This event is FREE and OPEN to the public.

First come-first serve seating, subject to venue capacity.

PROGRAM

Welcome and Opening Remarks

V. Kumar Murty, Director, Fields Institute
Vivek Goel, Vice-President, Research and Innovation, and Strategic Initiatives, University of Toronto
Alejandro Adem, President, Natural Sciences and Engineering Research Council of Canada
Andrei Okounkov, International Mathematical Union, and Columbia University (Fields Medal 2006)

Introduction

Marcelo Viana, Instituto Nacional de Matemática Pura e Aplicada (IMPA)

Talk Title: Renormalization - The work of Artur Avila

Abstract: Artur Avila is an outstanding mathematician. A dynamicist through and through, he combines the powers of a consummate analyst with a remarkable strategic flair for approaching and solving difficult problems. The sheer breadth and depth of his work – extending over fields as diverse as smooth dynamics, Schrödinger operators, rational billiards, one-dimensional maps, and many others – cannot be summarized in a few sentences. And yet, there is a unifying concept behind many of his most important results: that of renormalization. The idea originates from Physics: in the simplest form, renormalization expresses the physical fact that certain phenomena are not affected when different quantities – such as length and temperature – are rescaled suitably. Renormalization was proven equally fruitful in the realm of Mathematics, and Artur is its most skillful user.

Public Lecture

Artur Avila, University of Zurich and IMPA

Talk Title: Dealing with Chaos

Abstract: Dynamicists have been occupied by a question since Isaac Newton’s era: given a system that evolves in time, what can be said about its behaviour over long time scales? Since Newton’s day, our understanding of the question has changed significantly with the discovery of chaos and its presence even in some of the simplest situations. In this public lecture, Avila will reflect on how his field has changed over time, and examine current questions at the forefront of dynamical systems theory.