Zilu Ma

Email: zim022 "at" ucsd dot edu
Office: APM 1101

My name is Zilu Ma and I am a fifth year PhD student in Mathematics at UCSD. My advisors are Professor Bennett Chow and Professor Lei Ni. I did my undergraduate studies at Xi'an Jiaotong University.

My main research interests lie in geometric analysis, and more specifically, intrinsic and extrinsic geometric flows, with an emphasis on Ricci flow and its applications to geometry and topology. I am also interested in some other geometric PDEs, such as Cheeger-Colding theory and its applications to Riemannian and Kaehler geometry.

Here is my CV (last updated in May 2022).

Research Papers

1. Volume growth estimates of gradient Ricci solitons
   (with Pak-Yeung Chan, and Yongjia Zhang) arxiv, 2022
2. The rate of F-convergence for Ricci flows with closed and smooth tangent flows.
   (with Pak-Yeung Chan, and Yongjia Zhang) arxiv, 2022
3. Hamilton-Ivey estimates for gradient Ricci solitons
   (with Pak-Yeung Chan, and Yongjia Zhang) arXiv, 2021
4. A local Sobolev inequality on Ricci flow and its applications
   (with Pak-Yeung Chan, and Yongjia Zhang) arXiv, 2021
5. An optimal volume growth estimate for noncollapsed steady gradient Ricci solitons
   (with Richard H. Bamler, Pak-Yeung Chan, and Yongjia Zhang) arXiv, 2021
6. On Ricci flows with closed and smooth tangent flows
   (with Pak-Yeung Chan and Yongjia Zhang) arXiv, 2021
7. A uniform Sobolev inequality for ancient Ricci flows with bounded Nash entropy
   (with Pak-Yeung Chan and Yongjia Zhang) IMRN, to appear; arXiv
8. Ancient Ricci flows with asymptotic solitons
   (with Pak-Yeung Chan and Yongjia Zhang) arXiv, 2021
9. Four-dimensional steady gradient Ricci solitons with 3-cylindrical tangent flows at infinity
   (with Richard H Bamler, Bennett Chow, Yuxing Deng and Yongjia Zhang)
   Adv. Math. 401 (2022): 108285. Journal link; arXiv
10. Perelman's entropy on ancient Ricci flows
    (with Yongjia Zhang) J. Funct. Anal. 281 (2021), no. 9. Journal link; arXiv.
11. On four-dimensional steady gradient Ricci solitons that dimension reduce
    (with Bennett Chow and Yuxing Deng) Adv. Math. 403 (2022): 108367 Journal link ; arXiv

I worked on some machine learning projects in undergrad.