Research Interest:   Numerical Analysis, Discrete Differential Geometry, Computational Topology, Computational Physics.

Publications     Citations     Software     Discrete Exterior Calculus (DEC)

Current Teaching (Fall 2020):

• MATH 423 Differential Geometry

Current Ph.D students:

• Siqi Jiao
• Nikolas Wojtalewicz
• Vaibhav Karve

Former Ph.D students and postdoc:

• Mark Schubel, Ph.D (Physics) 2017. Now at Apple.
• Kaushik Kalyanaraman, Ph.D (CS) 2015. Now Assistant Professor of Mathematics at IIIT-Delhi, India.
• Han Wang, Ph.D (Mathematics) 2014. Now postdoc at University of Texas, San Antonio.
  Advisor: Yuliy Baryshnikov. Coadvised 2010-2013.
• Seth Watts, Ph.D (Mechanical Engineering) 2013. Now at Lawrence Livermore Lab.
  Advisor: Dan Tortorelli. Coadvised during 2010-2012.
• Evan VanderZee, Ph.D (Mathematics), 2009. Now at Argonne National Lab.
  Coadvised with Vadim Zharnitsky.
• Andrew Colombi, Ph.D (CS) 2008. First job after Ph.D: Palantir, now a founder of a startup in Silicon Valley.
• John Jossey (Postdoc), September 2006 - August 2007. Now Senior Manager at RBC Capital Markets in Canada.

Computational Bootcamp: Learn Python programming for scientific computing in 10 days.

Previous Teaching:

• MATH 490 Computational Mathematics
• MATH 461 (Two sections) Probability Theory
• Spring 2019: MATH 490 Computational Mathematics
• Spring 2019: MATH 519 Differentiable Manifolds II
• Fall 2018: MATH 518 Differentiable Manifolds I
• Spring 2018 (Second Half): MATH 595 Calculus on Meshes
• Spring 2018: MATH 461 Probability Theory
• Fall 2017: MATH 423 Differential Geometry
• Spring 2017: MATH 553 Partial Differential Equations
• Fall 2016: MATH 461 Probability Theory
• Summer 2016: CBMG16 Computational Bootcamp
• Fall 2015: MATH 285 Introduction to Differential Equations
• Spring 2015: MATH 286 Introduction to Differential Equations Plus
• Fall 2014: MATH 595 TTA Top 10 Algorithms of 20th and 21st Century (with Y. Baryshnikov)
• Summer 2014: CBMG 2014 Computational Boot camp for Mathematics Graduate Students
• Fall 2013: MATH 285 Introduction to Differential Equations
• Spring 2013: CS 450 / CSE 401 / ECE 491 / MATH 450 Numerical Analysis
• Fall 2012: CS 357 / MATH 357 Numerical Methods I
• Spring 2012: CS 555 / MATH 552 / CSE 510 Numerical Methods for PDEs
• Fall 2011: CS 450 / CSE 401 / ECE 491 / MATH 450 Numerical Analysis
• Fall 2011: CS 199ANH (Discovery Course) What is Shape ? A Computer Based Exploration
• Spring 2011: CS 555 / MATH 552 / CSE 510 Numerical Methods for PDEs
• Fall 2010: CS 357 / MATH 357 Numerical Methods I
• Spring 2010: CS 555 / MATH 552 / CSE 510 Numerical Methods for PDEs
• Fall 2009: CS 558 / CSE 513 Laplacians on Networks and Meshes (Topics in Numerical Analysis)
• Spring 2009: CS 450 / CSE 401 / MATH 450 / ECE 491 Introduction to Numerical Analysis
• Fall 2008: CS 558 / CSE 513 Calculus on Meshes (Topics in Numerical Analysis)
• Spring 2008: CS 450 / CSE 401 / MATH 450 / ECE 491 Introduction to Numerical Analysis
• Fall 2007: CS 257 / MATH 257 Numerical Methods
• Spring 2007: CS 257 / MATH 257 Numerical Methods
• Fall 2006: CS 598ANH Symplectic Integrators and Discrete Mechanics
• Spring 2006: CS 450 / CSE 401 / MATH 450 / ECE 491 Introduction to Numerical Analysis
• Fall 2005: CS 598ANH Calculus on Meshes

Awards:

• 2012 : Best Paper Award (Second Place) in Solid and Physical Modeling 2012, for paper Delaunay Hodge Star.
• 2007 : NSF CAREER Award, Division of Mathematical Sciences (Algebraic Topology and Exterior Calculus in Numerical Analysis)

Short CV:

• 2013-, Associate Professor, University of Illinois at Urbana-Champaign, Department of Mathematics
• 2005-2013, Assistant Professor, University of Illinois at Urbana-Champaign, Department of Computer Science
• 2004-05, Senior Engineer, Jet Propulsion Laboratory Guidance, Navigation and Control Section
• 2003-04, CIMMS Postdoctoral Scholar, California Institute of Technology (Caltech), Control and Dynamical Systems
• 2003, Ph.D, California Institute of Technology (Caltech), (Advisor: Jerrold E. Marsden),
  Ph.D in Computer Science with minors in Mathematics and Control and Dynamical Systems
  Ph.D Thesis, Discrete Exterior Calculus ( Abstract, PDF, BibTeX)
• Engineer, Sony Corporation
• Software Engineer, Sun Microsystems
• M.S, Computer Science (Theoretical track), Stanford University
• Undergraduate degree, Computer Science Birla Institute of Technology and Science (BITS), Pilani, India
  

Affiliate:   Computational Science and Engineering Program

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.