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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. |
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Courses
Award & Grants
·
NSF
DMS-2406620 2024 – 2027. ·
Simons Fellowship 2022 – 2023. ·
NSF
DMS-2005469 2020 – 2024. ·
Dean’s
Office Research Fund 2019 – present. ·
NSF
DMS-1464869 2015 – 2019. ·
AMS-Simons
Travel Grant 2013 - 2015. |
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Research
Publications and Preprints
(My
papers can be found on arXiv. Here
is my Google
Scholar page.)
1.
(with
Shunlin Shen, Ping Zhang and Zhifei Zhang) Global Derivation of the 1D Vlasov-Poisson Equation from Quantum
Many-body Dynamics with Screened Coulomb Potential, arXiv:2408.14767, 46pp, preprint. 2.
(with
Jiahao Wu and Zhifei Zhang) The Second Order 2D
Behaviors of a 3D Bose Gases in the Gross-Pitaevskii Regime, arXiv:2401.15540, 142pp,
submitted. 3.
(with
Justin Holmer) The Derivation of the Boltzmann Equation from
Quantum Many-body Dynamics, arXiv:2312.08239, 106pp,
preprint. 4.
(with
Shunlin Shen and Zhifei Zhang) Sharp Global Well-posedness and Scattering of
the Boltzmann Equation, arXiv:2311.02008, 42pp,
submitted. 5.
(with
Shunlin Shen and Zhifei Zhang) Well/Ill-posedness of the Boltzmann Equation
with Soft Potential, under
revision for Communications in Mathematical Physics.
(arXiv:2310.05042). 6.
(with
Shunlin Shen and Zhifei Zhang) On the mean-field and semiclassical limit from
quantum N-body dynamics, arXiv:2304.03447, 40pp,
submitted. 7.
(with
Shunlin Shen and Zhifei Zhang) Quantitative derivation of the Euler-Poisson
equation from quantum many-body dynamics, Peking Mathematical Journal, 7 (2024) 643-711. DOI: 10.1007/s42543-023-00065-5. 8.
(with
Justin Holmer) Well/ill-posedness bifurcation for the Boltzmann
equation with constant collision kernel, Annals of PDE 10 (2024), Article 14, 1-44. DOI: 10.1007/s40818-024-00177-w. 9.
(with
Shunlin Shen, Jiahao Wu, and Zhifei Zhang) The derivation of the compressible
Euler equation from quantum many-body dynamics, Peking Mathematical Journal, 7 (2024), 35–90. DOI: 10.1007/s42543-023-00066-4. 10. (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. 11. (with Justin
Holmer) Quantitative Derivation
and Scattering of the 3D Cubic NLS in the Energy Space, Annals of PDE 8 (2022), Article
11, 1-39. DOI: 10.1007/s40818-022-00126-5. 12. (with Justin
Holmer) The Unconditional Uniqueness for the
Energy-critical Nonlinear Schrödinger Equation on T^4, Forum of Mathematics, Pi 10 (2022), Article e3 1-49. DOI: 10.1017/fmp.2021.16. 13. (with Justin
Holmer) The Derivation of the Energy-critical NLS from
Quantum Many-body Dynamics,Inventiones Mathematicae 217 (2019), no. 2, 433-547. DOI: 10.1007/s00222-019-00868-3. 14. (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. 15. (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. 16. (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 17. (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. 18. (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. 19. (with Walter
Strauss) Convergence to
Equilibrium of a Body Moving in a Kinetic Sea, SIAM Journal on Mathematical Analysis 47 (2015), no. 6, 4630-4651. DOI: 10.1137/15M1035549. 20. (with Yan Guo) On the Weak
Coupling Limit of Quantum Many-body Dynamics and the Quantum Boltzmann
Equation, Kinetics and
Related Models 8 (2015), no. 3, 443-465. DOI: 10.3934/krm.2015.8.443. 21. (with Walter
Strauss) Velocity Reversal
Criterion of a Body Immersed in a Sea of Particles, Communications in Mathematical Physics 338 (2015), no. 1, 139-168. DOI: 10.1007/s00220-015-2368-y 22. (with Paul
Smith) On the Unconditional
Uniqueness of Solutions to the Infinite Radial Chern-Simons-Schrödinger
Hierarchy, Analysis & PDE 7 (2014), no. 7,
1683-1712. DOI: 10.2140/apde.2014.7.1683. 23. (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. 24. (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. 25. 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. 26. 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. 27. 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. 28. Elementary Proofs
for Kato Smoothing Estimates of Schrödinger-Like Dispersive Equations, Contemporary
Mathematics 581 (2012), 63-68. DOI: 10.1090/conm/581/11487. 29. 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
30. (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
1.
