Ming Xiao        Associate Professor        Department of Mathematics        University of California, San Diego        9500 Gilman Drive #0112        La Jolla, CA 92093-0112        Office: 7426 AP&M        Email: m3xiao@ucsd.edu        Here is my [CV]

Research Interest:

Education:

• 2009 - May 2015, Ph.D. in Mathematics, Rutgers University, USA.

• 2005 - 2009, B.S. in Mathematics, Univ. of Science and Technology of China, Hefei, China.

Appointment:

• July 2021-Present Associate Professor, Department of Mathematics, UCSD

• July 2017-June 2021 Assistant Professor, Department of Mathematics, UCSD

• August 2015-June 2017 J. L. Doob Assistant Professor, Department of Mathematics, UIUC

Publications and submitted papers:

• On the smooth version of the reflection principle for mappings between CR manifolds, (joint with Shiferaw Berhanu), Amer. J. Math. 137 (2015), no.5, 1365-1400. [PDF].

• Nonembeddability into a fixed sphere for a family of compact real algebraic hypersurface, (joint with Xiaojun Huang and Xiaoshan Li), Int. Math. Res. Not.(IMRN). 16 (2015), 7382-7393. [DOI: 10.1093/imrn/rnu167].

• On the regularity of CR mappings between CR manifolds of hypersurface type, (joint with Shiferaw Berhanu), Trans. Amer. Math. Soc. 369 (2017), no.9 6073-6086. [PDF].

• Symmetries in CR complexity theory, (joint with John D'Angelo), Adv. Math. 313 (2017), 590-627.

• Proper holomorphic maps from the unit disk to some unit balls. (joint with John D'Angelo, Zhenghui Huo), Proc. Amer. Math. Soc. 145 (2017), no.6, 2649-2660 [PDF].

• On the embeddability of real hypersurfaces into hyperquadrics, (joint with Ilya Kossovskiy), Adv. Math., 331 (2018), 239-267. arxiv: 1509.01962. [PDF].

• Holomorphic maps from the complex unit ball to type IV classical domains, (joint with Yuan Yuan), Journal de Math\'ematiques Pures et Appliqu\'ees , 133 (2020), 139-166. [PDF].

• Complexity of holomorphic maps from the complex unit ball to classical domains, (joint with Yuan Yuan), Asian J. Math. , 22 (2018), 729-760. (Special issue dedicated to Professor Ngaiming Mok) [PDF].

• Volume-preserving maps between Hermitian symmetric spaces of compact type, (joint with Hanlong Fang and Xiaojun Huang), Advances in Mathematics , 360 (2020), 106885. Here is an expanded note for the submitted version[PDF].

• Bergman-Einstein metrics, a generalization of Kerner's theorem and Stein spaces with spherical boundary (joint with Xiaojun Huang), Crelle's Journal , doi.org/10.1515/crelle-2020-0012.

• Regularity of CR-mappings of codimension one into Levi-degenerate hypersurfaces, (joint with Ilya Kossovskiy and Bernhard Lamel), Comm. Anal. Geom., 29 (2021), 151-181.

• Chern-Moser-Weyl tensor and embeddings into hyperquadrics, (joint with Xiaojun Huang), Harmonic Analysis, partial differential equations , 79-95, Appl. Numer. Harmon. Anal., Birkh\"auser/Springer, Cham, 2017 [PDF].

• Holomorphic isometries between products of complex unit balls, (joint with Shan-Tai Chan and Yuan Yuan), Intern. Math. J. , 28 (2017), no.9, 1740010, 22 pp.

• Symmetries and regularity for holomorphic maps between balls, (joint with John D'Angelo), Math. Res. Lett., 25 (2018), 1389-1404. arxiv: 1711.06539.

• Regularity of mappings into classical domains, Math. Annalen , doi.org/10.1007/s00208-019-01911-7. [PDF].

• A CR embedding problem for an algebraic Levi non-degenerate hypersurface into a hyperquadric, (joint with Xiaojun Huang), Geometric Comlex Analysis, (Special issue dedicatec to Professor Kang-Tae Kim), pp 185-198, Springer Proceedings in Mathematics & Statistics, vol 246. Springer, Singapore.

• A uniformization theorem for Stein spaces, (joint with Xiaojun Huang), Complex Analysis and its Synergies , (2020), 6:6, doi.org/10.1007/s40627-020-00044-x.

• Bergman-harmonic functions on classical domains, Int. Math. Res. Not.(IMRN) , doi.org/10.1093/imrn/rnz260. [PDF].

• Boundary characterization of holomorphic isometric embeddings between indefinite hyperbolic spaces, (joint with Xiaojun Huang, Jin Lu and Xiaomin Tang), Advances in Mathematics , 374, 107388 (2020).

• A high order Hopf lemma for mappings into classical domains and applications, Comm. Anal. Geom. , 29 (2021), 1937-1977.

• Algebraicity of the Bergman kernel, (joint with Peter Ebenfelt and Hang Xu), submitted, arXiv: 2007.00234.

• On the classification of normal Stein spaces and finite ball quotients with Bergman-Einstein metrics, (joint with Peter Ebenfelt and Hang Xu), Int. Math. Res. Not.(IMRN) , doi.org/10.1093/imrn/rnab120.

• Holomorphic mappings between hyperquadrics with positive signature, (joint with Xiaojun Huang), Pure and Applied Math. Quarterly , 18 (2022), 599-616.

