I am a fourth year PhD student in applied mathematics, working under the supervision of Dr. Tobias Grafke and Dr. Colm Connaughton.

Currently, I am interested in rare events algorithms, where usually a bias (tilt) of the distribution is introduced to give an extra weight to the rare events of interest, e.g. importance sampling algorithms. In particular, I am investigating heavy-tailed distributions, or more generally when the rate function is non-convex. These kinds of distributions are challenging in particular, due to the nonexistence of its cumulant generating function, leading to undefined Radon-Nikodym derivative of exponentially tilted measures. A solution that we propose is a nonlinear reparameterization to regularize the cumulant generating function of events of interest, and at the same time deforming the landscape of the rate function.

The main applications are from Fluid dynamics and Turbulence theory. More precisely, rare events of fluid motion are studied, utilising turbulence models of the Navier–Stokes equations (e.g. passive scalar RFD turbulence model, magnetohydrodynamics RFD model), and the nonlinear Schrödinger system.

The main tools are from large deviations theory, and convex analysis.

The mathematical areas of interest are:

• Partial differential equations (PDEs),
• Stochastic differential equations (SDEs),
• Large deviations theory (LDT),
• Numerical analysis,
• Convex analysis,
• Mathematical physics.

Presentation events:

• Talk : Rare Events Computation in Fluid Dynamics, June 2019, Postgraduate Seminar, Mathematics Institute, University of Warwick.
• Talk: The Effect of Rate Function Properties on Exponential Tilting, December 2019, Young Researchers’ Meeting, Department of Statistics, University of Warwick.
• Poster: Computation of Rare Events with Non-convex Rate Functions, Applied Probability, Bernoulli-IMS One World Symposium 2020, August 2020, virtual event.

Teaching experience during my PhD:

• MA124: Maths by computer, 2019/20,
• MA259: Multivariable Calculus, 2020/21.

About me:

• I gained my BSc in mathematics and my MSc in applied mathematics from King Faisal University, Saudi Arabia.
• I work at the University of Hafr Al Batin in the mathematics department.
• I gained a full scholarship to do my PhD from the University of Hafr Al Batin, presented here in the UK by the Saudi Arabian Cultural Bureau (UKSACB).

E-mail: M.Alqahtani@warwick.ac.uk

Room No.: B0.13, Zeeman building.