Speaker: Dr. Joshua Padgett, Department of Mathematical Sciences
Date: Wednesday, September 29, 2021, 3:25 PM – 4:25 PM
Title: Lecture series on analysis of numerical time-integration methods — Lecture #1: Operator splitting methods
Abstract: Throughout this lecture series we will (briefly) consider the following areas:
i) Operator splitting methods,
ii) Singular partial differential equations,
iii) Adaptive-mesh numerical integration methods, and
iv) Theoretical aspects of deep neural networks.
In the first of these series of lectures, we will focus on the theory of operator splitting methods in the field of numerical integration of differential equations. For simplicity, we will focus initially on the simple case of vector-valued ordinary differential equations, but will discuss how potential research topics would extend these ideas to the setting of both stochastic and deterministic partial differential equations. In particular, we will demonstrate how classical operator splitting techniques can be extended to the nonlinear setting (and beyond). This extension yields multiple avenues of research with many open questions in computational mathematics, numerical analysis, functional analysis, and non-commutative algebra.
Bio: Josh Padgett is an Assistant Professor in the Department of Mathematical Sciences at the University of Arkansas. Prior to joining the University of Arkansas, Josh was a postdoc in the Department of Mathematics and Statistics at Texas Tech University. Josh earned his Ph.D. in mathematics at Baylor University under the supervision of Qin Sheng. His undergraduate research focused on the metabolic features of tumor cells and the occurrence of the so-called Warburg effect. Josh is also an affiliated faculty member at the Center for Astrophysics, Space Physics, and Engineering Research and is a honorary adjunct faculty at Texas Tech University. His research lies at the intersection of pure, applied, and computational mathematics. Current research interests include applied mathematics, numerical analysis, geometric and Lie group integration methods, mathematics of deep learning, operator splitting methods, algebraic structures of numerical methods, fractional differential equations, stochastic differential equations, and the use of spectral and operator theory in theoretical and experimental physics.
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