• Proper mappings between indefinite hyperbolic spaces and type I classical domains, (joint with Xiaojun Huang, Jin Lu and Xiaomin Tang), to appear in Trans. Amer. Math. Soc., https://doi.org/10.1090/tran/8618, [PDF].

• A theorem on Hermitian rank and mapping problems, to appear in Math. Res. Lett. , [PDF].

• Holomorphic isometric maps from the complex unit ball to reducible bounded symmetric domains, to appear in Crelle's Journal , [PDF].

• Algebraic Bergman kernels and finite type domains in C^2, (joint with Peter Ebenfelt and Hang Xu), to appear in Indiana Univ. Math. J. , arXiv: 2111.07175.

• Kähler-Einstein metrics and obstruction flatness of circle bundles, (joint with Peter Ebenfelt and Hang Xu), submitted, arXiv:2208.13367.

• A new Poincar\'e type rigidity phenomenon with applications, submitted, [PDF].

• Kähler-Einstein metrics and obstruction flatness II: unit sphere bundles, (joint with Peter Ebenfelt and Hang Xu), submitted, arXiv:2303.06408.

Awards:

• National Science Foundation CAREER grant DMS-2045104, 2021-2026.

• National Science Foundation grant DMS-1800549, 2018-2021.

• Named to list of teachers ranked as excellent by their students, UIUC, 2015, 2016, 2017.

• Fall 2012, TA Teaching Excellence Award, Rutgers University.

• Spring 2015, AMS Student Chapter Excellent Research Award at Rutgers University.

Synergistic Activities:

• Co-organizer: A math summer program for high school students [Program link], summer, 2023.

• Co-organizer: A math summer program for high school students [Program link], summer, 2022.

• Co-organizer: A high school math teaching program [Program link], 2021-2022.

• Co-organizer: Virtual Conference on Several Complex Variables, August 2020.

• Co-organizer: Tianyuan International Conference in Several Complex Variables, Changchung, China, July-August 2019.

• Co-organizer: Special Session on Several Complex Variables at AMS Spring Central and Western Joint Sectional Meeting, Honolulu, HI, March 2019.

• Co-organizer: Southern California Analysis and PDE conference (SCAPDE), University of California, San Diego, San Diego, CA, 2018.

• Co-organizer: AMS Fall Eastern Sectional Meeting, Special Session on CR geometry and PDE in complex analysis, SUNY Buffalo, Buffalo, NY, 2017.

• Co-organizer: International Workshop in Several Complex Variables at Jilin Normal University, Changchun, China, 2017

• Co-organizer: International Workshop in Complex Geometry at Capital Normal University, Beijing, China, 2016

• Co-organizer: Several Complex Variables and CR Geometry seminar, UIUC

• Led an Illinois Geometry Lab research project at UIUC, Fall 2015

Invited Talks:

• June 2022, Several Complex Variables Seminar (online), IBS Center for Complex Geometry, Korea.

• January 2022, AMS Special Session on Several Complex Variables, Geometric PDE and CR geometry, Joint Mathematics Meetings, Seattle, WA (changed to online).

• October, 2021, Brazilian Webinar on Approximation Theory, Harmonic Analysis and related topics (online), Brazil.

• March, 2021, PDE and Differential Geometry Seminar (online), University of Connecticut, CT.

• March, 2021, Seminar semiklassische Analysis und Darstellungstheorie (online), University of Cologne, Germany.

• November 2017, AMS Fall Western Sectional Meeting, Special Session on Several Complex Variables, University of California-Riverside, Riverside, CA.

• October 2017, Midwest Workshop on Asymptotic Analysis, IUPUI, Indianapolis, IN.

• August 2017, 9th Workshop on Geometric Analysis of PDEs and Several Complex Variables, Serra Negra, Brazil.

• January 2017, International Conference in Several Complex Variables and Partial Differential Equations, Texas A&M Univ. at Qatar, Doha, Qatar.

• May 2016, Midwest Several Complex Variables Conference, University of Toledo,Toledo,OH.

• April 2016, AMS Spring Western Sectional Meeting, Special Session on CR geometry and Partial Differential Equations in Complex Analysis, University of Utah, Salt Lake City, UT.

• January 2016, International Conference on PDE, Complex Analysis and Related Topics, Florida International University, Miami, FL.

• May 2015, Analysis Seminar. University of California-San Diego, San Diego, CA.

• April 2015, Analysis Seminar. University of California-Irvine, Irvine, CA.

• January 2015, International Conference on Several Complex Variables, Texas A&M Univ. at Qatar, Doha, Qatar.

• November 2014, Analysis Seminar, Temple Univ., Philadelphia, PA.

• October 2014, AMS Fall Western Sectional Meeting, Special Session on Recent Progress in Harmonic Analysis and Complex Variables, San Francisco State University, San Francisco, CA.

• September 2014, Analysis Seminar, Syracuse University, Syracuse, NY.

• May 2014, International Conference on Complex Analysis and Geometry, Wuhan University, Wuhan, Hubei, China.

• March 2014, AMS Spring Eastern Sectional Meeting, Special Session on Interaction between Complex and Geometric Analysis, Univ. of Maryland, Baltimore, MD.

• October 2013, AMS Fall Eastern Sectional Meeting, Special Session on Several Complex Variables and CR geometry, Temple University, Philadelphia, PA.