分野別セミナー

In general, scientific data obtained by a simulation or an experiment can be represented as a discrete set of sample points of a smooth map between manifolds. In computer science, visualization of such data has long been studied, and it has been clarified that differential topological techniques are essential for such visualization. However, they are encountering various mathematical problems for further development. In this talk, we first survey existing techniques based on Morse theory. Then, we present recently developed visualization techniques based on singular fibers of stable maps and their Stein factorizations. We also present the reverse direction: in fact, these visualization techniques can also be used for the research of singularity theory as a new tool.