Marcella Manivel from the University of Minnesota will give this semester's Mary Winston Newson lecture.  

Title: Number Theory, Sturm-Liouville Problems, and the quantum harmonic oscillator

Abstract:   What do the quantum harmonic oscillator and Sturm-Liouville problems have to teach us about number theory? And how does any of this relate to attempts to prove the Riemann Hypothesis? Regarding the latter, Bombieri and Garrett showed that the discrete spectrum (if any) of a Friedrichs' extension of a suitable restriction of the Laplacian is s(s-1), for s a zero of the Riemann zeta function or another L-function. However, they proved that the discrete spectrum of this operator is small: Montgomery's Pair Correlation would imply that at most 94% of the zeros of the Riemann Zeta function participate in its spectrum. This motivates understanding analogous operators with demonstrably large discrete spectrum. To understand this, we'll take inspiration from a well-known operator with purely discrete spectrum: the quantum harmonic oscillator. This talk gives an overview of each of these ideas, connects them together, and concludes with how this story relates to my thesis work.

More information on the Mary Winston Newson Lecture Series can be found here: https://www.math.ksu.edu/student-success/ugrad/professional_organizations/awm/MWN.html. If you have suggestions for future MWN Lecturers email kklingerlogan@ksu.edu).