# Symposium in honor of Abel laureate John Milnor

The Royal Swedish Academy of Science hosted a seminar on May 27, to honor the Abel Prize 2011 laureate John Milnor and his mathematical work. In 1962 Milnor received the Fields Medal - togehter with Lars Hörmander - at the International Congress of Mathematicians in Stockholm.

**Description:**The purpose of this seminar is to honor John Milnor and his mathematical work.

Milnor's discovery of "exotic spheres" was completely unexpected. It lead to the creation of the field of "differential topology" and an explosion of work by a generation of brilliant mathematicians; this explosion has lasted for decades and changed the landscape of mathematics. Milnor's disproof of the long-standing Hauptvermutung overturned expectations about combinatorial topology dating back to Poincaré. Milnor also discovered homeomorphic smooth manifolds with nonisomorphic tangent bundles, for which he developed the theory of microbundles.

Outside topology, Milnor made significant contributions to differential geometry, algebra, and dynamical systems. In each area Milnor touched upon, his insights and approaches have had a profound impact on subsequent developments.

More recently, John Milnor turned his attention to dynamical systems in low dimensions. With Thurston, he pioneered "kneading theory" for interval maps, laying down the combinatorial foundations of interval dynamics, creating a focus of intense research for three decades. The Milnor−Thurston conjecture on entropy monotonicity prompted efforts to fully understand dynamics in the real quadratic family, bridging real and complex dynamics in a deep way and triggering exciting advances.

Milnor is also a wonderfully gifted expositor of sophisticated mathematics. He has often tackled difficult, cutting-edge subjects, where no account in book form existed. Adding novel insights, he produced a stream of timely yet lasting works of masterly lucidity. Like an inspired musical composer who is also a charismatic performer, John Milnor is both a discoverer and an expositor.

**Program**

14.30 Coffee and registration

15.00 Opening of the symposium

Nils Christian Stenseth, Vise-Preses i Det Norske Videnskaps-Akademi

15.05 Introduction - The Abel Prize

Ragni Piene, Abelkomiteen, University of Oslo, Norway

15.20 Spheres

John Milnor, Institute for Mathematical Sciences, Stony Brook University, New York

16.20 Lagrangian submanifolds and differential topology

Tobias Ekholm, Uppsala University & the Academy's Class for mathematical sciences

17.15 One-dimensional quasiperiodic dynamics: from circle diffeomorphims to interval exchange maps

Jean-Christophe Yoccoz, Collège de France & Tage Erlanderprofessor, KTH

### Abel in Oxford" with lecture by Sir Andrew Wiles

It has become a tradition that the Abel Committee after its final meeting hosts an Abel seminar. This year the committee meeting at London Mathematical Society was followed by "Abel in Oxford" with Abel Laureate Andrew Wiles as the main speaker. Martin Bridson, head of the Mathematical Institute, University of Oxford and Camilla Serck-Hanssen, Vice President of the Norwegian Academy of Science and Letters gave introductory talks.

(02.02.2018) More### Yves Meyer received the Abel Prize from H.M. King Harald

H.M. King Harald presented the Abel Prize to Yves Meyer of the École normale supérieure Paris-Saclay, France at an award ceremony in Oslo on 23 May. He receives the prize for his pivotal role in the development of the mathematical theory of wavelets, says John Rognes, chair of the Abel committee. Among the prominent guests attending the award ceremony was the French ambassador to Norway, Jean-François Dobelle and the Norwegian Minister of Education and Research, Torbjørn Røe Isaksen.

(26.05.2017) More### Three days of celebration for Abel Laureate Yves Meyer

His Majesty King Harald will present the Abel Prize to Yves Meyer at an award ceremony in Oslo on 23 May. He receives the prize "for his pivotal role in the development of the mathematical theory of wavelets", to quote the Abel committee. Yves Meyer, of the École normale supérieure Paris-Saclay, was the visionary leader in the modern development of this theory, at the intersection of mathematics, information technology and computational science.

(12.05.2017) More### The Abel lectures 2017

Abel Laureate Yves Meyer gave his prize lecture at the University of Oslo on the 24th of May, with following Abel lectures by Stéphane Mallat, Ingrid Daubechies og Emmanuel Jean Candès. Watch the lectures here.

(08.05.2017) More### Congratulations from AMS President

"On behalf of the American Mathematical Society, it is my great pleasure to congratulate Professor Yves Meyer, recipient of the 2017 Abel Prize. Professor Meyer has been a visionary in a broad range of fields, including number theory and differential equations. His fundamental work in the theory of wavelets has transformed the world of signal processing and has led to a myriad of practical applications." -- AMS President Kenneth A. Ribet (University of California, Berkeley)

Photo: Jim Brook

(02.04.2017) More