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 – 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.

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

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

https://en.wikipedia.org/wiki/Artur_Avila

https://www.thecanadianencyclopedia.ca/en/article/john-charles-fields

https://www.mathunion.org/imu-awards/fields-medal

http://www.fields.utoronto.ca/activities/19-20/fieldsmedalsym

https://www.eventbrite.ca/e/public-opening-of-the-2019-fields-medal-symposium-artur-avila-on-dealing-with-chaos-tickets-71072438577?utm_source=eventbrite&utm_medium=email&utm_campaign=reminder_attendees_48hour_email&utm_term=eventname&ref=eemaileventremind

Suketu Mehta's This is Our Land

My sister Sonal, who has lived in the United States since the late 1980s, sent me Maximum City: Bombay Lost and Found by Suketu Mehta in 2005, probably a year after it was published in the US.

For a person who had lived his entire life in Bombay and had covered it fairly extensively as a journalist for nearly two decades, the idea that a New Yorker could have anything new to say about one’s hometown was entirely preposterous, if not totally insulting.

But Suketu Mehta, even while talking about everything that was familiar, was saying it differently.

As a journalist one had witnessed and reported the deathly carnage of the 1992-93 rioting up close, but Mehta brought alive the horror of the bloodbath with passages such as this:

“What does a man look like when he’s on fire?” I asked Sunil.

It was December 1996, and I was sitting in a high-rise apartment in Andheri with a group of men from the Hindu nationalist Shiv Sena party. They were telling me about the riots of 1992-93, that followed the destruction of the Babri Masjid in Ayodhya.

The two other Shiv Sena men with Sunil looked at each other. Either they didn’t trust me yet or they were not drunk enough on my cognac. “I wasn’t there. The Sena didn’t have anything to do with the rioting,” one man said.

Sunil would have none of this. He put down his glass and said, “I’ll tell you. I was there. A man on fire gets up, falls, runs for his life, falls, gets up, runs.”

He addressed me.

“You would bear to see it. It is horror. Oil drips from his body, his eyes become huge, huge, the white shows, white, white, you touch his arm like this” – he flicked his arm – “the white shows. It shows especially on the nose” – he rubbed his nose with two fingers as if scrapping off the skin – “oil drips from him, water drips from him, white, white all over.”

“Those were not days for thought,” he continued. “We five people burnt one Mussulman. At four a.m. after we heard of Radhabai Chawl, a mob assembled, the likes of which I have never seen. Ladies, gents. They picked up any weapon they could. Then we marched to the Muslim side. We met a pavwallah on the highway, on a bicycle. I knew him; he used to sell me bread every day.” Sunil held up a piece of bread from the pav bhaji he was eating. “I set him on fire. We poured petrol on him and set him on fire. All I thought was, This is a Muslim. He was shaking. He was crying. ‘I have children, I have children!’ I said, ‘When your Muslims were killing the Radhabai Chawl people, did you think of your children?’ That day we showed them what Hindu dharma is.”

Maximum City not only defined Bombay but also went on to become a genre for writing creatively about complexities that cities – especially cities in the developing world – evolve and how they transform their inhabitants.

Fifteen years later, Suketu Mehta has published another path breaking book. This is Our Land – An immigrant’s manifesto’.  He has obviously written it in anger, desperation and frustration at the rapid transformation of the manner in which immigrants and immigration are being treated globally.

The developed economies have, in unison, decided that they have had enough of the unwashed masses that obstinately keep on showing up at their borders, and that these immigrants are really not their problem, and that they might as well drown in the ocean for all they care. The world has suddenly become inhospitable for immigrants.

I’m a Canadian citizen, an immigrant in a country that is unique in its tolerance of immigrants. Fortunately, my experience as an immigrant has been without the horrors of racism and discrimination.

Let me hasten to clarify that while Canada by and large accepts the inevitability of immigrants to in its society; it still has not been able to evolve a mechanism that ensure the economic integration of the immigrant.

Yes, there is a crazy, right-wing fringe in Canada, too, that turns abusive and occasionally even violent towards newcomers or people who look different, but their numbers are few. It wouldn’t be erroneous to claim that most immigrant in Canada don’t experience the terror and horror their counterparts feel in some parts of Europe and the United States.

Mehta’s book while authentically portraying the conditions immigrants face in the developed world, especially in the United States and western Europe, also analyses the causes of immigration. He says it is the fear of the immigrant that is more dangerous than the immigrants themselves. He cautions that if anything perennial economic subjugation (economic colonialism) and climate change will ensure more immigration than the world is prepared to accept or even understand.

Mehta was in Toronto on two occasions recently promoting his book. In September, he participated in the maiden Toronto edition of the Jaipur Literature Festival and in October he was here to participate in the Toronto International Festival of Authors.

Meenakshi Alimchandani, litterateur and literary curator, had organised Mehta’s session at the Toronto International Festival of Literature, and agreed to my suggestion to interview Mehta after the session.

My friend Gavin Barrett, a poet and founder of the immensely successful Tartan Turban Secret Reading Series (for which he also unjustifiably credits me) agreed to my suggestion that we chat with Mehta together, giving our Bombay connection.