Jul. 12th,
Colloquium, Institute of Theoretical Physics, Chinese Academy of Sciences,
Beijing, China. 2.
Jun. 12th,
PDE Seminar, Shanghai Jiao Tong University, Shanghai, China. 3.
Jun. 12th, PDE
Seminar, ShanghaiTech University, Shanghai, China. 4.
May. 17th,
2024, PMJ Meeting, Peking University, Beijing, China. 5.
Aug. 30th,
2023, Special Lectures for Top Global University Project, Waseda University,
Tokyo, Japan. 6.
Jun. 9th, 2023,
IMS PDE Seminar, the Institute of Mathematical Sciences, Chinese University
of Hongkong. 7.
Apr. 25th,
2023, Mini-Workshop on Nonlinear Analysis, Tohoku University, Sendai, Japan. 8.
Apr. 21st,
2023, NLPDE seminar, Kyoto University, Kyoto, Japan. 9.
Mar. 22nd,
2023, Colloquia, Morningside Center of Mathematics, Chinese Academy of
Sciences, Beijing, China. 10. Mar. 7th, 2023, Colloquia, Academy of Mathematics and Systems
Science, Chinese Academy of Science, Beijing, China. 11. Dec. 14th, 2022, Colloquium, Peking University, Beijing, China. 12. Nov. 14th, 2022, Analysis Seminar, University of Texas, Austin,
TX. 13. Apr. 11th, 2022, Analysis and Geometric Analysis Seminar,
Cornell University, Ithaca, NY. 14. Dec. 12th, 2019, Colloquium, University of Melbourne, Melbourne,
Australia. 15. Mar. 28th, 2019, Random Matrices and Probability Seminar,
Harvard University, Cambridge, MA. 16. Feb. 1st, 2019, Colloquium, Nagoya University, Nagoya, Japan 17. Sep. 28th, 2018, Analysis Seminar, University of Texas, Austin,
TX. 18. Nov. 30th to Dec 4th, 2016 University of Illinois,
Urbana-Champaign, IL. 19. Oct. 28th, 2016, Colloquium, Georgetown University, DC. 20. July. 11th to July 22nd, Applied Math Summer School of Peiking
University, Beijing, China. 21. Apr. 13th, 2016, Colloquium, University of Maryland, College
Park, MD. 22. Mar. 10th, 2016, Analysis Seminar, University of Illinois,
Urbana-Champaign, IL. 23. Dec. 2015, SIAM Conference on Analysis of Partial Differential
Equations, Scottsdale, AZ. 24. Nov. 20th, 2015, Analysis Seminar, University of Toronto,
Toronto, Canada. 25. Nov. 2nd, 2015, International Conference on Nonlinear Analysis
in Honor of Tai-Ping Liu's 70th Birthday, Academia Sinica, Taiwan. 26. Dec. 10th, 2014, BU/Brown PDE Seminar, Boston University,
Boston, MA. 27. Nov. 17th, 2014, Analysis Seminar, Princeton University,
Princeton, NJ. 28. Nov. 14th, 2014, Analysis and PDE Seminar, University of
California, Los Angeles, CA. 29. Oct. 13th, 2014, University of Wisconsin, Madison, WI. 30. Oct. 7th, 2014, PDE Seminar, Georgia Tech, Atlanta, GA. 31. Mar. 4th, 2014, Analysis/PDE Seminar, MIT, Cambridge, MA. 32. Dec. 7th, 2013, 2013 SIAM Conference on Analysis of PDE, Lake
Buena Vista, FL. 33. Oct. 10th, 2013, PDE/Applied Math Seminar, University of
Maryland, College Park, MD. 34. Feb. 6th, 2013, Mathematical Physics & Probability Seminar, University
of California, Davis, CA. 35. Feb. 4th, 2013, PDE/Analysis Seminar, University of California,
Berkeley, CA. 36. May 23rd, 2012, PDE Seminar, Tsinghua University, Beijing,
China. 37. Mar. 18th, 2012, 2012 Spring Eastern AMS Sectional Meeting,
George Washington University, Washington, DC. 38. Jan. 17th, 2012, Harmonic Analysis and Differential Equations
Seminar, University of Illinois, Urbana, IL. 39. Nov. 30th, 2011, Analysis Seminar, University of Texas, Austin,
TX. 40. May 21st, 2010, Analysis Seminar, SUNY Stony Brook, Stony Brook,
NY. |