Title: Modeling lamprey swimming with mathematics and computation
Abstract: Locomotion — swimming, running, flying — is one of the most basic animal behaviors. In order for an animal (like a lamprey) to swim, a lot has to happen, including neural signaling, muscle contractions, interactions between the body and the water, and adjustments from sensory feedback. How do we use mathematics to better understand the underlying mechanisms that drive locomotion? We will explore how we can use mathematical models to describe these individual systems and then coordinate the systems to produce a naturally emerging behavior in computer simulations of swimming lampreys.
Title: The multiplicity one theorem for paramodular forms.
Abstract: Classical modular forms are known to have the “strong multiplicity one” property: A cuspidal eigenform is determined by almost all of its Hecke eigenvalues. Siegel modular forms, on the other hand, do not have this nice property. The main theorem presented in this talk states that strong multiplicity one still holds for an important class of Siegel modular forms known as “paramodular forms”. The latter have gained prominence because of their appearance in the “paramodular conjecture”, a degree-2 version of Shimura-Taniyama-Weil.
Title: What is Number Theory?
Abstract: In its original meaning, Number Theory is concerned with the properties of the “natural” numbers 1, 2, 3, … In this talk we will attempt to explain how the consequent study of “elementary” properties of numbers leads naturally to the theory of automorphic forms and the vast web of conjectures known as the “Langlands program”.