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Research Interests

Algorithms (numerical and combinatorial) in geometry, topology, and scientific applications. Applications of geometry and topology to problems of current interest. Specific areas: discrete exterior calculus, finite element exterior calculus, applied and computational topology, discrete differential geometry, computational geometry, aggregation in unstructured and nonlinear spaces.

News

• February 1, 2012: NSF-CBMS lecture series on Finite Element Exterior Calculus website is up. The Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University is hosting the series. Prof. Doug Arnold (keynote speaker, 10 lectures), Prof. Richard Falk, and I will be speakers (I'll give 1 lecture).
• January 29, 2012: DDG@SoCG ! I am co-organizing a special workshop (with Mathieu Desbrun) at this year's ACM Symposium on Computational Geometry: Discrete Differential Geometry: Geometry Processing and Physical Simulations. It will be on one of the days during June 17-20, 2012. Details coming soon.
• February 21, 2011: See our NCAA basketball rankings and predictions page.
• December 13, 2010: Open problem solved: Least spanning area problem for knots in R^3 is in P.
  ACM Symposium on Computational Geometry (SoCG), 2011. See paper for details.
• February 5, 2010: Going from binary to integer coefficients makes an NP-hard problem tractable.
  Papers in ACM Symposium on Theory of Computing, 2010, and SIAM Journal on Computing.
  (Details)
• May 22, 2009: Open problem solved : Dihedral acute triangulation of cube. (Details)

Award

Teaching

• 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

Group Alumni

• Evan VanderZee, Completed Ph.D in Mathematics, December 2009. Now at Argonne National Lab.
  Coadvised with Vadim Zharnitsky of Mathematics department.
• Andrew Colombi, Graduated with Ph.D in CS, August 2008. Now software engineer at Palantir, a start-up software company in Californina.
• John Jossey (Postdoc), September 2006 - August 2007

Short CV

• 2005-current, 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
  
• 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
  

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