## Faculty Profile

- M. Holst, G. Nagy, and O. Sarbach, Stability reversal in fluid models of black strings for high space dimensions. Preprint.
- M. Holst, E. Lunasin, and G. Tsogtgerel, Partial Regularity Results for Generalized Navier-Stokes Equations. Preprint.
- M. Holst, G. Tsogtgerel, and Y. Zhu, Adaptive Finite Element Approximation of Nonlinear Geometric PDE. Preprint.
- M. Holst, R. Szypowski, and G. Tsogtgerel, The Cauchy Problem of Cosmological Topologically Massive Gravity in 2+1 Dimensions. Preprint.
- B. Aksoylu, S. Bond, E. Cyr, and M. Holst, Adaptive Solution of the Poisson-Boltzmann Equation using Goal-Oriented Error Indicators. Preprint.

## Michael Holst

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### Research Statement

Professor Holst's general research background and interests are in a broad area called computational and applied mathematics; his specific research areas are in adaptive numerical methods, finite element methods, geometric partial differential equations (PDE), biophysics, and general relativity. His research projects center around developing mathematical techniques (theoretical techniques in PDE and approximation theory) and mathematical algorithms (numerical methods) for using computers to solve certain types of mathematical problems called nonlinear PDE. These types of problems arise in nearly every area of science and engineering; this is just a reflection of the fact that physical systems that we try to manipulate (e.g., the flow of air over an airplane wing, or the chemical behavior of a drug molecule), or build (e.g., the wing itself, or a semiconductor), or simply study (such as the global climate, or the gravitational field around a black hole) are described mathematically by nonlinear PDE. In simple cases, these problems can be simplified so that purely mathematical techniques can be used to solve them, but in most cases they can only be solved using sophisticated mathematical algorithms designed for use with computers. Computational simulation of PDE is now critical to almost all of science and engineering; the mathematicians provide the mathematical tools and understanding so that scientists in physics, chemistry, biology, engineering, and other areas can confidently use the modern techniques of computational science in the pursuit of new understanding in their fields of study. To learn more about Professor Holst's particular research program, please see his webpage: http://ccom.ucsd.edu/~mholst/