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.

Academic events:

• Publication: Instantons for Rare Events in Heavy-tailed Distributions, with Dr. Tobias Grafke, February 2021, Journal of Physics A: Mathematical and Theoretical.

• Preprint: Extreme events and instantons in Lagrangian passive scalar turbulence models, with Dr. Leonardo Grigorio and Dr. Tobias Grafke, August 2021.

• Award: 'Excellence award' received from UKSACB for the scientific achievements during 20/2021.
• 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, August 2020, Applied Probability, Bernoulli-IMS One World Symposium 2020, virtual event.

• Talk: Instantons for Rare Events in Heavy-tailed Distributions, February 2021, SPAAM Seminar, Mathematics Institute, University of Warwick, virtual event.

• Poster (Prize winner): Extreme Events of Lagrangian Model of Passive Scalar Turbulence via Large Deviation Theory, April 2021, BMC-BAMC GLASGOW 2021, virtual event.

• Talk: Extreme events of dynamical systems: from large deviation theory to instanton calculus, June 2021,

  Young Researchers in Mathematics, University of Bristol, virtual event.

Teaching experience during my PhD:

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

• MA261: Differential Equations: Modelling and Numerics, 2020/21.

About me:

• I gained a BSc in mathematics and a MSc in applied mathematics from King Faisal University, Saudi Arabia.
• I worked 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.