School of Mathematics

The University of Edinburgh

James Clerk Maxwell Building, Room 5213

The King's Buildings, Peter Guthrie Tait Road

Edinburgh, EH9 3FD, United Kingdom

I am a third year PhD student in the MIGSAA CDT, based at the University of Edinburgh supervised by Tadahiro Oh.

- Global well-posedness for the two-dimensional stochastic complex Ginzburg-Landau equation .
- (with P. Sosoe and T. Xiao) Quasi-invariance of fractional Gaussian fields nonlinear wave equation with polynomial nonlinearity.
- (with J. Forlano) On the transport of Gaussian measures under the one-dimensional fractional nonlinear Schrödinger equations, Ann. Inst. H. Poincare Anal. Non Lineaire 36 (2019), no. 7, 1987-2025.

- Renormalisation in quantum field theory and in stochastic partial differential equations, 3 - 7 September 2018, Isaac Newton Institute for Mathematical Sciences, Cambridge. PDF
- 3rd MIGSAA Annual Colloquium, 22 September 2017, International Centre for Mathematical Sciences, Edinburgh. PDF

- Summer School in Analysis of PDEs and Fluid Dynamics, 23 - 26 July 2019, ICMS, Edinburgh (UK).
- Advanced topics in life insurance mathematics, 20 - 24 May 2019, ICMS, Edinburgh (UK).
- Mean-field games, energy systems, and other applications, 2 - 5 April 2019, ICMS, Edinburgh (UK).
- Renormalisation in quantum field theory and in stochastic partial differential equations, 3 - 7 September 2018, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.
- British Mathematical Colloquium 2018, June 11 - 14, 2018, University of St. Andrews (UK).
- MIGSAA mini-course on Regularity structures by A. Chandra (Imperial), April 30 - May 2, 2018, University of Edinburgh (UK).
- Hausdorff school on dispersive equations, solitons and blow-up, September 4 - 8, 2017, Hausdorff center for mathematics, (Germany).
- Nonlinear dispersive PDE, quantum many particle systems and the world between, July 16-28, 2017,MSRI, INdAM and MSI, Cortona (Italy).
- Warwick EPSRC Symposium: School in Analysis and PDE, June 12-16, 2017, University of Warwick (UK).
- Probabilistic perspectives in nonlinear PDEs, June 5 - 9, 2017, ICMS, Edinburgh (UK).
- Nonlinear PDEs, stochastic control and filtering: new methods and applications, May 29- June 2, 2017, ICMS, Edinburgh (UK).
- Geometric PDEs, December 12-16, 2016, University of Warwick (UK).

Github link. Python code for simulating the Ising model using the Metropolis-Hastings algorithm. The Ising model is known for being one of the simplest statistical models to exhibit phase transitions. It models phenomenon such as ferromagnetism. The long term behavior of the sytem depends heavily on the temperature parameter. Below are some animations for a very low. As can be seen, given a 'television snow' background, that is on the 50 by 50 grid each square is randomly either 1, black, or -1, white, the system evlolves to be either completely black or completely white.

If instead we start from a 'white background'. Then the long term behaviour also depends heavily on the temperature paramter. If the temrperature is low enough, below on the left. The system will remain mostly white. If instead the temperature is high enough, below on the right, the system will become roughly equally white as it is black.

This models the behaviour of magents. If a magent is heated to a high enough temperature it loses its magnetization.

- (Sep. 2016 - Present) PhD candidate, Maxwell Institute Graduate School in Analysis and its Applications (MIGSAA), The University of Edinburgh
- (Jun. 2015 - Jun. 2016) BSc (Hons) with First Class Honours Majoring in Mathematics, The University of Auckland
- (Mar. 2013- Jun. 2015) BSc Majoring in Mathematics and Physics, The University of Auckland

- Autumn (2019): Workshops and marking for Python Programming (PP, MATH11199)
- Autumn (2018): Workshops for Honours Analysis (HA, MATH10068)
- Spring (2019): Workshops for Fundementals of Pure Mathematics (FPM, MATH08064)
- Spring (2019): Workshops for Honours Complex Variables (HCV, MATH10067)
- Spring (2019): Exam marking for Calculus and its Applications (CAP, MATH08508)
- Autumn (2018): Workshops for Honours Analysis (HA, MATH10068)
- Autumn (2018): Workshops and exam marking for Several Variable Calculus and Differential Equations (SVCDE, MATH08063)
- Spring (2018): Workshops for Calculus and its Applications (CAP, MATH08508)

- Autumn (2016): Tutor in the Mathematics Assistance Room
- Autumn (2016): Tutorials and assignment marking for General Mathematics 1 (MATHS 108)
- Spring (2015): Tutor in the Mathematics Assistance Room
- Spring (2015): Tutorials for General Mathematics 1 (MATHS 108)
- Spring (2015): Assignment marking for Advancing Mathematics 1 (MATHS 150)
- Autumn (2015): Tutor in the Mathematics Assistance Room
- Autumn (2015): Tutorials and assignment marking for General Mathematics 1 (MATHS 108)
- Spring (2014): Assignment marking for Advancing Mathematics 1 (MATHS 150)
- Spring (2014): Assignment marking for Advancing Mathematics 2 (MATHS 250)
- Autumn (2014): Tutor in the Mathematics Assistance Room

- 3rd MIGSAA Annual Colloquium, International Centre for Mathematical Sciences, Edinburgh. (Co-organiser)