Justin Forlano
Hi! I am currently a Postdoctoral Research Associate in the School of Mathematics at The University of Edinburghfrom 2023-2026.
During 2020-2023, I was a Hedrick Assistant Adjunct Professor in the Department of Mathematics at UCLA.
I obtained my PhD at Heriot-Watt University, as part of the MIGSAA CDT, under the supervision of Oana Pocovnicu and Tadahiro Oh.
I am interested in questions related to dispersive PDEs.
Email: j.forlano@ed.ac.uk.
Papers and preprints
- (with G. Li, T. Zhao) Unconditional deep-water limit of the intermediate long wave equation in low-regularity.
- (with R. Killip, M. Visan) Invariant measures for mKdV and KdV in infinite volume.
- (with A. Chapouto, G. Li, T. Oh, D. Pilod) Intermediate long wave equation in negative Sobolev spaces, to appear in Proc. Amer. Math. Soc. Ser. B..
- (with A. Chapouto) Invariant measures for the periodic KdV and mKdV equations using complete integrability.
- A remark on the well-posedness of the modified KdV equation in L2.
- (with L. Tolomeo) Quasi-invariance of Gaussian measures of negative regularity for fractional nonlinear Schrödinger equations.
- (with K. Seong) Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations, Comm. PDE, 47 (2022), no. 6, 1296--1337.
- (with L. Tolomeo) On the unique ergodicity for a class of 2 dimensional stochastic wave equations, Trans. Amer. Math. Soc., 377 (2024), 345--394.
- (with M. Okamoto) A remark on norm inflation for nonlinear wave equations, Dynamics of Partial Differential Equations, Vol. 17, No. 4 (2020), pp. 361--381.
- (with T. Oh) Normal form approach to the one-dimensional cubic nonlinear Schrödinger equation in Fourier-amalgam spaces, preprint.
- Almost sure global well-posedness of the BBM equation with infinite L2 initial data, Discrete Contin. Dyn. Syst. A., 40 (2020), 267--318.
- (with W. J. Trenberth) On the transport of Gaussian measures under the one-dimensional fractional nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 7, 1987--2025.
- (with T. Oh, Y. Wang) Stochastic cubic nonlinear Schrödinger equation with almost space-time white noise, J. Aust. Math. Soc. (2019), 1--24, DOI: https://doi.org/10.1017/S1446788719000156
Talks
- Probability and Stochastic Analysis Seminar, EPFL, Switzerland (February 2024)
- Mathematics Seminar, University of Dundee, UK (January 2024)
- Partial Differential Equations Seminar, Cambridge University, UK (October 2023)
- Analysis Seminar, University of Edinburgh, UK (October 2023)
- North-East and Midlands Stochastic Analysis Seminars, Oxford University, Oxford, UK (September 2023)
- Workshop: Random dispersive PDEs 2023, University of Birmingham, Birmingham, UK (July 2023)
- Recent Advances in Infinite-Dimensional Stochastic Analysis, 2023 AMS Spring Eastern Virtual Sectional Meeting, USA (April 2023)
- Participating Analysis Seminar, University of California, Los Angeles, USA (February 2023)
- Workshop on Nonlinear Dispersive Equations, Peking University, China (August 2022)
- Conference "Harmonic Analysis, Stochastics and PDEs" in Honor of the 80th Birthday of Nicolai Krylov, ICMS, Edinburgh, UK (June 2022)
- Graduate Seminar on Advanced Topics in PDE, University of Bonn, Germany (December 2020)
- Analysis and PDE seminar, University of California, Los Angeles, USA (November 2020)
- (Cancelled) Second Edinburgh-Vienna PDEs workshop, ICMS, Edinburgh, UK (May 2020)
- University of Birmingham, UK (February 2020)
- Stochastic Analysis Seminar, Imperial College London, UK (February 2020)
- East Midlands Stochastic Analysis Seminar, University of York, UK (February 2020)
- Analysis and PDE seminar, University of California, Los Angeles, USA (December 2019)
- Analysis and Applied Math seminar, University of Toronto, Canada (December 2019)
- (Cancelled) Analysis seminar, Cornell University, USA (December 2019)
- Nonlinear and stochastic partial differential equations, Research Institute for Mathematical Sciences, Kyoto, Japan (November 2019)
- (poster) Summer School "New Frontiers in Singular SPDEs and Scaling Limits'', Hausdorff center for mathematics, Germany (September 2019)
- (poster) Recent trends in Stochastic Analysis and Partial Differential Equations, University of Chester, UK (September 2019)
- EMS/LMS sponsored network on hyperbolic equations and related topics, ICMS, Edinburgh, UK (May 2019)
- Analysis Seminar, University of Edinburgh, UK (January 2019)
- British Mathematical Colloquium, University of St. Andrews, UK (June 2018)
- PhD talks in stochastic analysis, Heriot-Watt University (March 2018)
- PG Colloquim, University of Edinburgh (March 2018).
Events organised
Conferences/workshops attended
- Nonlinear Waves and Dispersive Equations, 26 June-2 July 2022, Oberwolfach (Germany).
- Summer School "New Frontiers in Singular SPDEs and Scaling Limits'', 23-27 September 2019, Hausdorff center for mathematics (Germany).
