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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
·
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. |
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Research
Publications and Preprints
(My
papers can be found on arXiv. Here
is my Google
Scholar page.)
24. (with Shunlin Shen and Zhifei Zhang) Quantitative
derivation of the Euler-Poisson equation from quantum many-body dynamics, Peking Mathematical Journal, 71pp. DOI: 10.1007/s42543-023-00065-5. 23. (with Justin
Holmer) Well/ill-posedness
bifurcation for the Boltzmann equation with constant collision kernel, arXiv:2206.11931, 31pp. 22. (with Shunlin Shen, Jiahao Wu, and Zhifei Zhang)
The derivation of the compressible Euler equation from quantum many-body
dynamics, Peking Mathematical
Journal, 58pp. DOI: 10.1007/s42543-023-00066-4. (arXiv:2112.14897) 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. 20. (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. 19. (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. 18. (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. 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. 12. (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. 11. (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. 10. (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 9.
(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. 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
34. Apr. 25th, 2023, Mini-Workshop on Nonlinear Analysis, Tohoku
University, Sendai, Japan. 33. Apr. 21st, 2023, NLPDE seminar, Kyoto University, Kyoto, Japan. 32. Mar. 22nd, 2023, Colloquia, Morningside Center of Mathematics,
Chinese Academy of Sciences, Beijing, China. 31. Mar. 7th, 2023, Colloquia, Academy of Mathematics and Systems
Science, Chinese Academy of Science, Beijing, China. 30. Dec. 14th, 2022, Colloquium, Peking University, Beijing, China. 29. Nov. 14th, 2022, Analysis Seminar, University of Texas, Austin,
TX. 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. |