Name: Mitchell Scott
Pronouns: he/they
Institution: Emory University
Department: Department of Mathematics
Biography:
I am a first year PhD computational mathematics student at Emory University. Previously, I received my BS in biological engineering from Cornell University, and an MS in mathematics from Tufts University. I have done research in tensor methods, PDEs, numerical linear algebra, preconditioning, and iterative methods. While I am very passionate about computational mathematics, I also see firsthand how beneficial making the mathematics community more inclusive can be. As a queer, non-binary mathematician, I have often felt I don’t belong in these math spaces, or have been talked down to and ignored. I hope to find an inclusive environment where together we can do great math by listening to everyone and making sure everyone feels valued and can do their best work. Through these differences, mathematical collaboration can make it to the next level which benefits everyone.
Academic Status: PhD Student
Year in program: 1st
Research Area/Department: Applied Mathematics; Mathematics
Other, specify:
Major/Specialty: Computational Mathematics, Applied Mathematics, Numerical Linear Algebra, Partial Differential Equations.
Degrees Earned or in Progress: BS / Computational Biological Engineering / 2020 MS / Mathematics / 2023 MS / Computer Science / 2025 PhD / Computational Mathematics / 2028
What courses or academic preparation have you completed to prepare for a summer internship experience?
I have taken many graduate level mathematics courses such as Partial Differential Equations (PDEs), Numerical Analysis, Probability, Analysis, Complex Analysis, and Numerical Optimization. Similarly, I am taking graduate coursework in computer science like algorithms, matrix computations, and systems programming. Lastly, I have taken many science classes through my biological engineering major, where I had to take organic chemistry, physical chemistry, biochemistry, and special relativity. I will take continuum mechanics at the graduate level next semester.
Have you published any research or worked on research/technical projects? No
Where has your research been published or where have you conducted research/technical projects?
Please describe your research/academic interests:
I am interested in the intersection of numerical linear algebra and partial differential equations especially in speeding up computations in nonlinear PDEs with nonlinear solvers. Previously I have studied how to use tensor based methods to construct a tunable preconditioner for fractional PDEs. Currently I am working on expanding Krylov subspace methods from a linear to nonlinear context to tackle fully nonlinear PDEs as opposed to solving the linearized form of them. I am studying curvature information to locally update the search direction with a hope of getting a faster and more stable convergence properties. I am also looking at how machine learning can be incorporated in estimating the curvature information of these high dimensional, nonlinear equations.
Computational and Data Science Areas:
Applied Mathematics; Computational Science Applications, i.e., Bioscience, Cosmology, Chemistry, Environmental Science, Nanotechnology, Climate, etc.; High-Performance Computing
Research Synergy:
Partial Differential Equations model the world around us and can be used to solve problems that effect real situations, e.g. how to allocate energy over the energy grid, how to model wind turbines to make a more efficient design, etc. These digital twin simulations can mean the difference between a community having electricity or experiencing a black-out. These equations deserve to be solved in a timely manner as they have an effect on peoples’ lives. We shouldn’t wait around to have a closed form solution to these PDEs (if we will ever get one); instead, we should use the computational resources to model and start solving these equations with real world applications. We rely on computers daily, so as opposed to treating them like a “”black-box”” solver, I want to use my knowledge of math, computer science, and engineering to solve these hard engineering problems. The DOE does exactly this. It takes data and problems from across the country and finds way to make more efficient, more timely solutions to the problems plaguing our nation.
Motivation:
I am interested in applying my knowledge of mathematics, engineering, and computer science to projects that go beyond the textbook, and are actual problems that impact people. I am also interested in the inclusive nature of this program. It is great to find community and support in the mathematics community, as I have often found bringing my whole self to work can be hard as sometimes the mathematics community can be very judgmental and make comments that impact me negatively.
Lightning Talk Title: Accelerating Nonlinear Multiphysics Simulations with Nonlinear Solvers