César was born and raised in San José,Costa Rica, where he studied mathematics at the Universidad de CostaRica. After graduating, he taught for one semester at the Universityof Costa Rica and then moved to the United States to start his PhD inmathematics at Purdue University.

One of his main motivations for pursuingmathematics, and especially research, is the joy he finds in tacklingdifficult problems. He sees math as a profound challenge and a way toconstantly compete against himself.

His main research interests are numerical partial differential equations(PDEs). His long-term goal is designing efficient numerical methods for PDEs coming from hyperbolic conservation laws, which can be used to model physical phenomena such as fluid and gas dynamics. These equations are numerically challenging, as traditional numerical methods yield approximations that do not correspond to the physical phenomena they are trying to model. He currently designs these numerical methods using neural networks, which he considers a highly effective tool for solving these problems.

Inparallel, he has also been designing mixed-precision Runge-Kutta (RK)methods. RK methods are a family of numerical methods for solvingPDEs, and the goal of mixed-precision RK methods is to expedite theruntime needed to obtain a particular approximation.

Overthe past two years, he has published several papers across bothresearch areas and has regularly presented his findings at majorvenues, including the SIAM Annual Meeting, SIAM TXLA, the CopperMountain Conference on Iterative and Multigrid Methods, and ENUMATH.

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