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)

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

Secondary: Harmonic Analysis, Optimization.

- 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, 893923, 261-280.
- 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, to appear.
- One 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.

- 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