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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 –present. ·
Schwartz Discover Grant for Undergraduate
Summer Research 2025 (Mentor). ·
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 Jiahao
Wu and Zhifei Zhang) The second order
Huang-Yang approximation to the Fermi thermodynamic pressure, arXiv:2505.23136,
89pp. 2.
(with Shunlin Shen and Zhifei Zhang)
l^2-decoupling and the unconditional uniqueness for the Boltzmann equation,
under revision for Communications
in Mathematical Physics. (arXiv:2501.14697, 31pp) 3.
(with Jiahao
Wu and Zhifei Zhang) The second order
Huang-Yang formula to the 3D Fermi gas: the Gross-Pitaevskii regime, arXiv:2410.16620,
122pp. 4.
(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. 5.
(with Jiahao
Wu and Zhifei Zhang) The Second Order 2D
Behaviors of a 3D Bose Gases in the Gross-Pitaevskii Regime, under revision for Communications
of the American Mathematical Society. (arXiv:2401.15540, 142pp) 6.
(with Justin Holmer) The Derivation of the Boltzmann
Equation from Quantum Many-body Dynamics, arXiv:2312.08239, 106pp. 7.
(with Shunlin Shen and Zhifei Zhang)
Sharp Global Well-posedness and Scattering of the Boltzmann Equation, arXiv:2311.02008, 42pp. 8.
(with Shunlin Shen and Zhifei Zhang)
Well/Ill-posedness of the Boltzmann Equation with Soft Potential, Communications in Mathematical Physics
405 (2024), Article 283, 1-51.
DOI: 10.1007/s00220-024-05157-6. 9.
(with Shunlin Shen and Zhifei Zhang) On the
mean-field and semiclassical limit from quantum N-body dynamics, Journal of Functional Analysis 28 (2025),
Article 111100, 1-54. DOI: 10.1016/j.jfa.2025.111100. 10. (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. 11. (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. 12. (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. 13. (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. 14. (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. 15. (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. 16. (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. 18. (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. 19. (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 20. (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. 21. (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. 22. (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. 23. (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. 24. (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 25. (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. 26. (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. 27. (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. 28. 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. 29. 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. 30. 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. 31. Elementary
Proofs for Kato Smoothing Estimates of Schrödinger-Like Dispersive Equations,
Contemporary Mathematics 581 (2012), 63-68.
DOI: 10.1090/conm/581/11487. 32. 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
33. (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. Undergraduate Research Publication Advised
1.
A. Rohrbach,
Bernstein polynomials: a bridge between the Weierstrass Theorem and a Landau
temperature fluctuation problem,
SIAM Journal of Undergraduate Research,
18 (2025) 205-212. DOI: 10.1137/25S172954X. Selected Invited Talks or Visits
1.
Oct. 25th, 2025, Brown-Yale Seminar, Brown
University, Providence, RI. 2.
Jul. 7th, 2025, Oberseminar Mathematische Physik,
Institute for Applied Mathematics, Universität Bonn, Bonn, Germany. 3.
Nov. 28th, 2024, Mathematical Physics and PDE
Seminar, ETH Zürich, Switzerland. 4.
Jul. 12th, 2024, Colloquium, Institute of
Theoretical Physics, Chinese Academy of Sciences, Beijing, China. 5.
Jun. 12th, 2024, PDE Seminar, Shanghai Jiao
Tong University, Shanghai, China. 6.
Jun. 12th, 2024, PDE Seminar, ShanghaiTech
University, Shanghai, China. 7.
May. 17th, 2024, PMJ Meeting, Peking
University, Beijing, China. 8.
Aug. 30th, 2023, Special Lectures for Top
Global University Project, Waseda University, Tokyo, Japan. 9.
Jun. 9th, 2023, IMS PDE Seminar, the Institute
of Mathematical Sciences, Chinese University of Hongkong. 10. Apr. 25th,
2023, Mini-Workshop on Nonlinear Analysis, Tohoku University, Sendai, Japan. 11. Apr. 21st,
2023, NLPDE seminar, Kyoto University, Kyoto, Japan. 12. Mar. 22nd,
2023, Colloquia, Morningside Center of Mathematics, Chinese Academy of
Sciences, Beijing, China. 13. Mar. 7th,
2023, Colloquia, Academy of Mathematics and Systems Science, Chinese Academy
of Science, Beijing, China. 14. Dec. 14th,
2022, Colloquium, Peking University, Beijing, China. 15. Nov. 14th,
2022, Analysis Seminar, University of Texas, Austin, TX. 16. Apr. 11th,
2022, Analysis and Geometric Analysis Seminar, Cornell University, Ithaca, NY. 17. Dec. 12th,
2019, Colloquium, University of Melbourne, Melbourne, Australia. 18. Mar. 28th,
2019, Random Matrices and Probability Seminar, Harvard University, Cambridge,
MA. 19. Feb. 1st,
2019, Colloquium, Nagoya University, Nagoya, Japan 20. Sep. 28th,
2018, Analysis Seminar, University of Texas, Austin, TX. 21. Nov. 30th to
Dec 4th, 2016 University of Illinois, Urbana-Champaign, IL. 22. Oct. 28th,
2016, Colloquium, Georgetown University, DC. 23. July. 11th
to July 22nd, Applied Math Summer School of Peiking University, Beijing,
China. 24. Apr. 13th,
2016, Colloquium, University of Maryland, College Park, MD. 25. Mar. 10th,
2016, Analysis Seminar, University of Illinois, Urbana-Champaign, IL. 26. Dec. 2015,
SIAM Conference on Analysis of Partial Differential Equations, Scottsdale,
AZ. 27. Nov. 20th,
2015, Analysis Seminar, University of Toronto, Toronto, Canada. 28. Nov. 2nd,
2015, International Conference on Nonlinear Analysis in Honor of Tai-Ping
Liu's 70th Birthday, Academia Sinica, Taiwan. 29. Dec. 10th,
2014, BU/Brown PDE Seminar, Boston University, Boston, MA. 30. Nov. 17th,
2014, Analysis Seminar, Princeton University, Princeton, NJ. 31. Nov. 14th,
2014, Analysis and PDE Seminar, University of California, Los Angeles, CA. 32. Oct. 13th,
2014, University of Wisconsin, Madison, WI. 33. Oct. 7th,
2014, PDE Seminar, Georgia Tech, Atlanta, GA. 34. Mar. 4th,
2014, Analysis/PDE Seminar, MIT, Cambridge, MA. 35. Dec. 7th,
2013, 2013 SIAM Conference on Analysis of PDE, Lake Buena Vista, FL. 36. Oct. 10th,
2013, PDE/Applied Math Seminar, University of Maryland, College Park, MD. 37. Feb. 6th,
2013, Mathematical Physics & Probability Seminar, University of
California, Davis, CA. 38. Feb. 4th,
2013, PDE/Analysis Seminar, University of California, Berkeley, CA. 39. May 23rd,
2012, PDE Seminar, Tsinghua University, Beijing, China. 40. Mar. 18th,
2012, 2012 Spring Eastern AMS Sectional Meeting, George Washington
University, Washington, DC. 41. Jan. 17th,
2012, Harmonic Analysis and Differential Equations Seminar, University of
Illinois, Urbana, IL. 42. Nov. 30th,
2011, Analysis Seminar, University of Texas, Austin, TX. 43. May 21st,
2010, Analysis Seminar, SUNY Stony Brook, Stony Brook, NY. |