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News

• New   October 30, 2012: Our Delaunay Hodge Star paper just won the Best Paper Award (Second Place) in Solid and Physical Modeling 2012 (Second out of 38 papers).
• New   September 21, 2012: Our paper Geometric and Combinatorial Properties of Well-Centered Triangulations in Three and Higher Dimensions has been accepted in Computational Geometry: Theory and Applications. On the plane a vertex needs at least 5 neighbors to allow for well-centered (acute) triangles. How many does one need in three dimensional space ? This paper answers these and many other related questions.
• July 30, 2012: Our Delaunay Hodge Star paper accepted for Solid and Physical Modeling (SPM 2012) conference and Computer-Aided Design journal. We show in this paper that the dual lengths, areas, volumes etc. for a Voronoi dual can be assembled from signed elementary duals if the primal is Delaunay. (You have to read the proofs to see this point.) See paper for details. By the way the SPM acceptance rate this year was 44% (38/87).
• I am co-organizing (with Yuliy Baryshnikov and Susan Holmes) Topology and Geometry of Networks and Discrete Metric Spaces as part of the 2013-14 IMA Thematic Year on Scientific and Engineering Applications of Algebraic Topology.
• April 26, 2012: DDG@SoCG (Discrete Differential Geometry: Geometry Processing and Physical Simulations) website is now live and has the list of confirmed speakers and registration info. This is a special workshop I am co-organizing with Mathieu Desbrun on June 18 at this year's ACM Symposium on Computational Geometry at UNC Chapel Hill.
• April 2, 2012: Just posted a paper on Delaunay Hodge star. We define a signed dual volume and show that DEC Hodge star can be defined for Delaunay meshes under mild boundary assumptions. This opens up use of DEC on a much wider class of meshes. See arxiv.
• March 5, 2012: Alan Demlow and I have just posted our paper on adaptive finite element exterior calculus on arxiv.
• February 29, 2012: Our PyDEC paper has been accepted by ACM Transactions on Mathematical Software. PyDEC is a Python library that implements (i) discrete exterior calculus, (ii) lowest order finite element exterior calculus; and (iii) many objects and operators useful for experiments in topology. See the preprint on arxiv.
• 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).
• 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 (and similarly for knots in other orientable 3-manifolds with trivial 2-homology group). ACM Symposium on Computational Geometry (SoCG), 2011. See paper for details.
• February 5, 2010: Going from mod 2 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)

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)

Teaching

• 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

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 some kind of big shot at Palantir in Silicon Valley.
• John Jossey (Postdoc), September 2006 - August 2007

Theses

• Ph.D Thesis, Discrete Exterior Calculus ( Abstract, PDF, BibTeX), Caltech, 2003 (advisor Jerrold E. Marsden).
• M.S. Thesis, Linearization Methods for Variational Integrators and Euler-Lagrange Equations, Caltech, 2000.

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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