# 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

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### Sir Michael Atiyah gives Abel lecture at ICM in Rio

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(26.07.2018) More