I am actively seeking motivated graduate students in mathematics, physics, or engineering (current or prospective). Our research group focuses on structure-preserving discretizations of exterior calculus and differential geometry, alongside their applications in computational physics and engineering. We primarily develop and use Discrete Exterior Calculus (DEC), Finite Element Exterior Calculus (FEEC), and Discrete Differential Geometry (DDG). In the process, we make contact with Hodge theory, algebraic topology, homological algebra, differential geometry, category theory, and numerical analysis in addition to application areas in engineering and physics. The work can range from theoretical mathematical to applied and computational. For a detailed overview of current projects, please see my research page, and for information regarding currently available Research Assistant (RA) positions, please check the home page. Please email your CV and a brief statement of interest (see my contact page).
Siqi Jiao (Mathematics) — sjiao@illinois.edu
Ph.D. students who worked in the group for a period before transitioning to their primary advisors.