Osamu Saeki from Kyushu University, will present a William J. Spencer Lecture titled “Simplifying generic smooth maps to the 2-sphere and to the plane” as part of the Mathematics Department Colloquium Lecture Series.

Abstract: Every smooth function on a manifold can be approximated by a Morse function. In the 1960s Smale proved the generalized Poincaré conjecture in high dimensions by establishing a simplification method for such functions. On the other hand, in the 1950s, Whitney and Thom showed that every smooth map of a manifold into a surface can be approximated by a generic map, which has only fold and cusp singularities. In this talk, some simplification algorithms for such generic maps will be discussed and a result similar to Smale's will be presented.

The Math Department is a part of K-State’s College of Arts and Sciences.  To learn more about opportunities in Math at K-State, visit the math department website.