Teaching and supervision

Former Ph.D. students and postdocs

Justin Forlano (MIGSAA and Heriot-Watt University, co-supervised with T. Oh), 2020, Ph.D. thesis: On the deterministic and probabilistic Cauchy problem of nonlinear dispersive partial differential equations, currently a lecturer/assistant professor at Monash University, Australia

Kelvin Cheung (MIGSAA and Heriot-Watt University, co-supervised with T. Oh), 2019, Ph.D. thesis: On the dynamics of stochastic nonlinear dispersive partial differential equations, currently a secondary school teacher in Birmingham area, UK

Luigi Forcella, PostDoc at Heriot-Watt University, October 2018-March 2022, currently associate professor at University of Pisa, Italy.

Guopeng Li, PostDoc at Heriot-Watt University and Maxwell Institute for Mathematical Sciences, April 2023-October 2023, currently assistant professor at Beijing Institute of Technology, China.

Website of the Ph.D. level course Advanced PDE II: Hyperbolic PDE (MIGSAA and SMSTC 2016-2018): here

Past teaching

Spring 2026: Ordinary Differential Equations (F19MO, course leader, lectures, tutorials), Heriot-Watt University, UK,
Coordinator of 4th year and 5th year Mathematics Project Dissertations (F10GP, F11GS), Heriot-Watt University, UK,

Spring 2025: Mathematics for Engineers and Scientists 4 (F18XD, course leader, lectures), Heriot-Watt University, UK,
Coordinator of 4th year and 5th year Mathematics Project Dissertations (F10GP, F11GS), Heriot-Watt University, UK,

Spring 2024: Mathematics for Engineers and Scientists 4 (F18XD, course leader, lectures), Heriot-Watt University, UK,
Coordinator of 4th year and 5th year Mathematics Project Dissertations (F10GP, F11GS), Heriot-Watt University, UK,

Spring 2023: Mathematics for Engineers and Scientists 4 (F18XD, course leader, lectures), Heriot-Watt University, UK,
Coordinator of 4th year and 5th year Mathematics Project Dissertations (F10GP, F11GS), Heriot-Watt University, UK,

Spring 2022: Mathematics for Engineers and Scientists 4 (F18XD, course leader, lectures, tutorials), Heriot-Watt University, UK,
Coordinator of 4th year and 5th year Mathematics Project Dissertations (F10GP, F11GS), Heriot-Watt University, UK,

Spring 2021: Mathematics for Engineers and Scientists 4 (F18XD, course leader, lectures, tutorials), Heriot-Watt University, UK,

Spring 2020: Mathematics for Engineers and Scientists 4 (F18XD, lectures, tutorials), Heriot-Watt University, UK,

Autumn 2018: Introductory Mathematics A (course leader, lectures, tutorials), Heriot-Watt University, UK,

Spring 2018: Advanced PDE II: Hyperbolic PDE (lectures), MIGSAA and SMSTC course, Edinburgh, UK,
Mathematics for Engineers and Scientists 4 (F18XD, course leader, lectures, tutorials), Heriot-Watt University, UK,

Spring 2017: Advanced PDE II: Hyperbolic PDE (lectures), MIGSAA and SMSTC course, Edinburgh, UK,
Mathematics for Engineers and Scientists 4 (F18XD, lectures, tutorials, Matlab workshops), Heriot-Watt University, UK

Spring 2016: Advanced PDE II: Hyperbolic PDE (lectures), MIGSAA and SMSTC course, Edinburgh, UK

Spring 2015: Multivariable Calculus (lectures), Princeton University, USA

Autumn 2014: Multivariable Calculus (lectures, 2 sections), Princeton University, USA

Spring 2013: Linear Algebra with Applications (lectures), Princeton University, USA

Autumn 2012: Multivariable Calculus (lectures, 2 sections), Princeton University, USA

Spring 2012: Complex Analysis (tutorials), Mathematics (tutorials) for second year Chemical Engineering students, Imperial College London, UK

Autumn 2011: Functional Analysis (lectures), Imperial College, London, UK

Spring 2011: Algebra (tutorials) for second year undergraduate students in the Mathematics and Informatics program, Université Paris-Sud, Orsay, France

Autumn 2010: Calculus (tutorials) for first year undergraduate students in the Mathematics, Physics and Informatics program, Université Paris-Sud, Orsay, France

