I am a Tamarkin Assistant Professor in the Department of Mathematics at Brown University. Prior to coming to Brown, I received my Ph.D. in Mathematics from University of Maryland – College Park in 2012. Here is my CV. I am co-organizing the Brown PDE seminar with Yan Guo. Here is the PDE seminar schedule.
Research Papers and Preprints
(My papers can be found on arXiv. Here is my Google Scholar page.)
15. (with Yan Guo) On the Weak Coupling Limit of Quantum Many-body Dynamics and the Quantum Boltzmann Equation, Kinetics and Related Model 8 (2015), no. 3, 443-465. DOI: 10.3934/krm.2015.8.443. (arXiv:1412.1775)
12. (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. (arXiv:1406.2649).
11. (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. (arXiv:1404.0652).
9. (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. (arXiv:1305.5219)
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. (arXiv:1212.0787)
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. (arXiv:1204.0125)
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. (arXiv:1102.0593)
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. (arXiv:1011.5997)
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 (arXiv:1003.4330)
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.
· AMS-Simons Travel Grant 2013 - 2015.
Selected Invited Talks
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.