- Paths between Probability, PDEs, and Physics, 1-5 July 2019, Imperial College London (UK).
- Dispersive waves and related topics, 17-21 June 2019, University of Bergen (Norway).
- EMS/LMS sponsored network on hyperbolic equations and related topics, 16 May 2019, ICMS, Edinburgh (UK).
-
Renormalisation in quantum field theory and in stochastic partial differential equations: a gentle introduction and some recent developments,
Scaling limits, rough paths, quantum field theory, 3 - 7 September 2018, Isaac Newton Institute for Mathematical Sciences (UK). - Conference on Mathematics of Wave Phenomena, 23 - 27 July 2018, Karlsruhe Institute of Technology (Germany).
- British Mathematical Colloquium 2018, 11 - 14 June 2018, University of St. Andrews (UK).
- MIGSAA mini-course on Regularity structures by A. Chandra (Imperial), 30 April - 2 May 2018, University of Edinburgh (UK).
- Dispersive equations with random initial data, 10-12 January 2018, University of Bristol (UK).
- Hausdorff school on dispersive equations, solitons and blow-up, 4 - 8 September 2017, Hausdorff center for mathematics (Germany).
- Nonlinear dispersive PDE, quantum many particle systems and the world between, 16-28 July 2017, MSRI, INdAM and MSI, Cortona (Italy).
- Warwick EPSRC Symposium: School in Analysis and PDE, 12-16 June 2017, University of Warwick (UK).
- Probabilistic perspectives in nonlinear PDEs, 5 - 9 June 2017, ICMS, Edinburgh (UK).
- Nonlinear PDEs, stochastic control and filtering: new methods and applications, 29 May - 2 June 2017, ICMS, Edinburgh (UK).
- Geometric PDEs, 12-16 December 2016, University of Warwick (UK).
- LMS Harmonic Analysis Network Meeting, 4 November 2016, ICMS, Edinburgh (UK).
- MIGSAA summer school: fluid mechanics, 13-15 September 2016, ICMS, Edinburgh (UK).
- Workshop on Analysis, Geometry and Mathematical Relativity, 22 - 26 February 2016, Monash University (Australia).
Notes
- Paracontrolled distributions and singular stochastic PDEs (Ongoing short course by Tadahiro Oh) -- Handwritten notes (2018)
- Expanded details on a paper of Bourgain-Bulut -- Handwritten notes (2017)
- Dynamics near the ground state energy for the Cubic Nonlinear Klein-Gordon equation in three dimensions -- MIGSAA Extended project (2017), Slides part 1, Slides part 2, Poster
Teaching
| Winter '24: |
(UoE) Instructor for SMSTC Functional Analysis |
| Spring '23: |
(UCLA) Instructor for Math 131A (Analysis) |
| Winter '23: |
(UCLA) Instructor for Math 170E (Introduction to Probability and Statistics: Part 1 Probability) |
| Fall '22: |
(UCLA) Instructor for Math 170E (Introduction to Probability and Statistics: Part 1 Probability)
(UCLA) Instructor for Math 32B (Calculus of Several Variables) |
| Spring '22: |
(UCLA) Instructor for Math 170E (Introduction to Probability and Statistics: Part 1 Probability) |
| Winter '22: |
(UCLA) Instructor for Math 32A (Calculus of Several Variables) |
| Fall '21: |
(UCLA) Instructor for Math 131A (Analysis), 2 sections, course coordinator |
| Spring '21: |
(UCLA) Instructor for Math 131A (Analysis) |
| Winter '21: | (UCLA) Instructor for Math 32B (Calculus of Several Variables) |
| Fall '20: |
(UCLA) Instructor for Math 131A (Analysis) (UCLA) Instructor for Math 170E (Introduction to Probability and Statistics: Part 1 Probability) |
| Fall '19: |
(UoE) Workshops for Linear Analysis (MATH10082, one-hour tutorial) (UoE) Workshops for Accelerated Algebra and Calculus for Direct Entry (AAC, MATH08062, two-hour tutorial) (UoE) Workshops for Several Variable Calculus and Differential Equations (SVCDE, MATH08063, two one-hour tutorials) |
| Spring '19: | (UoE) Workshops for Honours Complex Analysis (HCV, MATH10067, one-hour tutorial + two-hour presentation skills) |
| Fall '18: | (UoE) Workshops for Honours Analysis (HA, MATH10068, one-hour tutorial + two-hour presentation skills) |
| Spring '18: | (UoE) Tutorials for Proofs and Problem Solving (PPS, MATH08059, two-hour tutorial) |
| Fall '15: | (Monash) Tutorials for Engineering mathematics (ENG1091, two-hour tutorial) |
| Spring '15: | (Monash) Tutorials for Engineering mathematics (ENG1090, two-hour tutorial) |
Education
- (Sep. '16 - Sep. '20) PhD, Maxwell Institute Graduate School in Analysis and its Applications (MIGSAA), Heriot-Watt University, Edinburgh, UK (Advisors: Oana Pocovnicu and Tadahiro Oh)
- (Mar. '12 - Nov. '15) Bsc. Adv. with Hons., Monash University, Melbourne, Australia (Advisor: Todd Oliynyk)