CVC Seminar Web Mar 2, 1:30-3pm, ACES 4.304

Anil Hirani

Optimal (Co)homologous (Co)chains

There is an optimization idea that we have found in topology, in finite element methods, and in ranking problems. I will sketch this common thread in these three diverse fields. Then I will pick one of these and talk about it in detail. In topology this shows up in finding optimal chains [STOC 2010, arXiv:1001.0338] and in the knot spanning area problem [SoCG 2011, arxiv:1012.3030]. In FEM we see it in the computation of harmonic cochains [arxiv:1012.2835]. And in ranking it appears in least-squares ranking on graphs [arxiv:1011.1716]. It would be quite impossible to talk about all these in one talk, were it not for the common, specific, optimization concept connecting them all. It is just a matter of picking integers versus reals, and 1-norm versus 2-norm.