Paper dedicated to Jon Borwein

EXTREMALITY OF CONVEX SETS WITH SOME APPLICATIONS by Boris S. Mordukhovich and N. M. Nam Dedicated to the memory of Jonathan Michael Borwein

Abstract: In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the convex case. Then we apply this machinery to deriving new calculus results on intersection rules for normal cones to convex sets and on infimal convolutions of support functions.

From Introduction: Convex analysis has been well recognized as an important area of mathematics with numerous applications to optimization, control,

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My father (by Naomi Borwein)

Talk by Naomi Borwein at Jonathan Borwein’s funeral, 10 August 2016.

Jonathan was a complicated figure, of profound and intense contradiction, and a formidable and DEVOTED father. He cared deeply, thought deeply, and felt deeply about most things. A lot of people will be discussing the impact and scope of Jon’s academic output or his sheer brilliance — his genius. But, year after year his work evolved as I watched from the sidelines. So, I am going to share a snapshot of Jon as a fixture of my daily life, through the lens of the everyday.

A ubiquitous aspect of

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Jonathan was a great man

Jonathan was a great man and a great mathematician and his death represents a great loss to mathematics,throughout the world.

As a mathematician he was original innovative and inspirational. As a scientific colleague he was respectful, courteous and generous.

He will be sadly missed. Yours sincerely, John. [John Butcher, University of Auckland, New Zealand]

My brother Jon (by Sarah Borwein)

Talk by Sarah Borwein at the funeral of Jonathan Borwein, August 10, 2016:

My Brother Jon

Jon was a brilliant man. We all know that. I can’t speak about his work or the incredible impact I know he had on the world of mathematics. I knew Jon very simply as my big brother. When I was very small, and he was still Jonathan not Jon, I couldn’t pronounce his name properly, so I called him Jofnan. I don’t think I ever went rock-fishing with him, but I do have a vague memory of him taking me swimming in the North

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My brother Jon (by Peter Borwein)

Talk by Peter Borwein at the funeral of Jonathan Borwein, August 10, 2016 (read by Sarah Borwein):

My brother Jon was a remarkable and unusual talent. He was also an unusual and remarkable brother.

I have fond memories of growing up with Jon, as young boys in St. Andrews, Scotland.

An early memory of Jon is of us fishing off the pier in St. Andrews with our dad David. We would catch rock cod, and make my mother Bessie clean them and make fish cakes. This delighted Jon.

He and I also spent much of our childhood with

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His optimism seemed unconquerable

I heard Jon’s lecture here at Western University back in April. I am not a mathematician, but from what I could understand, I was in the presence of genius. He ranged over so many topics and with such breezy fluency that I had the impression of immersing myself into the entirety of modern mathematics. Jon was affable, funny, versatile, curious and just an all-round pleasant person. His optimism seemed unconquerable. My family and I extend our deepest sympathy to all the grieving Borweins. [Vlad Tumanov, Associate Professor, Dept. of Modern Languages and Literatures, Western University, Ontario, Canada]

A small tribute to a giant

Jonfest 2011 T-shirt

Back in the Spring of 2011, I attended JonFest at IRMACS, a conference marking Jon’s 60th birthday. Part of the swag was the following T-shirt, with a background of what I was certain was a visualization from some of Jon’s (at-the-time) recent work. It was often on the presentation monitor between speakers, and during conference lulls I tried to construct theories around what it might be visualizing.

After exhausting mathematical ideas, I moved onto more symbolic ones, and my favourite of the latter was the following: the center circle was Jon’s brain, and all

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Jon was a truly special person

Apart from his accomplishments, Jon was a truly special person with respect to his habits of mind, his enthusiasm for life, his sense of humor, his overall graciousness and his perspectives on mathematics and on life. It was a privilege for me to have known him over the years. After his sudden death, I suddenly conceived of and wrote a paper that I have dedicated to him. None of this existed in my mind before his passing, and I deeply believe in the (Christian) idea of annunciation as a spur to creative action. [Gerald Beer, California State University, Los Angeles,

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An absolutely brilliant mathematician

We are shocked and saddened by this unbelievable news.

Jon was an absolutely brilliant mathematician and visionary with incredible gifts also for exposition, for sharing mathematics, and for inventing new ways of doing mathematics. Jon was also a fantastic person who was friendly, encouraging and loving; and he was full of fun and vigour.

We lovingly remember our supper together on July 7th at Massey’s Indian restaurant, and Jon’s great colloquium talk delivered on the same day. Here attached is a poster we made in Jon’s honour for his talk at Western.

We are sending our deepest

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Jon was a creator

Jon was a creator, a great mind, a creative mind, and a light for many, many mathematicians, from many countries. He was a gem, and I still can’t believe he is gone. Everywhere Jon went, he created new opportunities for other mathematicians, by initiating so many fascinating and fruitful research directions, and also by initiating so much infrastructure for collaborations among mathematicians from geographically diverse locations around the world. One of his most recent feats, for example, was the creation of CARMA, which is the research center in Newcastle University, Australia, for ‘Computer Assisted Research Mathematics and its Applications’. This

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