Anil Nirmal Hirani

Anil Nirmal Hirani serves as a Professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign, specializing in the intersection of geometric theory and computational methods.

Education:

• PhD, Caltech, 2003

Hirani's research centers on applied geometry and topology, with significant contributions to Discrete Exterior Calculus (DEC) as a framework for numerical analysis. His work bridges abstract mathematical concepts like cohomology and Hodge theory with practical computational physics applications, particularly in fluid dynamics and dynamical systems. The fingerprint analysis of his publications reveals dominant themes including Calculus (100%), Discrete Exterior Calculus (78%), and Finite Element Methods (27%), indicating a consistent focus on structure-preserving discretizations of physical systems.

Recent publications demonstrate an evolving trajectory toward multi-physics problems, combining DEC with phase-field methods for fluid interfaces and developing conservative integrators for non-smooth systems. This reflects a strategic expansion from theoretical foundations to complex real-world simulations while maintaining mathematical rigor.

Scientific Awards:

• NSF CAREER Award (2007) for "Algebraic Topology and Exterior Calculus in Numerical Analysis" (2007–2012)

Hirani maintains active research collaborations evidenced by multi-institutional publications and global network connections. His advising activities, though not explicitly detailed in the source, are inferred through co-authored works with junior researchers. Current investigations appear focused on extending DEC frameworks to multi-material systems and non-smooth dynamics, supported by continued NSF engagement beyond the initial CAREER grant period.