Topology, the “rubber sheet geometry,” studies the properties of objects that do not change when they are pulled and stretched. Accepting somewhat fuzzy input, it is the part of mathematics that is typically applied when qualitative conclusions are reached. However, it has a — fascinating and not very well understood — quantitative aspect that is important in understanding singularities, and potentially, high-dimensional noisy data as well as aspects of large-scale geometry of networks. The talk will be a series of vignettes that display a number of different phenomena that arise or are illuminated when one keeps track of the complexity of geometric constructions.
Shmuel Weinberger is a Professor of Mathematics and Chair of the Department of Mathematics at the University of Chicago. He received his Ph.D. from the Courant Institute in 1982 and has been at the University of Chicago since 1984. He is a geometer and enjoys studying geometric problems — or any problem that has a hidden geometric aspect — using tools of algebra or analysis. He is a fellow of the AMS and of the AAAS, has been a Sloan Fellow, a Presidential Young Investigator and a Hardy lecturer of the London Mathematical Society, and has given a number of other distinguished lectures. In fall of 2011, he was Simons Professor at MSRI.