I am a final year PhD student in applied mathematics, working under the supervision of Dr. Tobias GrafkeLink opens in a new window and Dr. Colm ConnaughtonLink opens in a new window.

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 DistributionsLink opens in a new window, with Dr. Tobias Grafke, Journal of Physics A: Mathematical and Theoretical, February 2021.

• Publication: Extreme Events and Instantons in Lagrangian Passive Scalar Turbulence ModelsLink opens in a new window, with Dr. Leonardo Grigorio and Dr. Tobias Grafke, Physical Review E, April 2022.

• Award: 'Excellence award' (PDFLink opens in a new window ) received from UKSACBLink opens in a new window for the scientific achievements during 20/2021.
• Talk: Rare Events Computation in Fluid DynamicsLink opens in a new window, Postgraduate Seminar, Mathematics Institute, University of Warwick, June 2019.
• Talk: The Effect of Rate Function Properties on Exponential TiltingLink opens in a new window, Young Researchers’ Meeting, Department of Statistics, University of Warwick, December 2019.
• Poster: Computation of Rare Events with Non-convex Rate FunctionsLink opens in a new window, Applied Probability, Bernoulli-IMS One World Symposium 2020, virtual event, August 2020.

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

• Poster (Prize winnerLink opens in a new window): Extreme Events of Lagrangian Model of Passive Scalar Turbulence via Large Deviation TheoryLink opens in a new window, BMC-BAMC GLASGOW 2021, virtual event, April 2021.

• Talk: Extreme Events of Dynamical Systems: From Large Deviation Theory to Instanton CalculusLink opens in a new window, Young Researchers in Mathematics, University of Bristol, virtual event, June 2021.
• Talk: Large Deviation Theory of Sample Paths in Turbulence Models, Ruhr-Universität Bochum - Institut für Theoretische Physik I, virtual event, January 2022.

• Talk: Rare Events in Heavy-Tailed Distributions Through Large Deviation TheoryLink opens in a new window, SIAM Conference on Uncertainty Quantification (UQ22), April 2022.

• Award: 'SIAM Student Travel AwardLink opens in a new window' received from SIAM Conference on Uncertainty Quantification (UQ22), April 12-15, 2022.

• Talk: “Between rare events and optimisation problems”, Early Career Researchers in Mathematics (ECRM) 2022Link opens in a new window, University College London, June 2022.

Teaching experience during my PhD:

• MA124: Maths by computerLink opens in a new window, 2019,
• MA259: Multivariable CalculusLink opens in a new window, 2020,

• MA261: Differential Equations: Modelling and NumericsLink opens in a new window, 2021,

• MA3G1: Theory of Partial Differential EquationsLink opens in a new window, 2021,

• MA3H7: Control TheoryLink opens in a new window, 2022,

• MA390: Topics in Mathematical BiologyLink opens in a new window, 2022.

About me:

• I gained a BSc in mathematics and an MSc in applied mathematics from King Faisal UniversityLink opens in a new window, Saudi Arabia.
• I worked at the University of Hafr Al BatinLink opens in a new window 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 BureauLink opens in a new window (UKSACB).

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

Room No.: C1.02, Zeeman building.