Short CV

Education

B.S. in Mathematics: Nankai University, Chern's class, 2006.09-2010.06.

Ph.D. in Mathematics: Nankai University, 2010.09-2015.06. Supervisor: Prof. Wenchang Sun.

Employment

Postdoctoral researcher: University of Helsinki, 2015.08-2016.10. Mentor: Prof. Tuomas P. Hytönen.

Postdoctoral researcher: BCAM-Basque Center for Applied Mathematics, 2016.11-2019.08. Mentor: Prof. Carlos Pérez.

Research professor: Center for Applied Mathematics, Tianjin University, 2019.09-present.

Grants and Awards

  • Collectanea Mathematica Best Paper Award 2017
  • Juan de la Cierva 2015
  • Excellent Doctoral Dissertation of Nankai University
  • National Scholarship for Graduate students (2012, 2013, 2014)
  • Ten outstanding students in Nankai University (2012, 2013, 2014)

Research interest and selected publications

My research interest lies in the field of harmonic analysis, including wavelet theory, weighted theory and also (multilinear, multiparameter) singular integrals.

About wavelet theory, although I haven't worked on it for several years, I still pay attention to the development in this field from time to time. Wavelet theory also has many applications on pure harmonic analysis, for example, we can use it to characterize function spaces.

Weighted theory is the main topic that I am currently working on. Specifically I am quite interested in the separated bump conjecture, Hytonen-Lacey's one supremum conjecture and the characterization of two weight inequality (Nazarov-Treil-Volberg conjecture). Besides, sparse domination and matrix weight theory are also among my interest.

Regarding to (multilinear, multiparameter) singular integrals, I am very interested in some classical problems. For example the local Tb theorem for multilinear CZOs. Weighted theory related to multilinear (and multiparameter) singular integrals is also one of my favorite topic. Selected publications are listed in below:

  1. K. Li, S. Ombrosi, C. Perez, Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates, Mathematische Annalen, to appear. (arxiv)
  2. K. Li, H. Martikainen, Y. Ou, E. Vuorinen, Bilinear representation theorem, Transactions of the American Mathematical Society, to appear. (arxiv)
  3. W. Damian, M. Hormozi, K. Li, New bounds for bilinear Calderón-Zygmund operators and applications, Revista Matemática Iberoamericana. 34(2018), 1177-1210 (arxiv)
  4. M. Lacey, K. Li, Two weight norm inequalities for the g function, Mathematical Research Letters, 21(2014), no. 3, 521–536.
  5. K. Li, W. Sun, Weak and strong type weighted estimates for multilinear Calderón-Zygmund operators, Advances in Mathematics, 254(2014), 736–771.

Ph.D. Students