 years of General Relativity July, 28- August 1, 2014 at ESI,Vienna.

5. Summer school: KAM theory and dispersive PDEs, Università di Roma; September1-5, 2014.

6. Geometric non-linear analysis: Conference on the occasion of Michael Struwe’s 60th birthday, June 6-12, at FIM, ETH Zurich.

7. Harmonic Analysis and Partial Differential Equations, 26-31 July 2015 at ICMS,Edinburgh.

8. New challegens in PDE: Deterministic dynamics and rondomness in high and infinite dimensional systems, October 19-30, at MSRI, Berkeley.

9. Talks in Seminar Numerical Analysis and Partial Differential Equations, Orsay,April 2015: Probabilistic well-posedness for wave eqaution of power type.

10. Poster in Harmonic Analysis and Partial Differential Equations at ICMS, Edinburgh,26-31 July 2015: Generic ill-posedness for semi-linear wave equations.

论文发表: 

1. Probabilistic well-posedness for semi-linear wave equation of power 3 ≤ p < 5, M2thesis, available at http://www.math.u-psud.fr/~santambr/xia.pdf.

2. Probabilistic well-posedness for semilinear wave equation on 3D torus, preprint available by request.

3. Generic ill-posedness for wave equation of power type on 3D torus, arXiv:1507.07179, submitted.

4. (with Chenmin Sun) Probabilistic well-posedness for supercritical wave equation on T3, arXiv:1508.00228,submitted.

5. Preservation of log-Sobolev type inequality under generalized BBM flow, preprint available by request.

6. Invariant measures for beam equation on T3, preprint available by request.