Mehta wanted to have “something Indian” so we went to the Indian Roti House across the Harbourfront Centre. It turned out to be a rather modest desi restaurant, that served roti wraps in extra spicy chickpeas gravy.

Gavin and Suketu discovered they had common friends and that eased the conversation. What follows below are excerpts of an interview that talked about both Maximum City and This is Our Land. Mehta spoke freely, frankly and authoritatively.  

Suketu Mehta interview - 1

Mayank: Maximum City – there is no book written on a city like Maximum City. It is the first of its kind. And I don't think there have been many that have followed that were as ambitious.

Suketu: About once a month, I get a request to write a blurb for a book that is the Maximum City of Johannesburg, or the Maximum City about Beijing. There have been some books similar to Maximum City. But to me Maximum City evolved into the book that it became.  When I began, I had no idea what I was doing. It was part memoir, part travelogue, part investigative journalism. And it was my first book. I began with an idea – that I wanted to go home. I was a Bombay boy who had been abroad long enough, and I wanted to go home. I wanted my children to have a sense of what home meant to me and to them.

But that home turned out to be very different from what I thought it was. So, I just followed my nose and wherever I found interesting story I just followed it. When the book came out, no one had any expectations of it. I remember the editor of The Times of India’s Bombay edition, asking me, “Why would the Knopf reader be interested in a book about Bombay?” And I said, “You live here, and you don’t understand why?” I met Murli Deora, who was this long-time Member of Parliament. I met him at a party at the US Consulate, and he asked me, “How long will you take to write the book?” At that time, I was being optimistic, and said, “a couple of years.” And he responded, “Couple of years? Bapa na paisa bahu vadhi gaya chhe? Chha mahin ma patavi do.” (Couple of years. Does your father have a lot of money? Complete the book in six months).

Nobody had any clue what I was doing. One of the gangsters who I had interviewed, asked me, “Book likh rahe ho? PhD thesis jaisa book?” (You’re writing a book, just like a PhD thesis).

But it was a big book. It took me seven years.

I attribute its success to the interest that people have in the notion of a global city, the megalopolis. Since then, there have been a few wonderful books on Bombay.

I wanted my book to reach more than a certain kind of audience. My book is widely pirated on the streets of Bombay. So, once while I was in Bombay, this kid came up to me at the traffic lights carrying a stack of books and on the top was Maximum City. And he is shouting, “Chalo le lo, Maximum City, Maximum City…”

Gavin: That’s probably the ultimate compliment – to be sold a pirated version of your own book on Bombay on the streets of Bombay.

Suketu: I asked the boy, “Kitne ka hai?” (How much is it for?” And he replied, “Panso rupiya.” (Five hundred rupees). I tried to bargain with him and said, “Panso ruipya? Tere ko malum hai yeh kitab maine likhe hai?” (Five hundred rupees! Do you know, I have written this book?) Without losing momentum, the boy replied, “Thek hai, agar apne likhe hai to charso rupiya de do.” (OK, if you have written it, then give four hundred rupees).

I called my publisher and told him, “David, fire your sales force and hire this kid.”

Mayank: I don’t know whether Gavin has introduced himself, but his book of poems is being published next year.

Suketu: Congratulations!

Gavin: Thank you. I have a story about this involving Ranjit (Hoskote) and Nissim Ezekiel. I don’t know whether you know Nissim.

Suketu: Oh, I know Nissim. I’d meet him at the Theosophical Society at Churchgate.

Gavin: Yes, me too.

Suketu: And then, he would take me to the Udupi across the street, and then when I put in the tip, he would, with his boney hands, push back some coins to me, muttering, “too much, too much.”

Gavin: My goodness! You have a Nissim story. I can’t believe it. So, the story I have is that Nissim was to publish me when I was young, as part of Rupa’s Young Poets series, which I believe now doesn’t exist because they went bankrupt. They published Ranjit and two other poets. They were to publish 14 poets in that series. And that was the end of it. Now, I am an old poet, and some of the same work is being published now in 2020. Jerry, I think, was among that group, too. Do you know Jerry? Jerry Pinto?

Suketu: Maybe a little too well.

Gavin: I was a member of the Bombay Poetry Circle. I was there at its very first meeting. Ranjit was there, I was there, so was Anju Makhija, and a couple of others, George Oommen, and Nissim was also my professor when I was doing my MA at Bombay University. He was wise, witty, gentle, all-in-all a remarkable man.

Mayank: Coming back to our Q&A. You have written a book on immigration, and as you explained earlier today (at Toronto International Festival of Authors) it is a manifesto. You are very angry with the situation and you want the world to know that the entire debate around immigration has been wrongly construed. But immigration is not a new phenomenon. Opposition and resistance to immigration is also not new. Why now?