Autumn 2008, 2009: Calculus (tutorials) for first year undergraduate students in the Mathematics, Physics and Informatics program,
Projet Professionnel ("Project for Professions") for first year undergraduate students, Université Paris-Sud, Orsay, France

Past supervision: projects for 1st year MIGSAA Ph.D. students

Seminar taster project in analysis (co-supervised with A. Carbery, H. Gimperlein, T. Oh, D. Roxanas, project for 1st year MIGSAA Ph.D. students, Spring 2018)

Singularity formation in the focusing nonlinear Schrödinger equation: conservation laws, global well-posedness in the mass-subcritical case, sharp upper bound on the blowup rate in the mass-supercritical case; and in the mass-critical case: the virial argument for showing blowup in finite time, a scaling lower bound on the blowup rate, concentration of mass phenomenon at blowup, classification of minimal mass blowup solutions. Following the lecture notes by Pierre Raphaël published in Clay Math. Proc. 2013 (taster project for 1st year MIGSAA Ph.D. students, Autumn 2017)

Invariant manifolds and the nonlinear Klein-Gordon equation: following the book "Invariant Manifolds and dispersive Hamiltonian Evolution Equations" of K. Nakanishi and W. Schlag (co-supervised with T. Oh, working group and extended project for 1st year MIGSAA Ph.D. students, Spring 2017): Project 1, Project 2

Some aspects of energy-critical dispersive PDEs. Global well-posedness of the energy-critical defocusing nonlinear Schrödinger equation (NLS) on ℝ³: profile decomposition, perturbation theory, construction of a minimal blowup solution, long-time Strichartz estimates with application to ruling out rapid frequency cascades, frequency-localized Morawetz inequality with application to ruling out quasisolitons (co-supervised with T. Oh, working group and extended project for 1st year MIGSAA Ph.D. students, Spring 2016): Project 1, Project 2

Past supervision: projects for undergraduate, MMath and MSc students

The linear Schrödinger equation in Sobolev spaces : distributions and tempered distributions, Sobolev spaces, the fundamental solution of the linear Schrödinger equation, the Cauchy problem for linear Schrödinger equations in Sobolev spaces, the asymptotic behaviour of solutions of the linear Schrödinger equation (4th year project Spring 2018, Spring 2026)

Distributions and fundamental solutions of partial differential equations: distributions, tempered distributions, the Fourier transform, Sobolev spaces, fundamental solutions, solvability in Sobolev spaces of the Cauchy problems for the inhomogeneous heat, wave and Schrödinger equations (MMath project Spring and Autumn 2017, MSc project Summer 2023)

Entire functions and the Weierstrass theorem: Jensen's formula, functions of finite order, infinite products, infinite product formula for the sine function, Weierstrass theorem (4th year project Spring 2017)

Standing waves for the nonlinear Schrödinger equation: existence, orbital stability with respect to radial perturbations / orbital instability (4th year project Spring 2016, MSc project Summer 2020)

Oscillatory integrals of the first kind and applications to PDEs: van der Corput lemma, method of stationary phase, application to asymptotic expansions of Bessel functions, application to a dispersive estimate for the linear Schrödinger equation on ℝ, based on Chapter VIII in Stein's book (4th/MSc year project Spring 2016, Summer 2023, Spring 2024)

Hahn-Banach theorem and applications: Hahn-Banach extension theorem, Hahn-Banach separation theorem, applications, based on Chapter 3 in Rudin's book (4th year project Spring 2026)

The mathematics of soap bubbles: the isoperimetric inequality and the standard double bubble in 2D (4th year project Spring 2025)

Introduction to stochastic calculus: properties of the Brownian motion, the Wiener integral, the stochastic integral, Ito's formula, stochastic differential equations, applications to Finance, based on Kuo's book (4th year project Spring 2024, Spring 2025)

The Fourier transform and its applications: The Fourier transform of functions and its properties, the Fourier transform of tempered distributions and its properties, Sobolev spaces, Sobolev embeddings (MSc project Summer 2023)

Solution theory for nonlinear wave equations: the Fourier transform and its properties, Sobolev spaces and Sobolev embeddings, the well-posedness in H^1 of the cubic nonlinear wave equation on ℝ^3 (MSc project Summer 2020, Summer 2022)