I will give an introduction to quantitative operator K-theory and discuss its applications to positive scalar curvature and filling radius. In particular, I will explain how to estimate the filling radius using the data involving scalar curvature, as conjectured by Gromov. I will make an effort for this talk to be accessible to graduate student.

Bio: Guoliang Yu earned his PhD from State University of New York at Stony Brook in 1991, under supervision of Ronald Douglas. He held positions at MSRI, University of Colorado at Boulder, and Vanderbilt University. Since 2012 he holds the Powell Chair and University Distinguished Professorship at Texas A&M University. His research has largely concerned Noncommutative Geometry, K-theory and Index theory, and their applications to geometry and topology of manifolds.