- Conformal Fields and the Structure of the Space of Solutions of the Einstein Constraint Equations M. Holst, D. Maxwell, and R. Mazzeo Advances in Theoretical and Mathematical Physics, Vol. 26, No. 5, pp. 1157-1201 (2022)
- Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent Horizon Boundaries M. Holst, C. Meier, and G. Tsogtgerel Comm. Math. Phys., Vol. 357, pp. 467-517 (2018)
- The Emergence of Gravitational Wave Science: 100 Years of the Development of Mathematical Theory, Detectors, Numerical Algorithms, and Data Analysis Tools M. Holst, O. Sarbach, M. Tiglio, and M. Vallisneri Bull. Amer. Math. Soc., Vol. 53, pp. 513-554 (2016)
- The Lichnerowicz Equation on Compact Manifolds with Boundary M. Holst and G. Tsogtgerel Class. Quantum Grav., Vol. 30, pp. 1-31 (2013)
- Rough Solutions of the Einstein Constraints on closed manifolds without near-CMC conditions M. Holst, G. Nagy, and G. Tsogtgerel Comm. Math. Phys., Vol. 288, pp. 547-613 (2009)
My research program lies at the intersection of mathematics, physics, and computation, and involves working in the areas of numerical analysis, applied analysis, partial differential equations (PDE), and mathematical physics. My main area of expertise is the analysis and numerical treatment of PDE, with a particular focus on nonlinear geometric PDE and adaptive numerical methods. My research projects typically center around developing mathematical theorems (for analyzing nonlinear PDE and developing approximation theory) and mathematical algorithms (for efficient and reliable numerical solution of nonlinear PDE problems). Although my current focus is on mathematical and numerical general relativity in astrophysics, the same general types of mathematical problems arise in nearly every area of science and engineering, and I continue to be involved in long-term projects in other fields such as biophysics, biochemistry, and engineering. In addition to my journal publications, I am the coauthor of a graduate textbook on applied analysis and PDE with Ivar Stakgold.