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Curriculum Vitae, Nam Q Nam Q. Le Contact Indiana University, Bloomington Tel: (1) 812-855-8538 (office) Information Department of Mathematics Fax: 812-855-0046 Rawles Hall 432 Email: [email protected] 831 E 3rd St, Bloomington, IN 47405 https://nqle.pages.iu.edu/ Research Partial Differential Equations, the Calculus of Variations, Geometric Analysis Interests Education Courant Institute of Mathematical Sciences, New York University Ph.D in Mathematics, September 2008; M.S. in Mathematics, May 2006 • Dissertation: Analysis of Several Sharp-interface Limits in Variational Problems • Advisor: Professor Sylvia Serfaty Vietnam National University at Hochiminh City B.S. in Mathematics, 2002 • Valedictorian Academic 2018- Associate Professor of Mathematics, Department of Mathematics, In- Appointments diana University at Bloomington, Indiana, USA 2014-2018 Vaclav Hlavaty Assistant Professor of Mathematics, Department of Mathematics, Indiana University at Bloomington, IN, USA 2013-2014 Researcher, Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam 2013-2013 Senior Researcher, the Vietnam Institute for Advanced Study in Math- ematics, Hanoi, Vietnam 2008-2013 Ritt Assistant Professor, Department of Mathematics, Columbia Uni- versity, New York, NY, USA (on leave 07/2011-06/2012) 2011- 2012 Assistant Professor of Mathematics, Tan Tao University, Vietnam 2002- 2004 Instructor, Vietnam National University at Hochiminh City Visiting positions 2016 Visiting Associate Professor, Tokyo Institute of Technology, from Oc- tober 01, 2016 to October 31, 2016. 2012 Visiting Fellow, Mathematical Sciences Institute, Australian National University from January 10, 2012 to February 20, 2012. Honors and June 2018 Work with Ovidiu Savin, published in Inventiones, was included in a Awards Bourbaki Seminar on the Monge-Amp`ereequation by Alessio Figalli 2018 Trustees' Teaching Award, Indiana University Bloomington 2018 Outstanding Junior Faculty Award, Indiana University Bloomington 2013 Scientific Prize of the Institute of Mathematics, Vietnam Academy of Science and Technology 2006 Harold Grad Memorial Prize, Courant Institute, New York University 2005{2008 Henry MacCracken Fellowship, New York University 2004-2008 Vietnam Education Foundation Fellowship 2002 Valedictorian, Vietnam National University at Hochiminh City 1997 Gold Medal, Asian Pacific Mathematics Olympiad Editorial Boards 05/2020{ Indiana University Mathematics Journal (IUMJ), Editor Curriculum Vitae, Nam Q. Le, May 2021, 1 Grants 2021 NSF Grant DMS-2054686 ($178,120), Partial Differential Equations with and without Convexity Constraints, 2021-2024 2018 NSF Grant DMS-1764248 ($168,820), Regularity Estimates for the Lin- earized Monge-Amp`ere and Degenerate Monge-Amp`ere Equations and Applications in Nonlinear Partial Differential Equations, 2018-2021 2015 NSF Grant DMS-1500400 ($150,000), The linearized Monge-Amp`ere equation and applications in nonlinear, geometric partial differential equations, 2015-2018 2015 Indiana University Summer Faculty Fellowship ($8000) 2010 NSF Travel grant ($3050) to ICM-2010, Hyderabad, India. Book 29. N. Q. Le, H. Mitake and H. V. Tran, Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Amp`ere Equations, Lecture Notes in Math- ematics, vol. 2183, Springer, Cham, 2017, vii + 228. Publications 1. D. M. Duc, N. L. Luc, L. Q. Nam and T. T. Tuyen, On Topological Degree for Potential Operators of Class (S)+ , Nonlinear Anal. 55 (2003), no. 7-8, 951{968. 2. D. D. Trong, N. L. Luc, L. Q. Nam and T. T. Tuyen, Reconstruction of Hp- functions: Best Approximation, Regularization and Optimal Error Estimates, Complex Var. Theory Appl. 49 (2004), no. 4, 285{301. 3. D. M. Duc, N. L. Luc, L. Q. Nam and T. T. Tuyen, Multiple Solutions for a Nonlinear Singular Dirichlet Problem, Abstract and applied analysis, 51{63, World Sci. Publishing, River Edge, NJ, 2004. 4. N. Q. Le, A Gamma-Convergence Approach to the Cahn-Hilliard Equation, Calc. Var. Partial Differential Equations. 32 (2008), no. 4, 499{522. 5. 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. 6. 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. 7. 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. 8. 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. 9. N. Q. Le and 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. 