# Nam Le

Mathematics Department
Columbia University
New York, NY 10027

Office: Room 607
Phone: (212) 854-3210
Email: namle at math dot columbia dot edu

I am a Ritt Assistant Professor in the department of mathematics at Columbia University.
I received my Ph.D. from New York University in 2008 under the supervision of Professor Sylvia Serfaty .

My mathematical interests are Partial Differential Equations, Geometric Analysis and the Calculus of Variations . Specifically, I have been studying the Linearized Monge-Ampere equations and their applications to nonlinear, fourth order, geometric partial differential equations, the Mean Curvature Flow, and Gamma-convergence and its applications in Mathematical Physics.

## Teaching

Spring 2013:
Fall 2012: Spring 2010:

## Publications

Geometric PDE: Linearized Monge--Ampere equations and applications to nonlinear, fourth-order equations

17 .  N. Q. Le, O. Savin, On global $C^{1,\alpha}$ estimates for solutions to the linearized Monge-Amp\`ere equations, arXiv:1303.3305v2 [math.AP], to appear in Proc. Amer. Math. Soc .pdf file

16.   N. Q. Le, T. Nguyen, Global $W^{2,p}$ estimates for solutions to the linearized Monge-Ampere equations, Math. Ann. 358 (2014), no. 3-4, 629-700 .pdf file

15.   N. Q. Le, T. Nguyen, Geometric properties of boundary sections of solutions to the Monge-Ampere equation and applications, J. Funct. Anal. 264 (2013), no. 1, 337-361 .pdf file

14 .  N. Q. Le, O. Savin, Some minimization problems in the class of convex functions with prescribed determinant, Anal. PDE. 6 (2013), no. 5, 1025-1050 .pdf file

13 .  N. Q. Le, O. Savin, Boundary regularity for solutions to the linearized Monge-Ampere equations, Arch. Ration. Mech. Anal. 210 (2013), no. 3, 813-836 .pdf file

12 .  N. Q. Le, Global second derivative estimates for the second boundary value problem of the prescribed affine mean curvature and Abreu's equations, Int Math Res Notices, 11 (2013) 2421-2438 .pdf file

Geometric Analysis: Mean curvature flow and Ricci flow

11 .  N. Q. Le, N. Sesum, Remarks on the curvature behavior at the first singular time of the Ricci flow, Pacific J. Math, 255 (2012), no. 1, 155-175 .pdf file

10 .  N. Q. Le, N. Sesum, Blow-up rate of the mean curvature during the mean curvature flow and a gap theorem for self-shrinkers, Comm. Anal. Geom, 19 (2011), no. 4, 633-659 .pdf file

9 .  N. Q. Le, Blow up of subcritical quantities at the first singular time of the mean curvature flow, Geom. Dedicata, 151 (2011), no. 1, 361--371 .pdf file

8 .  N. Q. Le, N. Sesum, On the extension of the mean curvature flow, Math. Z, 267 (2011), no. 3--4, 583--604 .pdf file

7 .  N. Q. Le, N. Sesum, The mean curvature at the first singular time of the mean curvature flow, Ann. Inst. H. Poincare Anal. Non Lineaire, 27 (2010), no. 6, 1441--1459 .pdf file

Calculus of Variations: Aspects of Gamma-convergence

6 .  N. Q. Le, On the second inner variation of the Allen-Cahn functional and its applications, Indiana Univ. Math. J. 60 (2011), no. 6, 1843-1856 .pdf file

5 .  N. Q. Le, On the convergence of the Ohta-Kawasaki Equation to motion by nonlocal Mullins-Sekerka Law, SIAM. J. Math. Analysis. 42 (2010), no. 4, 1602--1638 .pdf file

4.  N. Q. Le, Convergence results for critical points of the one-dimensional Ambrosio-Tortorelli functional with fidelity term, Adv. Differential Equations. 15 (2010), no. 3-4, 255-282 .pdf file

3.  G. A. Francfort, N. Q. Le and S. Serfaty, Critical Points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case, ESAIM Control Optim. Calc. Var. 15 (2009), no. 3, 576--598 .pdf file

2.  N. Q. Le, Regularity and Non-existence Results for Some Free-interface Problems Related to Ginzburg-Landau Vortices, Interfaces Free Bound. 11 (2009), no. 1, 139--152.pdf file

1.  N. Q. Le, A Gamma-Convergence Approach to the Cahn-Hilliard Equation, Calc. Var. Partial Differential Equations. 32 (2008), no. 4, 499--522 .pdf file

3. D. D. Trong, N. L. Luc, L. Q. Nam and T. T. Tuyen, Reconstruction of $H^{p}$-functions: Best Approximation, Regularization and Optimal Error Estimates, Complex Var. Theory Appl. 49 (2004), no. 4, 285--301. pdf file