Suketu: There is a global backlash against immigration. There is this new populism against immigration and immigrants. Around the turn of the century, it seemed like globalisation had won the day. It was supposed to be end of history and we could all go wherever we wanted to go. Tom Friedman wrote in the New York Times that no two countries that have a McDonalds ever fought a war against each other. But then Russia and Ukraine went to war. There was a kind of backlash against this kind of global invasion and around the same time, more people started moving than ever before.

I felt my position as a migrant being challenged. I can’t stay silent as a writer.

Suketu Mehta interview - 2

Mayank: Immigration is relatively new in the West. But that is not the case in India. Indians have immigrated to Africa, to Fiji, to the Southeast Asia and other parts of the world long before the process of formal immigration began in the west.

Suketu: Immigration is also not new to the West. Every single western country has witnessed mass migration. We have been taught that Europe is where nationalism was born. Where geographical boundaries defined national identities. We were told to be like the British and the French. They were all united. But then it turned out that the French had their separatists, so did the Spanish and the English and all the rest of them. The notion that we have one identity – that we are Indian, or Canadian, or American is hogwash.

Mayank: Let me rephrase the question slightly. Would be correct to state that the West has an issue with non-white immigration. So, in essence, the problem is not immigration. It’s racism.

Suketu: It is both. America had the alien exclusion act where in the 1920s when they excluded Chinese immigrants. Non-white immigrants, particularly Asians, have traditionally faced difficulties in North America – both in America and in Canada. Australia had an only white immigration policy.

That has changed. Now, we are seen as good immigrants. Everyone wants Indians and Chinese because they are nice techies and doctors and they don’t make trouble. We are the ideal immigrants.

What is new is that the anti-immigrant prejudice is global. I recently went to India and gave a speech at the India Today Conclave. It’s gone viral, it has a quarter million views and counting.  They thought I will talk about global migration, and I began with that, but then I turned my attention to the NRC; it is horrific what India is doing. The NRC is basically an anti-Muslim policy.

We have seen that kind of a situation in Bombay with the Shiv Sena. I have known Bal Thackeray and I have interviewed him. I wrote in the New York Times comparing Trump to Bal Thackeray, and how both are gifted story tellers. Remember Thackeray’s Dushera rally?

Gavin: I wonder about Brexit. The worse own goal in British history. That is the example of anti-immigration not only having a race element but also anti other Europeans. The Poles are strong presence in Britain, and the Brits and the people in the countryside don’t want Polish people around them. This is a backlash of white against whites.

Suketu: Yes, in Britain absolutely. Yes, they don’t want Romanians, they don’t want Poles. They want to retreat into old England. All the sins of colonialism are being visited upon them, and it stems from an incredibly stupid fear of migrants. This fear is doing more damage to country after country. All the goals of the fascists are re-emerging – Hungary, Poland, Austria, Germany are being driven by fear of migrants.

And the fact is that this fear is based on illusion and an unwillingness to understand their realities. These societies are not producing enough babies and people there are growing old. They need young people to work and pay their pensions, and as they aren’t making enough of their own babies, they need to import.

They will be screwed without migrants. Look at Japan. It is stagnating under 4 percent because they have kept migrants out, and now they are desperate.

Gavin: This is so interesting because I am a real mongrel. My mother is from East Africa, my father is Anglo-Indian, and we almost moved to Japan in the 1970s when my dad was in the merchant navy.  He wanted us to live there because he loved the place, but we were not allowed to live there. I have a question – we look at the US and India because we are familiar with these societies, and we exclaim, “Oh! My God!” but are there are other flash points that we should be watching with even more fear and caution because the world’s eyes are not on them. As Indians abroad, we are always watching India, and the world watches the US.

Suketu: I don’t think that the focus on India is adequate. The subject of my talk in India was that Indian Muslims are being systematically being ‘othersied’ which I have never seen in my life. The situation is changing. When I was in Bombay last, a Muslim man came up to me and told me about his predicament. He went to Cathedral. He went to Stanford. He came back and joined a private equity firm. He is part of the elite of Bombay. It is just that he is a Muslim. He has always been glad that he is an Indian and not a Pakistani.

After Mr. Modi gets re-elected, this man’s Hindu friends tell him not to worry in case the private equity market tanks, “Aap kyun fikr karte hain? Aap ka toh ek tang Pakistan mein hain! (Why should you worry about market collapse. Your other leg is in Pakistan).

To say such a thing to a person like that is unimaginable. He was truly shocked. He has never felt like this in his entire life. He is around 50. Even during the riots, he didn’t feel like this. He realised that there was a fringe that was indulging in rioting. Now, the rot is throughout the Indian society.

I for one am truly scared about the Indian situation. What we are witnessing is a change in basic humanity and values. My grandfather had a jewelry shop in Calcutta. He was a member of the RSS. But when a Muslim man ran into his shop, he protected him and told the mob that chased him to his shop that he would shoot all of them if they so much as even touched him. That man was now his guest and it was his obligation to protect him. Such values are fast disappearing from India, I think.

Among this generation there is no knowledge of this past because history is so badly taught. There is an absence of intimate knowledge of the other. My grandfather, despite his RSS allegiance was deeply appreciative of the Persian language, which, he said, was the purest of languages.