10. N. Q. Le and N. Sesum, On the extension of the mean curvature flow, Math. Z. 267 (2011), no. 3{4, 583{604. 11. 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. 12. N. Q. Le and 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), Curriculum Vitae, Nam Q. Le, May 2021, 2 no. 4, 633{659. 13. 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. 14. N. Q. Le and 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. 15. N. Q. Le and T. Nguyen, Geometric properties of boundary sections of solutions to the Monge{Amp`ereequation and applications, J. Funct. Anal. 264 (2013), no. 1, 337{361. 16. 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 (2013), 2421{2438. 17. N. Q. Le and O. Savin, Boundary regularity for solutions to the linearized Monge- Amp`ereequations, Arch. Ration. Mech. Anal. 210 (2013), no. 3, 813{836. 18. N. Q. Le and O. Savin, Some minimization problems in the class of convex functions with prescribed determinant, Anal. PDE. 6 (2013), no. 5, 1025{1050. 19. N. Q. Le and T. Nguyen, Global W 2;p estimates for solutions to the linearized Monge{Amp`ereequations, Math. Ann. 358 (2014), no. 3-4, 629{700. 20. N. Q. Le and O. Savin, On boundary H¨oldergradient estimates for solutions to the linearized Monge-Amp`ereequations, Proc. Amer. Math. Soc. 143 (2015), no. 4, 1605{1615. 21. N. Q. Le, On the second inner variations of Allen-Cahn type energies and appli- cations to local minimizers, J. Math. Pures Appl. 103 (2015), no. 6, 1317-1345. 22. N. Q. Le, W 4;p solution to the second boundary value problem of the prescribed affine mean curvature and Abreu's equations, J. Differential Equations. 260 (2016), no. 5, 4285{4300. 23. N. Q. Le, Remarks on the Green's function of the linearized Monge-Amp`ere operator, Manuscripta Math. 149 (2016), no. 1, 45{62. 24. N. Q. Le, The second boundary value problem of the prescribed affine mean curvature equation and related linearized Monge-Amp`ereequation, Lecture Notes in Mathematics, Springer, Cham, 2017, vol. 2183, pp. 1{123. 25. N. Q. Le and O. Savin, Schauder estimates for degenerate Monge-Amp`ereequa- tions and smoothness of the eigenfunctions, Invent. Math. 207 (2017), no. 1, 389{423. 26. N. Q. Le, On optimal H¨olderregularity of solutions to the equation ∆u+b·ru = 0 in two dimensions, C. R. Math. Acad. Sci. Paris 355 (2017), no. 4, 439{446. 27. N. Q. Le, Boundary Harnack inequality for the linearized Monge-Amp`ereequa- tions and applications. Trans. Amer. Math. Soc. 369 (2017), no. 9, 6583{6611. 28. N. Q. Le and T. Nguyen, Global W 1;p estimates for solutions to the linearized Curriculum Vitae, Nam Q. Le, May 2021, 3 Monge{Amp`ereequations. J. Geom. Anal. 27 (2017), no. 3, 1751-1788. 29. N. Q. Le, H. Mitake and H. V. Tran, Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Amp`ere Equations, Lecture Notes in Math- ematics, vol. 2183, Springer, Cham, 2017, vii + 228. 30. N. Q. Le, On the Harnack inequality for degenerate and singular elliptic equations with unbounded lower order terms via sliding paraboloids, Commun. Contemp. Math. 20 (2018), no.1, 1750012 (38 pages). 31. N. Q. Le, H¨olderregularity of the 2D dual semigeostrophic equations via analysis of linearized Monge-Amp`ereequations, Comm. Math. Phys. 360 (2018), no. 1, 271{305. 32. N. Q. Le, The eigenvalue problem for the Monge-Amp`ereoperator on general bounded convex domains, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 18 (2018), no. 4, 1519-1559. 33. N. Q. Le and P. Sternberg, Asymptotic Behavior of Allen-Cahn Type Energies and Neumann Eigenvalues via Inner Variations, Ann. Mat. Pura Appl. (4) 198 (2019), no. 4, 1257{1293. 34. N. Q. Le, Global H¨olderestimates for 2D linearized Monge{Amp`ereequations with right-hand side in divergence form, J. Math. Anal. Appl. 485 (2020), no. 2, 123865, 13pp. 35. N. Q. Le, Polynomial decay in W 2;" estimates for viscosity supersolutions of fully nonlinear elliptic equations, Math. Res. Lett. 27 (2020), no. 1, 189-207. 36. N. Q. Le, Singular Abreu equations and minimizers of convex functionals with a convexity constraint, Comm. Pure Appl. Math. 73 (2020), no. 10, 2248-2283. 37. N. Q. Le, On approximating minimizers of convex functionals with a convexity constraint by singular Abreu equations without uniform convexity, Proc. Roy. Soc. Edinburgh Sect. A. 151 (2021), no.
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