In this talk, I will give a brief and intuitive overview of the methods of Topological Data Analysis we developed in my Discuri Centre. Starting from Euler numbers and its generalization we will get to the regime of statistical goodness of fit test. We will explore alternative methods of constructing graph based visualization of data.…

The interpolation method is a very powerful tool to construct special solutions in geometric analysis. I will present two applications in mean curvature flow: one is constructing a new genus one self-shrinking mean curvature flow, and another one is constructing immortal mean curvature flow with higher multiplicity convergence. The talk is based on joint work…

A fundamental question in Differential Geometry which has spurred much recent work is whether every orientable compact surface with boundary can be minimally embedded in the Euclidean 3-ball with free boundary.  I will discuss work (joint with M. Karpukhin, R. Kusner, and D. Stern)  which resolves this problem.