Shachar Weinbaum, Technion

Abstract

Is this number irrational? This question has been troubling mathematicians since the time of Pythagoras, and inspired a search for good rational approximations of constants. Examining the literature on irrationality, we notice a recurring theme: holonomic sequences. These recursive sequences have dominated this field, generating very good approximations. In this talk we shall detail an experimental journey into the "forest" of holonomic functions. In our exploration, we will pick up a powerful object - the Conservative Matrix Field. With this map in hand, we shall re-discover many known Diophantine approximations (Apery, Beukers, Zudilin, Aptekareve), and some new ones as well. If time permits, we will detail more deeply the conjectured properties of these Matrix Fields.

Link to video: https://vimeo.com/1052128191?share=copy

Presented Via Zoom: https://rutgers.zoom.us/j/91865817691

Password: 6564120420

For further information see: https://sites.math.rutgers.edu/~zeilberg/expmath/