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Tuesday, November 05, 2019

Understanding chaos: Artur Avila, 2014 Fields Medal recipient

ArtutrAvila - recipient of 2014 Fields Medal

Dr. V. I. Lakshmanan introduced me to Dr. V Kumar Murty last year. Dr. Murty is a mathematician and a Vedanta scholar. He is the CEO and Scientific Director of the Fields Institute. He invited me to participate in a private reception and public opening of the Fields Medal 2014 yesterday.

The Fields Institute is a centre for mathematical research activity - a place where mathematicians from Canada and abroad, from academia, business, industry, and financial institutions, can come together to carry out research and formulate problems of mutual interest. 

Its mission is to provide a supportive and stimulating environment for mathematics innovation and education.

It was founded in 1992, and initially located at the University of Waterloo. Since 1995, it has occupied a purpose-built building on the St. George Campus of the University of Toronto.

Avila explaining chaos

The Institute is internationally renowned for strengthening collaboration, innovation, and learning in mathematics and across a broad range of disciplines.

The Fields Institute promotes mathematical activity in Canada, helps to expand the application of mathematics in modern society, and makes mathematics accessible and engaging for all audiences.

In the 27 years since its establishment, the Fields Institute has become a world-renowned mathematical research centre known for its support of mathematical collaboration, education, and outreach.

The Fields Institute is deeply committed to bridging and connecting scientific communities and fostering and promoting new and existing collaborations.

The Institute is named after John Charles Fields.

John Charles Fields (May 14, 1863 – August 9, 1932) was a Canadian mathematician and the founder of the Fields Medal for outstanding achievement in mathematics.

Fields is best known for his development of the Fields Medal, which is considered by some to be the Nobel Prize in Mathematics.

First awarded in 1936, the medal is considered by many as the Nobel Prize of Mathematics. It was reintroduced in 1950 and has been awarded every four years since. It is awarded to two to four mathematicians, under the age of 40, who have made important contributions to the field.

Fields began planning the award in the late 1920s but, due to deteriorating health, never saw the implementation of the medal in his lifetime. He died on August 9, 1932 after a three-month illness; in his will, he left $47,000 for the Fields Medal fund.

The medal has been awarded since its inception by the International Mathematical Union (IMU). Details on how the medal is awarded are here: https://www.mathunion.org/imu-awards/fields-medal .

The Fields Institute has hosted the annual Fields Medal Symposium since 2012. The Symposium has become the Fields Institute's flagship event and attracts top mathematicians from around the world.

Artur Avila, a Brazilian mathematician who received the Fields Medal in 2014 at a ceremony in Seoul, South Korea, was honoured in the Fields Medal Symposium held on November 4, 2019. (https://www.mathunion.org/imu-awards/fields-medal/fields-medals-2014)

He 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 Рextending over fields as diverse as smooth dynamics, Schr̦dinger operators, rational billiards, one-dimensional maps, and many others Рcannot 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.

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?

Avila at Isabel Bader Theatre, which was packed to capacity
with math enthusiasts 

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 reflected on how his field has changed over time, and examine current questions at the forefront of dynamical systems theory.

The Public Opening of the Fields Medal awardee was held at Toronto’s Isabel Bader Theatre on 4 November 2019 and attracted more than 300 attendees.

The Public Opening celebrates mathematics, attempts to demystify the medallist's area of research, and provides an opportunity for the public to enjoy, learn from, interact with, and be inspired by the “rock stars” of mathematics.

Public Opening featured remarks from 
  • 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, Columbia University (Fields Medal 2006) 
  • Marcelo Viana, Director of Instituto Nacional de Matemática Pura e Aplicada
  • Melanie Woodin, Dean of the Faculty of Arts and Science, University of Toronto 
  • Dr. Kumar Murty CEO and Scientific Director of the Fields Institute
Also read: Finding a horseshoe on the beaches of Rio

Information for this blog has been derived from the following sources:






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