Talks - Anil N. Hirani

Selection of recent talks

Many of my talks are chalkboard talks, but here are some recent talks with slides or video:

2026: Discrete Vector Bundles with Connection and Čech Cohomology
2026: Convergence and Stability of Discrete Exterior Calculus for the Hodge Laplace Problem in Two Dimensions
2025: ICTS Lecture Series on Discrete Exterior Calculus
2025: Contraction Wedge Duality and Double Forms
2025: Boundary Dual and Codifferential in DEC

Selected Invited & Contributed Talks

2026: Discrete Vector Bundles with Connection and Čech Cohomology. Workshop on Discretization of Differential Complexes, Erwin Schrödinger International Institute for Mathematics and Physics (ESI), Vienna, Austria.
2026: Elasticity, Double forms, and Vector Bundles. Department of Mechanical and Aerospace Engineering Seminar, University of Florida, Gainesville.
2026: BGG for DEC in two dimensions with applications to biharmonic equation and planar elasticity. Workshop on Finite Element Tensor Calculus, Tsinghua Sanya International Mathematics Forum (TSIMF), Sanya, China.
2026: Convergence and Stability of Discrete Exterior Calculus for the Hodge Laplace Problem in Two Dimensions. International Workshop on Structure-Preserving Finite Element Methods, The Institute of Computational Mathematics and Scientific/Engineering Computing, Beijing, China.
2025: Lecture series on Discrete Exterior Calculus (3 lectures). Geometry, Mechanics and the Physics of Growth, International Centre for Theoretical Sciences (ICTS), Tata Institute of Fundamental Research, Bengaluru, India.
2025: Contraction Wedge Duality and Double Forms. Special Session on Numerical PDEs and Geometry, AMS Fall Central Section Meeting, St. Louis, Missouri.
2025: Discrete Exterior Calculus: Overview and Perspective. Discrete Exterior Calculus: Differential Geometry and Applications. NSF Institute for Mathematical and Statistical Innovation (IMSI). Chicago, Illinois.
2025: Tutorial Introduction to Exterior Covariant Derivatives of Double Forms. Geometric Mechanics, Structure Preserving Discretization, and Discrete Differential Geometry on General Fibered Manifolds, SUNY Polytechnic Institute, Utica, New York.
2025: Subdivision functor and vector bundle valued DEC. BIRS Workshop on Geometric Mechanics Formulations for Continuum Mechanics, Banff, Canada.
2025: Boundary dual and codifferential in DEC. SIAM CSE, Fort Worth, Texas.
2024: Marsden Memorial Lecture: Calculus and geometry on graphs and meshes. Distinguished Lecture Series of Pacific Institute for the Mathematical Sciences, UC Merced, California.
2024: Some Properties of Wedge Product in Discrete Exterior Calculus. NSF CompMath PI meeting, University of Washington at Seattle.
2024: Bianchi Identity for Discrete Vector Bundles. SIAM Annual Meeting, Spokane, Washington.
2024: Discrete Exterior Calculus: Introduction to calculus on graphs and meshes via examples. Discovery Partners Institute, Chicago, Illinois.
2023: Wedge product and naturality in discrete exterior calculus. Applied Mathematics Seminar, Department of Mathematics, University of Hawaii at Mānoa, Hawaii.
2023: Wedge Product and Naturality in Discrete Exterior Calculus. Sandia National Laboratory, Albuquerque, New Mexico.
2023: Naturality of Discrete Exterior Derivative and Discrete Wedge Product in DEC. University of Jyväskylä, Finland.
2022: Discrete vector bundles with connection and curvature. Hilbert Complexes: Analysis, Applications, and Discretizations, MFO Oberwolfach, Germany.
2022: Averaging property of a discrete wedge product. Minisymposium on Conservative and Geometric Discretizations, CAIMS Annual Meeting, UBC Okanagan, Canada.
2022: Discrete vector bundles with connection. Workshop on Discrete Shapes, Center of Mathematical Sciences and Applications, Harvard University, Massachussetts.
2021: Structure-preserving discretization of differential calculus and geometry (online). Kyushu-Illinois Strategic Partnership Colloquium, UIUC and Kyushu University, Japan.
2020: Discretizations of exterior calculus and differential geometry. Mathematics Seminar Series, Indraprastha Institute of Information Technology Delhi, New Delhi, India.
2020: Discretizations of exterior calculus and differential geometry. Department of Mathematics, Indian Institute of Science Education and Research, Pune, India.
2019: Discrete vector bundles with connection and the first Chern class. Geometry, Compatibility and Structure Preservation in Computational Differential Equations, Newton Institute for Mathematical Sciences, Cambridge University.
2019: Conservative methods for piecewise smooth dynamics. Annual Meeting of the Canadian Society of Applied and Industrial Mathematics.
2016: Discrete exterior calculus discretization of Navier-Stokes equations on surface meshes. Mathematical Soft Matter Unit, Okinawa Institute of Science and Technology, Japan.
2016: Discretizations of exterior calculus. Mathematical Soft Matter Unit, Okinawa Institute of Science and Technology, Japan.
2015: Introduction to PyDEC. Workshop on Geometry and Symmetry based Mathematical and Computational Methods, SUNY Polytechnic Institute, Utica, New York.
2014: New spaces for DEC. Geometric Discretization Methods and Adaptivity, Canadian Mathematical Society (CMS) Winter Meeting.
2014: Lectures on discretizations of exterior calculus. King Abdullah University of Science and Technology (KAUST), Saudi Arabia.
2014: First steps toward DEC Poisson convergence proofs. Structure-Preserving Discretizations of Partial Differential Equations, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, Minnesota.
2012: Applied topology and matrix methods. AMS Special Session on Applied Topology, AMS Fall Central Sectional Meeting, Columbus, Ohio.
