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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. |
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Current
Courses
·
Fall
2013, MATH 180, Intermediate Calculus, MWF 12:00-12:50,
2:00-2:50. ·
Spring
2013, MATH 180, Intermediate Calculus, MWF 12:00-12:50.
·
Fall
2012, MATH 180, Intermediate Calculus, MWF 10:00-10:50, 1:00-1:50.
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Research
Papers and Preprints
11.
(with Justin Holmer)
Focusing
Quantum Many-body Dynamics: The Rigorous Derivation of the 1D Focusing Cubic
Nonlinear Schrödinger Equation, submitted,
arXiv:1308.3895. 10.
(with Walter Strauss) Approach to
Equilibrium of a Body Colliding Specularly and
Diffusely with a Sea of Particles, to appear in Archive for Rational Mechanics and Analysis. (arXiv:1305.5219) 9.
(with Justin Holmer)
On the Klainerman-Machedon Conjecture of the
Quantum BBGKY Hierarchy with Self-interaction, submitted, arXiv:1303.5385. 8.
(with Justin Holmer)
On
the Rigorous Derivation of the 2D Cubic Nonlinear Schrödinger Equation from
3D Quantum Many-Body Dynamics, to
appear in Archive
for Rational Mechanics and Analysis. (arXiv:1212.0787) 7.
On the Rigorous Derivation of the 3D Cubic
Nonlinear Schrödinger Equation with A Quadratic Trap, Archive for Rational Mechanics and Analysis,
210 (2013), 365-408. DOI: 10.1007/s00205-013-0645-5.
(arXiv:1204.0125) 6.
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. MR2968164, DOI: 10.1016/j.matpur.2012.02.003.
(arXiv:1102.0593) 5.
Ph.D. Thesis, University of Maryland
- College Park, 2012. Methods of Harmonic
Analysis Applied to Bose-Einstein Condensation.
pdf 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. MR2885567, DOI: 10.1007/s00205-011-0453-8.
(arXiv:1011.5997) 3.
Elementary Proofs for Kato Smoothing Estimates of
Schrödinger-Like Dispersive Equations, Contemporary Mathematics 581
(2012), 63-68. DOI: 10.1090/conm/581/11487. (arXiv:1007.1491) 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. MR2757458 (2011m:35303). 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.
Grants
·
AMS-Simons Travel Grant
2013 - 2015. Invited
Talks
11.
Feb. 6th, 2013: On the Rigorous Derivation of the 3D Cubic Nonlinear Schroedinger Equation with A Quadratic Trap,
Mathematical Physics & Probability Seminar, University of California,
Davis, CA. 10.
Feb. 4th, 2013: On the Rigorous Derivation of the 2D Cubic Nonlinear Schroedinger Equation from 3D Quantum Many-Body Dynamics,
PDE/Analysis Seminar, University of California, Berkeley, CA. 9.
Feb. 1th, 2013: On the Rigorous Derivation of the 2D Cubic Nonlinear Schroedinger Equation from 3D Quantum Many-Body Dynamics,
PDE Seminar, Brown University, Providence, RI. 8.
Oct. 23rd, 2012: On the Rigorous Derivation of the 3D Cubic Nonlinear Schroedinger Equation with A Quadratic Trap,
BU/Brown PDE Seminar, Brown University, Providence, RI. 7.
May 23rd, 2012: On the Rigorous Derivation of the 3D Cubic Nonlinear Schroedinger Equation with A Switchable Quadratic Trap,
PDE Seminar, Tsinghua University, Beijing, China. 6.
Mar. 18th, 2012: The Rigorous Derivation of the 2d Cubic NLS with Anisotropic Switchable
Quadratic Traps, 2012 Spring Eastern AMS Sectional Meeting, George
Washington University, Washington, DC. 5.
Jan. 17th, 2012: The Rigorous Derivation of the 2d Cubic Nonlinear Schrödinger
Equation with Anisotropic Switchable Quadratic Traps, Harmonic Analysis
and Differential Equations Seminar, University of Illinois, Urbana, IL. 4.
Nov. 30th, 2011: The Rigorous Derivation of the 2d Cubic Nonlinear Schrödinger
Equation with Anisotropic Switchable Quadratic Traps, Analysis
Seminar, University of Texas, Austin, TX. 3.
May 5th, 2011: Second Order Corrections to Mean Field Evolution for Weakly
Interacting Bosons in The Case of 3-body Interactions, PDE/Applied
Math Seminar, University of Maryland, College Park, MD. 2.
March 14th, 2011: On the Uniqueness of Solutions to the Gross-Pitaevskii
Hierarchy with A Switchable Quadratic Trap, Applied PDE RIT,
University of Maryland, College Park, MD. 1.
May 21st, 2010: Classical Proofs of Kato Type Smoothing Estimates for the Schrödinger
Equation with Quadratic Potential in Rⁿ⁺¹ with Application,
Analysis Seminar, SUNY Stony Brook, Stony Brook, NY. |