I am a Professor in the Department of Mathematics at University of Rochester. Prior to coming to Rochester, I served as a Tamarkin Assistant Professor at Brown University. I received my Ph.D. in Mathematics from University of Maryland – College Park in 2012. Here is my CV.
Award & Grants
· Simons Fellowship 2022 – 2023
· NSF DMS-2005469 2020 – present.
· Dean’s Office Research Fund 2019 – present.
· NSF DMS-1464869 2015 – 2019.
· AMS-Simons Travel Grant 2013 - 2015.
Research Publications and Preprints
(My papers can be found on arXiv. Here is my Google Scholar page.)
22. (with Shunlin Shen, Jiahao Wu, and Zhifei Zhang) The derivation of the compressible Euler equation from quantum many-body dynamics, arXiv:2112.14897, 48pp.
21. (with Shunlin Shen and Zhifei Zhang) The unconditional uniqueness for the energy-supercritical NLS, Annals of PDE 8 (2022), Article 14, 1-82. DOI: 10.1007/s40818-022-00130-9.
17. (with Justin Holmer) The Rigorous Derivation of the 2D Cubic Focusing NLS from Quantum Many-body Evolution, International Mathematics Research Notices, 2017, no. 14, 4173–4216. DOI: 10.1093/imrn/rnw113.
16. (with Justin Holmer) Focusing Quantum Many-body Dynamics II: The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger Equation from 3D, Analysis & PDE 10 (2017), no. 3, 589-633. DOI: 10.2140/apde.2017.10.589.
15. (with Justin Holmer) Correlation structures, Many-body Scattering Processes and the Derivation of the Gross-Pitaevskii Hierarchy, International Mathematics Research Notices 2016, no. 10, 3051-3110. DOI: 10.1093/imrn/rnv228
14. (with Justin Holmer) On the Klainerman-Machedon Conjecture of the Quantum BBGKY Hierarchy with Self-interaction, Journal of the European Mathematical Society 18 (2016), no. 6, 1161-1200. DOI: 10.4171/JEMS/610.
13. (with Justin Holmer) Focusing Quantum Many-body Dynamics: The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger Equation, Archive for Rational Mechanics and Analysis 221 (2016), no. 2, 631-676. DOI: 10.1007/s00205-016-0970-6.
8. (with Walter Strauss) Approach to Equilibrium of a Body Colliding Specularly and Diffusely with a Sea of Particles, Archive for Rational Mechanics and Analysis 211 (2014), no. 3, 879-910. DOI: 10.1007/s00205-013-0675-z.
7. (with Justin Holmer) On the Rigorous Derivation of the 2D Cubic Nonlinear Schrödinger Equation from 3D Quantum Many-Body Dynamics, Archive for Rational Mechanics and Analysis 210 (2013), no. 3, 909-954. DOI: 10.1007/s00205-013-0667-z.
6. On the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with A Quadratic Trap, Archive for Rational Mechanics and Analysis 210 (2013), no. 2, 365-408. DOI: 10.1007/s00205-013-0645-5.
5. Collapsing Estimates and the Rigorous Derivation of the 2d Cubic Nonlinear Schrödinger Equation with Anisotropic Switchable Quadratic Traps, Journal de Mathématiques Pures et Appliquées 98 (2012), no. 5, 450-478. DOI: 10.1016/j.matpur.2012.02.003.
4. Second Order Corrections to Mean Field Evolution for Weakly Interacting Bosons in the Case of Three-body Interactions, Archive for Rational Mechanics and Analysis 203 (2012), no. 2, 455-497. DOI: 10.1007/s00205-011-0453-8.
3. Elementary Proofs for Kato Smoothing Estimates of Schrödinger-Like Dispersive Equations, Contemporary Mathematics 581 (2012), 63-68. DOI: 10.1090/conm/581/11487.
2. Classical Proofs of Kato Type Smoothing Estimates for the Schrödinger Equation with Quadratic Potential in Rⁿ⁺¹ with Application, Differential and Integral Equations 24 (2011), no. 3-4, 209-230. pdf
1. (with Yan-Ping Xiao, Mei-Mei Lai, Ji-Xuan Hou, and Quan-Hui Liu) A Secondary Operator Ordering Problem for a Charged Rigid Planar Rotator in Uniform Magnetic Field, Communication of Theoretical Physics, 44 (2005), no. 1, 49-50. DOI: 10.1088/6102/44/1/49.
Selected Invited Talks or Visits
28. Apr. 11th, 2022, Analysis and Geometric Analysis Seminar, Cornell University, Ithaca, NY.
27. Dec. 12th, 2019, Colloquium, University of Melbourne, Melbourne, Australia.
26. Mar. 28th, 2019, Random Matrices and Probability Seminar, Harvard University, Cambridge, MA.
25. Feb. 1st, 2019, Colloquium, Nagoya University, Nagoya, Japan
24. Sep. 28th, 2018, Analysis Seminar, University of Texas, Austin, TX.
23. Nov. 30th to Dec 4th, 2016 University of Illinois, Urbana-Champaign, IL.
22. Oct. 28th, 2016, Colloquium, Georgetown University, DC.
21. July. 11th to July 22nd, Applied Math Summer School of Peiking University, Beijing, China.
20. Apr. 13th, 2016, Colloquium, University of Maryland, College Park, MD.
19. Mar. 10th, 2016, Analysis Seminar, University of Illinois, Urbana-Champaign, IL.
18. Dec. 2015, SIAM Conference on Analysis of Partial Differential Equations, Scottsdale, AZ.
17. Nov. 20th, 2015, Analysis Seminar, University of Toronto, Toronto, Canada.
16. Nov. 2nd, 2015, International Conference on Nonlinear Analysis in Honor of Tai-Ping Liu's 70th Birthday, Academia Sinica, Taiwan.
15. Dec. 10th, 2014, BU/Brown PDE Seminar, Boston University, Boston, MA.
14. Nov. 17th, 2014, Analysis Seminar, Princeton University, Princeton, NJ.
13. Nov. 14th, 2014, Analysis and PDE Seminar, University of California, Los Angeles, CA.
12. Oct. 13th, 2014, University of Wisconsin, Madison, WI.
11. Oct. 7th, 2014, PDE Seminar, Georgia Tech, Atlanta, GA.
10. Mar. 4th, 2014, Analysis/PDE Seminar, MIT, Cambridge, MA.
9. Dec. 7th, 2013, 2013 SIAM Conference on Analysis of PDE, Lake Buena Vista, FL.
8. Oct. 10th, 2013, PDE/Applied Math Seminar, University of Maryland, College Park, MD.
7. Feb. 6th, 2013, Mathematical Physics & Probability Seminar, University of California, Davis, CA.
6. Feb. 4th, 2013, PDE/Analysis Seminar, University of California, Berkeley, CA.
5. May 23rd, 2012, PDE Seminar, Tsinghua University, Beijing, China.
4. Mar. 18th, 2012, 2012 Spring Eastern AMS Sectional Meeting, George Washington University, Washington, DC.
3. Jan. 17th, 2012, Harmonic Analysis and Differential Equations Seminar, University of Illinois, Urbana, IL.
2. Nov. 30th, 2011, Analysis Seminar, University of Texas, Austin, TX.
1. May 21st, 2010, Analysis Seminar, SUNY Stony Brook, Stony Brook, NY.