

I am an Associate 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. 

Courses


Research
Papers and Preprints
(My
papers can be found on arXiv. Here
is my Google
Scholar page.)
19.
(with
Justin Holmer) The Unconditional Uniqueness
for the Energycritical Nonlinear Schrödinger Equation on T^4, arXiv:2006.05915,
56pp. 18.
(with
Justin Holmer) The Derivation of the
Energycritical NLS from Quantum Manybody Dynamics,Inventiones Mathematicae 217
(2019), no. 2, 433547. DOI: 10.1007/s00222019008683. 17.
(with
Justin Holmer) The Rigorous
Derivation of the 2D Cubic Focusing NLS from Quantum Manybody Evolution, International Mathematics Research Notices, 2017, no. 14, 4173–4216. DOI: 10.1093/imrn/rnw113. 16.
(with
Justin Holmer) Focusing Quantum
Manybody Dynamics II: The Rigorous Derivation of the 1D Focusing Cubic
Nonlinear Schrödinger Equation from 3D, Analysis & PDE 10 (2017), no. 3,
589633. DOI: 10.2140/apde.2017.10.589. 15.
(with
Justin Holmer) Correlation
structures, Manybody Scattering Processes and the Derivation of the GrossPitaevskii Hierarchy, International Mathematics Research Notices 2016, no. 10,
30513110. DOI: 10.1093/imrn/rnv228 14.
(with
Justin Holmer) On the KlainermanMachedon Conjecture of the Quantum BBGKY
Hierarchy with Selfinteraction, Journal
of the European Mathematical Society 18 (2016), no. 6, 11611200. DOI: 10.4171/JEMS/610. 13.
(with Justin Holmer) Focusing Quantum
Manybody Dynamics: The Rigorous Derivation of the 1D Focusing Cubic
Nonlinear Schrödinger Equation, Archive for Rational
Mechanics and Analysis 221 (2016),
no. 2, 631676. 12.
(with Walter
Strauss) Convergence to
Equilibrium of a Body Moving in a Kinetic Sea, SIAM Journal on Mathematical Analysis 47 (2015), no. 6, 46304651. DOI: 10.1137/15M1035549. 11.
(with
Yan Guo) On the Weak
Coupling Limit of Quantum Manybody Dynamics and the Quantum Boltzmann
Equation, Kinetics and
Related Model 8 (2015), no. 3, 443465. 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, 139168. DOI: 10.1007/s002200152368y 9.
(with Paul
Smith) On the
Unconditional Uniqueness of Solutions to the Infinite Radial ChernSimonsSchrödinger Hierarchy, Analysis & PDE 7 (2014), no. 7,
16831712. 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, 879910.
DOI: 10.1007/s002050130675z. 7.
(with
Justin Holmer) On the Rigorous
Derivation of the 2D Cubic Nonlinear Schrödinger Equation from 3D Quantum
ManyBody Dynamics, Archive for Rational Mechanics and Analysis 210
(2013), no. 3, 909954. DOI: 10.1007/s002050130667z. 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, 365408. DOI: 10.1007/s0020501306455. 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, 450478. DOI: 10.1016/j.matpur.2012.02.003. 4.
Second Order Corrections to
Mean Field Evolution for Weakly Interacting Bosons in the Case of Threebody
Interactions, Archive for Rational Mechanics and Analysis
203 (2012), no. 2, 455497. DOI: 10.1007/s0020501104538. 3.
Elementary Proofs for Kato
Smoothing Estimates of SchrödingerLike Dispersive Equations, Contemporary
Mathematics 581 (2012), 6368. 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. 34, 209230. pdf
1.
(with YanPing Xiao, MeiMei Lai, JiXuan Hou,
and QuanHui Liu) A Secondary Operator Ordering Problem for a Charged Rigid Planar
Rotator in Uniform Magnetic Field, Communication
of Theoretical Physics, 44 (2005), no. 1, 4950. DOI: 10.1088/6102/44/1/49. Grants
·
NSF
DMS2005469 2020 – present. ·
NSF
DMS1464869 2015 – 2019. ·
AMSSimons
Travel Grant 2013  2015. Selected
Invited Talks or Visits
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, UrbanaChampaign, 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, UrbanaChampaign, 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 TaiPing
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. 