ICIAM '11 Minisymposium. Applied Hodge Theory

Vancouver, BC, July 18–19, 2011


Hodge theory is a classical topic in geometry and topology. Its best-known manifestation is probably the Helmholtz decomposition: Vector fields on a domain in 3-space may be orthogonally decomposed into a curl-free, a divergence-free, and a harmonic component. The topic has recently surfaced in unexpected areas of applied mathematics, notably in computer graphics, game theory, machine learning, numerical PDE, voting theory, sensor networks, and statistical ranking. Several variants of Hodge decomposition were applied in refreshingly new ways to obtain surprising results. This minisymposium brings together leading researchers behind these recent developments to discuss a promising new tool for applied mathematics.


Lek-Heng Lim, Yuan Yao, Anil Hirani


First Session: Monday, July 18, 3:00pm–5:00pm

Yuan Yao Peking University HodgeRank on Random Graphs
Sayan Mukherjee Duke University Towards Stratification Learning through Homology Inference
Pablo Parrilo Massachusetts Institute of Technology Flows and Decompositions of Games: Harmonic and Potential Games
Yinyu Ye Stanford University A FPTAS for Computing a Symmetric Leontief Competitive Economy Equilibrium

Second Session: Tuesday, July 19, 10:00am–12:00pm

Anil Hirani University of Illinois at Urbana-Champaign Numerical Methods for Hodge Decomposition
Douglas Arnold University of Minnesota at Twin Cities Hodge Theory, Hilbert Complexes, and Finite Element Differential Forms
Nat Smale University of Utah Abstract and Classical Hodge/De Rham Theory
Joel Friedman University of British Columbia Hodge Theory on Sheaves


For further information on this meeting, please email Lek-Heng Lim at lekheng(at)galton.uchicago.edu