The Atiyah portrait, commissioned in 2007 by the Royal Society of Edinburgh from the artist Juliet Wood (who retains copyright of the image).
The Atiyah portrait, commissioned in 2007 by the Royal Society of Edinburgh from the artist Juliet Wood (who retains copyright of the image).
The 80th birthday on 22nd April, 2009, of Sir Michael Atiyah was celebrated with the Atiyah80: Geometry and Physics conference organised by ICMS at the Informatics Forum of the University of Edinburgh and the Royal Society of Edinburgh, April 20–22, and a sequence of events Science, Politics and Drama at the Royal Society of Edinburgh and the Royal Lyceum Theatre, April 23–24.
About Sir Michael Atiyah: Wikipedia entry, MacTutor entry, mathematical ancestors, mathematical descendants.
Thanks to the Video Production Unit of University of Edinburgh Communications and Marketing for producing the videos, and to the Edinburgh Mathematical Physics Group for hosting the videos.
The Kervaire invariant of a 4k+2-dimensional framed differentiable manifold M is the Arf invariant Arf(q) ∈ {0,1} of the quadratic form q on H2k+1(M;Z2) determined by the framing. (The Arf invariant is worth 10 Turkish Lira). The original 1963 formulation of the Kervaire invariant problem: for which dimensions n=4k+2 do there exist 4k+2-dimensional framed differentiable manifolds M with 1? By the work of Browder (1969) it was known that n must be of the form n = 2i − 2; there were direct constructions for n = 2, 6, 14, 30 and an existence proof for n = 62. In his 21 April Atiyah80 lecture Hopkins stated:
Doomsday Theorem (Hill-Hopkins-Ravenel). For n ≠ 126 there exists an n-dimensional framed differentiable manifold with Kervaire invariant 1 if and only if n ∈ {2,6,14,30,62}.
News of the solution sparked discussions on the blogs
Not
even wrong, n-Category Café and a story in
Nature. Peter Woit’s Not even
wrong entry after the Singer85 MIT
conference 22–24 May: Of the conference talks I managed to get
to, probably the best was that of Mike Hopkins, who gave a blackboard
talk about the Kervaire invariant problem. This one was a lot more
accessible than his talk last month at the Atiyah80 conference, where
he unveiled his dramatic new results with Hill and Ravenel. In the
MIT talk, Hopkins concentrated on explaining the background and
significance of the problem, as well as giving some of the philosophy
of the proof, which uses what he describes as a ‘designer’ cohomology
theory.
See Andrew Ranicki’s slides on Michel Kervaire’s work in surgery and knot theory, for two lectures at the Kervaire Memorial Symposium, Geneva, 10–13 February, 2009, with an addendum Exotic spheres and the Kervaire invariant.
The Kervaire wing of Doug Ravenel's homepage has much more material about the Kervaire invariant one problem.
The Harvard-MIT Summer Seminar on the Kervaire Invariant.
Mathematicians solve 45-year-old Kervaire invariant puzzle (Story on the Simons Foundation website).
On the non-existence of elements
of Kervaire invariant one by M.A.Hill, M.J.Hopkins, D.C.Ravenel.
Arxiv preprint posted on 26th August, 2009.
On 21 April Sir Michael Atiyah chaired a panel discussion at the
RSE on The
Higgs boson: what, why, how?, with Peter Higgs, David Saxon and Edward Witten.
Summary report,
Audio
and slides of the discussion. The slides of Witten’s presentation, and the
slides of Saxon’s presentation.
The Atiyah80 photo album has photos from the panel discussion,
including
Peter Higgs blessing the RSE congregation. The 80th birthday of Peter Higgs on
29th May was celebrated by a reception at the Informatics Forum on 10th June.
The birthday cake illustrated the
Higgs mechanism.
Posters of Sir Michael’s life, which were displayed at Atiyah80 in Edinburgh, were made by Sebastia Xambo for the award to Sir Michael of an honorary degree in UPC Barcelona in April 2008.
©2009, Andrew Ranicki
Last updated: 16 July 2009
