Sir Michael Atiyah (portrait)

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, Celebratio entry of Michael Atiyah. Celebratio interview with Lily Atiyah.
Michael and Lily Atiyah Portrait Gallery James Clerk Maxwell Building, King's Buildings, University of Edinburgh, opened 22nd April 2013
Mathematical ancestors and descendants.
Publication list.

Conference related links

Media impact

Videos of the lectures

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 solution of the Kervaire invariant one problem

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.

The Higgs boson panel discussion

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.

Science, Politics and Drama


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.

  1. 0. Title
  2. 1. Youth
  3. 2. Early Landmarks
  1. 6. Collected Works A
  2. 7. Collected Works B
  3. 8. Photos
  1. 3. Bridge to Physics
  2. 4. European Mathematical Society
  3. 5. Abel Prize

Raoul Bott (1923–2005)

And more

©2009-17 Andrew Ranicki Valid HTML Last updated: 12 August 2017