Anil N. Hirani

Professor, Department of Mathematics

University of Illinois at Urbana-Champaign

Research:   I have always been attracted to the interplay between geometry/topology and algorithms. My main research area is structure-preserving discretizations of differential calculus on manifolds and of differential geometry. By discretization, I mean a combinatorial version of calculus and differential geometry. The structures preserved are some of the algebraic properties of spaces, operators and objects being discretized. (An example is the first theorem in the paper on vector bundles.) The structures in such discretizations are mathematically interesting in their own right and can be used for numerical solution of partial differential equations (PDEs), computation of geometric properties of spaces and for many other applications. Recently, I made an excursion outside my main area into the structure of satisfiable and unsatisfiable propositional logic sentences using the tools of graph theory. Current and recent research interests:

Publications     Citations     Software     Discrete Exterior Calculus (DEC)

Teaching (Fall 2022):

Graduate Students:

Co-advised partially:

Previous Recent Teaching (last few years):

Short CV:

Contact:   hirani at illinois dot edu, 375 Altgeld Hall, (217) 333 2727
Mailing Address: Department of Mathematics, 1409 W. Green St., M/C 382, Urbana, IL 61801.

Page maintained by Anil Hirani. Last modified: Thu Aug 18 10:43:18 CDT 2022