Apr 28
Math/Stats Colloquium: Lillian Pierce, Duke University
Here's an opportunity to hear our Frank G. and Jean M. Chesley Lecturer speak on mathematics. All are welcome!
Lillian Pierce, Duke University
Title: On superorthogonality
Abstract: How do we check if two vectors are orthogonal? We compute their dot product, which by definition takes two vectors as inputs. How do we check if two functions are orthogonal? We compute their inner product, which by definition takes two functions as inputs. Why only two? What would it mean for 4 functions to be “orthogonal”? Or 8 functions? Or 7 functions? Let’s call this superorthogonality. What can we deduce about collections of functions that are superorthogonal? We will explore how a wandering path through papers spanning 90 years led—completely by chance---to a systematic investigation of these questions, and a way to see that previously “unrelated” theorems share a very interesting structure deep under their surface.