Prospective Students

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).

Current Ph.D. Students

Siqi Jiao (Mathematics) — sjiao@illinois.edu

Ph.D. Alumni

2026
Bingyan Liu (Mathematics) — bingyanliu21@gmail.com
Thesis: Discrete Poincaré Operators and A-infinity Structures in Discrete Exterior Calculus
Currently: Jump Trading, Chicago.
2026
Chengbin Zhu (Mathematics) — chengbin.zhu@fitila.ai
Thesis: Convergence of DEC for Hodge-Laplace problem and extension of DEC for biharmonic equation and linear elasticity
Currently: Fitila, Chicago.
2022
Nikolas Wojtalewicz (Mathematics) — nikwoj@gmail.com
Thesis: Discontinuous differential equations
Currently: Vision Systems Inc. (VSI), Providence.
2021
Vaibhav Karve (Mathematics) — vaibhavskarve@gmail.com
Thesis: Graphical structure of unsatisfiable boolean formulae
Currently: SimSpace, Boston.
2018
Mark Schubel (Physics) — mdschubel@gmail.com
Thesis: Discretization of differential geometry for computational gauge theory
Currently: Apple, Cupertino.
2015
Kaushik Kalyanaraman (Computer Science) — kaushik@iiitd.ac.in
Thesis: Hodge Laplacians on simplicial meshes and graphs
Currently: IIIT-Delhi.
2010
Evan VanderZee (Mathematics) — vanderzee@anl.gov
Thesis: Well-centered meshing
Currently: Argonne National Laboratory, Chicago.
2008
Andrew Colombi (Computer Science)
Thesis: Quick Evaluation of Small Body Gravitation
Currently: Tonic, Inc., Bay Area.

Past Ph.D. Researchers in the Group

Ph.D. students who worked in the group for a period before transitioning to their primary advisors.