I am a postdoctoral researcher associate at Bielefeld University in Germany and a member of Prof. Dr. Michael Röckner's group under Project B1 of SFB 1283.
Email: zhao@math.uni-bielefeld.de
About Me
My research is mostly concerned with stochastic differential equations (SDE) and distributional dependent SDE (DDSDE), and in particular the regularization by noise with singular and distribution drifts. My research includs the second-order kinetic systems, non-linear Fokker-Planck equations, propagation of chaos of N-particle systems and averaging principle for DDSDE.
I completed my PhD (Dr. Math.) in July 2023 at Bielefeld University , under the supervision of Prof. Dr. Michael Röckner and in June 2023 at Wuhan University, under the supervision of Prof. Dr. Xicheng Zhang. Before starting PhD, I finished my Bachelor at Wuhan University.
Background
Education
Doctorate in Mathematics
07/2020-07/2023 / Bielefeld University
Thesis name: McKean-Vlasov SDEs with singular drifts.[pdf]
supervisor: Prof. Dr. Michael Röckner
Ph.D. in Mathematics
09/2018-06/2023 / Wuhan University
Thesis name: Singular kinetic mean-field SDEs. [pdf]
supervisor: Prof. Dr. Xicheng Zhang
B.S. in Mathematics
09/2014-06/2018 / Wuhan University
Thesis name: Hardy-Littlewood maximal function and singular integral.[pdf]
Thesis advisor: Prof. Dr. Xicheng Zhang
Employment
Postdoc
07/2023-Present / Bielefeld University
Advisor: Prof. Dr. Michael Röckner
Preprints and publications
To appear in Ann. Probab. [arXiv]
SIAM Journal on Mathematical Analysis 56(2) (March 2024) [arXiv]
Bernoulli 30(2): 1586-1610 (May 2024) [arXiv]
Ann. Probab. 52(2): 576-657 (March 2024) [arXiv]
Potential Anal. (October 2023) [arXiv]
Stochastic Process. Appl. 164 416–442 (October 2023) [arXiv]
J. Theoret. Probab. 34(4) 1870–1916 (December 2021) [arXiv]
J. Differential Equations 274 996–1014 (February 2021) [arXiv]
Electron. J. Probab. 25 1--23 (October 2020) [arXiv]
J. Math. Pures Appl. 140 139--184 (August 2020) [arXiv]
Conferences and Talks
- 17/09/2024 , Quantitative approximation of kinetic SDEs: from discrete to continuum Recent Developments in Dirichlet Form Theory and Related Fields, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany.[slides]
- 09/08/2024 , Supercritical McKean-Vlasov SDE driven by cylindrical alpha-stable process: well-posedness, propagation of chaos and Euler's approximation Summer School on Propagation of Chaos in Analysis and Probability, Peking University, Beijing, China.[slides]
- 25/07/2024 , Singular kinetic SDEs The 19th Workshop on Markov Processes and Related Topics, Fujian Normal University, Fuzhou, China.[slides]
- 17/07/2024 , Flow-distribution dependent SDEs and Navier-Stokes equations with fractional Brownian motion. the 9th European Congress of Mathematics--Mini-Symposia - 45 - Regularisation by noise, Seville ,Spain. [slides]
- 27/06/2024 , SDEs with supercritical distributional drifts. Young Summer School on Stochastic Analysis, Linnaeus University, Växjö, Sweden. [slides]
- 04/06/2024 , Flow-distribution dependent SDEs and Navier-Stokes equations with fractional Brownian motion. International-conference: One-parameter semigroups of operators 2024: Stochastic & Dynamics, Université Laval, Online. [slides]
- 29/05/2024 , Flow-distribution dependent SDEs and Navier-Stokes equations with fractional Brownian motion. Stochastic Webinar, Academy of Mathematic and Systems Science Chinese Academy of Sciences and Beijing Institute of Technology, Online. [slides] [video]
- 12/03/2024 , SDEs with supercritical distributional drifts. Research seminars-Non-local operators, probability and singularities, Online. [slides] [video]
- 20/12/2023 , Second order fractional mean-field SDEs with singular kernels and measure initial data. Mean field interactions with singular kernels and their approximations, Paris, Institut Henri Poincaré. [slides]
- 24/08/2023 , Strong convergence of propagation of chaos for McKean-Vlasov SDEs with singular interactions (Online talk). 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023), Waseda University, Tokyo, Japan. [slides]
- 31/07/2023 , SDEs with supercritical distributional drifts and RDEs with subcritical drifts. The 18th Workshop on Markov Processes and Related Topics, Tianjin University, Tianjin, China.[slides]
- 28/08/2022 , Singular kinetic equations. The 7th National Conference on Probability Theory, Shangdong University, Weihai, China.[slides]
- 14/05/2022 , Strong convergence of propagation of chaos for McKean-Vlasov SDEs with singular interactions. 15th Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis, Berlin, Germany.[slides]
- 17/08/2020 , Euler approximation for SDEs with irregular coefficients. CRC Retreat 2020, Bielefeld, Germany. [slides]
- 05/12/2019 , Gradient estimate for SDEs driven by cylindrical Levy processes. LSA winter meeting-2019, National Research University Higher School of Economics, Moscow, Russia.
- 09/08/2019 , Heat kernel of nonlocal kinetic operators. Workshop for Stochastic Analysis, Peking University, Beijing, China.[slides]
- 08/07/2019 , Gradient estimate for SDEs driven by cylindrical Levy processes. The 7th IMS-China, International Conference on Stochastic and Probability, Dalian University of Technology, Dalian, China.[slides]
- 05/06/2019 , Gradient estimates for SDEs driven by cylindrical \alpha-stable processes. Workshop on Stochastic Analysis and Applications, Nanyang Technological University, Singapore.[slides]
- 11/03/2029 , Schauder estimates for nonlocal kinetic equations and applications. Perturbation Techniques in Stochastic Analysis and Its Applications, CIRM, Marseille, France. [slides]