Tristan Roy

Designated Assistant Professor (YLC)
Department Of Mathematics,
Nagoya University

email: Tristan.Roy@math.nagoya-u.ac.jp
office: 507
mail: Graduate School of Mathematics, Nagoya University
        Furocho, Chikusaku, Nagoya, Japan

Curriculum vitae (September 2017)

Research interests

Primary: Partial Differential Equations (Asymptotic Behavior Of Solutions Of Dispersive Equations).

Secondary: Harmonic Analysis, Optimization.

Publications and preprints

Asymptotic Behavior For Focusing Subcritical And Critical Nonlinearities

• Global Dynamics Above The Ground State For The Critical Klein-Gordon Equation (with Kenji Nakanishi), preprint.

• A Weak Form Of The Soliton Resolution Conjecture For High-Dimensional Fourth-Order Schrodinger Equations , Journal of Hyperbolic Differential Equations, Vol. 14, No. 2 (2017) 249-300.

• Blow-up Of The Critical Sobolev Norm For Nonscattering Radial Solutions Of Supercritical Wave Equations In Space Dimension 3 (with Thomas Duyckaerts), to appear in Bulletin de la Societe de France, arXiv:1506.00788.

• Global Dynamics Above The Ground State For The Energy-critical Schrodinger Equation With Radial Data (with Kenji Nakanishi), Communications on Pure and Applied Analysis, Volume 15, Issue 6, November 2016, Pages: 2023 - 2058.

  Asymptotic Behavior For Defocusing Subcritical Nonlinearities

• On The Interpolation With The Potential Bound For Global Solutions Of The Defocusing Cubic Wave Equation on T2 , Journal Of Functional Analysis, Volume 270, Issue 9, May 2016, Pages 3280-3306.

• Scattering Of Rough Solutions Of The Nonlinear Klein-Gordon Equations In 3D (with Soonsik Kwon), Adv. Differential Equations Volume 21, Number 3/4 (2016), 333-372.

• On Control Of Sobolev Norms For Some Semilinear Wave Equations With Localized Data , Journal Of Functional Analysis, Volume 265, Issue 11, December 2013, Pages 2724-2752 (summary in RIMS Kokyuroku Bessatsu B42, August 2013).

• Global Well-Posedness Of The Maxwell-Klein-Gordon Equation Below The Energy Norm (with Markus Keel, Terence Tao), Disc. Cont. Dynam. Systems A.,30 (2011), no. 3, 573-621.

• Bootstrapped Morawetz Estimates And Resonant Decomposition For Low Regularity Global Solutions Of Cubic NLS On R2 (with Jim Colliander), Communications On Pure And Applied Analysis, 10 (2011), no. 2, 397-414.

• Introduction To Scattering For Radial 3D NLKG Below Energy Norm , J. Differential Equations (2010), no. 4, 893-923.

• Global Analysis Of The Defocusing Cubic Wave Equation In Dimension 3 , Ph.D thesis (advisor: Terence Tao), LAP LAMBERT Academic Publishing (November 6, 2013).

• Adapted Linear-Nonlinear Decomposition And Global Well-posedness For Solutions To The Defocusing Cubic Wave Equation On R3 , Disc. Cont. Dynam. Systems A,Vol 24, Number 4, 2009, 1307-1323.

• Global Well-posedness For The Radial Defocusing Cubic Wave Equation on R3 And For Rough Data , EJDE, 166, 2007, 1-22.

  Asymptotic Behavior For Barely Supercritical Nonlinearities

• On Jensen-type Inequalities For Unbounded Radial Scattering Solutions Of A Loglog Energy-supercritical Schrodinger Equation , preprint, arXiv:1709.01333

• Scattering Above Energy Norm Of Solutions Of A Focusing Size-Dependent Log Energy-Supercritical Schrodinger Equation With Radial Data Below Ground State , preprint, arXiv:1701.02689.

• Scattering Above Energy Norm Of Solutions Of A Loglog Energy-Supercritical Schrodinger equation With Radial Data , Journal Of Differential Equation, 250 (2011), no. 1, 292-319. Corrigendum, 264 (2018), no. 9, 6013-6024.

• A Remark On Barely Hsp Supercritical Wave Equations , Analysis And PDE 5-1 (2012), 199-218.

• Global Existence Of Smooth Solutions Of A 3D Loglog Energy-supercritical Wave Equation , Analysis And PDE, Vol 2, Num 3, 261-280, 2009.

  Miscellanous

• Construction Of Solutions For A Class Of Dispersive Equations , (with K. Tsugawa), in progress.

• Bilinear Local Smoothing Estimate For Airy Equation (with S. Kwon), Differential And Integral Equations, 25 (2012), No.1-2, 75-83.

• Segmentation Of A Vector Field: Dominant Parameter And Shape Optimization (with G. Aubert, M. Barlaud, E. Debreuve), J. Math Imaging Vis, 2006, vol 24, num 2, pp 259-276.

Teaching

• Winter 2016-2017: Partial Differential Equations, Nagoya University.

• Fall 2014: Lectures For Graduate Students (Title: Wave Equations), Nagoya University.

• Spring 2011: Linear Algebra, Courant Institute.

• Fall 2010: Calculus II, Section 9, Courant Institute.

• Fall 2007: Calculus For Life Sciences Students, UCLA.

• Winter 2007: Analysis, UCLA.

• Fall 2006: Applied Numerical Methods, UCLA.

• Spring 2006: Applied Numerical Methods, UCLA.

• Winter 2006: Complex Analysis, UCLA.

• Fall 2005: Optimization, UCLA