Online stream: The event will be streamed live from this page.

Watch The Abel lectures live here:

Program:

10:00: Dennis Sullivan, Abel Prize Laureate Gathering chestnuts of math related to fluid motion

11:00: Michael J. Hopkins, Harvard University The great wild manifold rodeo: Dennis Sullivan in algebraic topology

11:55: Lunch

12:45: Session in honour of Abel Laureates 2020 and 2021, with John Grue and Gunn Birkelund

13:05: Étienne Ghys, ENS Lyon Dynamics à la Dennis Sullivan

13:50: Jim Simons, mathematician, hedge fund manager and philanthropist, USA Jim Simons in conversation with Nicolai Tangen and Nils A. Baas: Mathematics, Common Sense and Good Luck

Summaries

By now the beautiful equations modeling incompressible fluid motion in three dimensional space have been singled out by a precise yes or no mathematical question that appears among the Clay Millennium Problems. If the answer is yes this gives credence to continue using only this model to build algorithms that will better predict and compute the complicated motion of fluids. If the answer is no the motivation for using this model for said algorithms persists especially if the counterexamples are not generic. However, the existence of observed turbulence with lots of structure suggests new ideas perturbing current modeling are called for. The lecture is about a few modest insights into this issue that have accrued over three decades of personal curiosity.

Modern geometry is often described as a study of "shapes." But what is a "shape" in the first place?. Can anything meaningful be said about the totality of all possible "shapes?" These are not easy questions, and in fact it's not so easy to even frame them clearly as questions. There are geometric structures that arise in navigation, engineering, biology, design, and many other subjects. Each has its own suitable notion of "shape." In the 1970s Dennis Sullivan rode into this area, reconnoitered the bestiary and the hills, fenced off pastures and tamed the wild country. In this talk I will describe this work of Sullivan and the profound impact it had, and continues to have, on our understanding of geometry and the great variety of ways it is understood and used.

A dynamical system is usually defined as a system whose state evolves over time according to a fixed rule. In many cases, it is the study of the asymptotic behavior of the trajectories of a vector field. For Dennis Sullivan, this definition is too restrictive. In this talk, I would like to present his global perspective in which he seeks to clarify a few simple and unifying principles. It goes without saying that I will not be able to present all of Dennis’ work in the field of dynamics, and I will have to limit myself to a few examples.