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I am
a Tamarkin Assistant Professor in the Department of Mathematics at Brown University. |
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Current Courses
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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
8.
(with Justin Holmer) On
the Rigorous Derivation of the 2D Cubic Nonlinear Schrödinger Equation from
3D Quantum Many-Body Dynamics, 41pp, submitted, arXiv:1212.0787. 7.
On
the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with A
Quadratic Trap, 30pp,
submitted, 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. 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.
DOI: 10.1007/s00205-011-0453-8.
MR2885567. (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. 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. |