2012: Numerical PDEs and applied topology. Center for Computational Mathematics Seminar, Department of Mathematics, University of California at San Diego.
2012: Applied topology and numerical PDEs. Applied Mathematics and Analysis Seminar, Department of Mathematics, Duke University, Durham, North Carolina.
2012: Applied topology and matrix methods. ECE Distinguished Seminar, Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolia.
2012: Discrete exterior calculus and its connection to finite element exterior calculus. ICERM, Brown University, Providence, Rhode Island.
2012: Optimization problems in computational topology. Applied Mathematics and PDE Seminar, Department of Mathematics, University of California at Davis, California.
2012: Relative torsion in homology computations. Oberwolfach Workshop on Triangulations, Mathematisches Forschungsinstitut Oberwolfach, Germany.
2012: Algebraic topology for computations. Topology Seminar, Department of Mathematics, Stony Brook University.
2012: Algebraic topology for computations. Topology Seminar, Department of Mathematics, City University of New York.
2012: Torsion in computations. Dagstuhl Seminar on Applications of Combinatorial Topology to Computer Science, Schloss Dagstuhl, Germany.
2012: Holes, handles, and tunnels. Center for Imaging Science, Johns Hopkins University, Baltimore, Maryland.
2012: Hodge decomposition: applications and numerics. Scientific and Statistical Computing Seminar, Departments of Computer Science, Mathematics, and Statistics, University of Chicago, Illinois.
2011: Optimization, knots, and differential equations. Workshop on Computational Topology, Fields Institute, Toronto, Canada.
2011: Optimal homology cycles and knots. Certified Geometry Processing Minisymposium, SIAM Conference on Geometric & Physical Modeling.
2011: Darcy flow using discrete exterior calculus. High Order Mimetic Discretizations Minisymposium, 7th International Congress on Industrial and Applied Mathematics.
2011: Optimal (co)homologous (co)chains. Department of Computer Science, University of Texas at Austin.
2011: Latest developments in discretization of exterior calculus. X-Computational Physics Division, Los Alamos National Laboratory.
2010: Optimal homologous cycles, total unimodularity, and linear programming. 42nd ACM Symposium on Theory of Computing (STOC'10), Cambridge, MA, June 6–8.
2010: Computational topology and linear programming. Departments of Computer Science and Mathematics, Stanford University.
2010: Computational topology and linear programming. Graphics, Vision and Interaction Seminar, Harvard University.
2010: Some PyDEC applications. Workshop on Discrete Differential Geometry for Multiphase Flow Problems, Indiana University Purdue University Indianapolis.
2010: Homologous chains, total unimodularity, and linear programming. Department of Computer Science, Caltech.
2009: Implementation of discrete exterior calculus. Guest Lecture in Topics in Scientific Computing, University of Chicago.
2009: Implementation of Hodge theory for simplicial complexes. Machine Learning Summer School, University of Chicago.
2009: Stiffness and Mass Matrices for Whitney Forms. Finite Element Circus, Newark, DE, April 24–25.
2009: Algorithms for Exterior Calculus. Finite Element Methods in Engineering and Science (FEMTEC 2009), Lake Tahoe, CA, January 5–9.
2008: Structure Preserving Approximations of Conservative Forces for Application to Small Body Dynamics. AAS/AIAA Astrodynamics Specialist Conference, Honolulu, HI, August 18–21.
2008: Software and algorithms for exterior calculus. Department of Mathematics Colloquium, Northern Illinois University.
2008: Calculus on meshes. Department of Computer Science and Engineering Seminar, Ohio State University.
2008: Calculus on meshes. Department of Mathematics Seminar, Mumbai, Indian Institute of Technology Bombay, India.
2006: Approximations of Distant Retrograde Orbits for Mission Design. AAS/AIAA Spaceflight Mechanics Meeting, Tampa, FL, January 22–26.
2006: Dynamical Systems and Space Mission Design. Department of Aerospace Engineering AE 590 Seminar, University of Illinois at Urbana-Champaign.
2005: Surface Structure of an Invariant Manifold of a Halo Orbit. AAS/AIAA Astrodynamics Specialists Conference, Lake Tahoe, CA, August 7–11.
2004: Discrete exterior calculus and the averaged template matching equations. Mathematics in Brain Imaging, Institute for Pure and Applied Mathematics, UCLA.
2004: Discrete exterior calculus. Oberwolfach Seminar on Discrete Differential Geometry, Mathematisches Forschungsinstitut Oberwolfach, Germany.
2004: Discrete exterior calculus: applications in mechanics and computer science. Los Alamos National Laboratory.
2004: Discrete exterior calculus: applications in computer science. Applied Mathematics and Mechanics, Sandia National Laboratory.
2003: Discrete Exterior Calculus. Mimetic Discretizations of Continuum Mechanics, San Diego, CA, July 9–11.
2003: Discrete Exterior Calculus. SIAM Conference on Applications of Dynamical Systems (DS03), Snowbird, UT, May 27–31.
2003: Discrete Exterior Calculus and its Applications. SIAM Conference on Computational Science and Engineering (CSE03), San Diego, CA, February 13.
2003: Template matching, EPDIFF and discrete exterior calculus. Center for Nonlinear Studies, Los Alamos National Laboratory.
2002: Analysis of 1D Template Matching Equations. 9th International Conference on Hyperbolic Problems (HYP2002), Pasadena, CA, March 25–29.
2001: Averaged Template Matching Equations. Energy Minimization Methods in Computer Vision and Pattern Recognition, Sophia-Antipolis, France, September 3–5.
1996: Combining Frequency and Spatial Domain Information for Fast Interactive Image Noise Removal. ACM SIGGRAPH, New Orleans, LA, August 4–9.