Atiyah80+
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
- Edward Witten (IAS, Princeton and CERN),
Nahm's equations, the Bogomolny equation, and an application to Geometric Langlands.
Slides. Paper.
Witten lecturing in Oxford (1988) (Painting by Sally Oswald).
- Nigel Hitchin (University of Oxford),
Hyperbolic monopoles and rational normal curves. Slides.
- Tom Bridgeland (University of Sheffield) Counting invariants and wall-crossing.
Slides.
- Frances Kirwan (University of Oxford).
Geometric invariant theory for non-reductive group actions and applications via jet differentials.
Slides.
- Mike Hopkins (Harvard University)
Applications of algebra to a problem in topology. Slides.
- Graeme Segal (University of Oxford)
Noncommutative geometry and quantum field theory
- Dusa McDuff (Stony Brook/Barnard)
Symplectic embeddings of 4-dimensional ellipsoids. Slides.
- Paul Seidel (MIT)
Homological mirror symmetry for the genus two surface
- Cumrun Vafa (Harvard University)
Strings and the geometry of particle physics. Slides.
- Simon Donaldson (Imperial College London)
Kähler-Einstein metrics and geometric quantisation
- Robert Dijkgraaf (Royal Netherlands Academy of Arts and Sciences)
Topological strings and quantum curves
- Fritz Hirzebruch (Max Planck Institute for Mathematics, Bonn)
Reminiscences of the Fifties.
Scans and transcription
of the 1957-1959 Atiyah/Hirzebruch letters which were displayed in the lecture.
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
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.
- 0. Title
- 1. Youth
- 2. Early Landmarks
- 6. Collected Works A
- 7. Collected Works B
- 8. Photos
- 3. Bridge to Physics
- 4. European Mathematical Society
- 5. Abel Prize
Raoul Bott (1923–2005)
And more
- Sir William Hodge, 1903--1975
Sir Michael's presentation at the Hodge Centenary Conference, Edinburgh, 2003.
Hodge was Atiyah's Ph.D. supervisor at Cambridge.
- Web of Stories.
Interview with Sir Michael (c. 1995, interviewer = N.Hitchin).
- Benjamin Franklin and the Edinburgh Enlightenment, Proc. American Philosophical Society
150, 591-606 (2006)
- Atiyah & friends at the Bonn Arbeitstagung.
(2009 photo with Hirzebruch in Munich)
- Introduction by Hirzebruch to lecture by Sir Michael in Munich, March, 2009.
-
Michael Atiyah - The Physicist's Mathematician (story on the Simons Foundation website).
- 80th birthday speech at Trinity College, Cambridge,
May 2009.
- Lessons from the Scottish Enlightenment Biennial Lecture of the Faculty of
Actuaries, Edinburgh, November 2009.
- A panoramic view of mathematics
Video of lecture at the Young Researchers in
Mathematics Conference, Cambridge, 26 March 2010.
- Grande Medaille of the French Academie des Sciences (22 June 2010).
There is a picture of the medal here.
Edinburgh
Evening News (29.6.2010).
Edinburgh University website
- On families of self adjoint operators 1987 Oxford paper by Ruth Lawrence.
MFA comments:
Ruth's approach, through perturbation theory, as used by physicists, brings out clearly the correspondence between the analysis
and the topology. The successive terms in the perturbation expansion correspond to small quadratic forms associated with the
Jordan blocks. Farber and Levine ("Jumps of the η-invariant", Mathematische Zeitschrift 223, 197-246 (1996)) do not delve so deeply
into things, but in their approach these quadratic forms appear as terms in the spectral sequence.
Clarifying all this might be a good exercise for a grad.student. (August, 2010)
- Sir Michael's 2008/9 Edinburgh Lectures on Geometry, Analysis and Physics
Notes by Thomas Köppe. (September 2010)
- Geometry and algebra
Spitalfields Day at the Royal Society of Edinburgh, 17 September 2010, which included the award of an RSE Honorary Fellowship to
F. Hirzebruch. ReSourcE report.
Photo album.
Slides of lectures by Atiyah, Hirzebruch
and Ranicki.
- Following on from her sketches at the Atiyah80 meeting,
Fionna Carlisle was commissioned in 2010 to make two double drawings of Michael
Atiyah and Fritz Hirzebruch by a group of their friends and admirers. The Edinburgh drawing
was presented to the School of Mathematics, and the Bonn drawing was presented
to the Max Planck Institute (May/June 2011).
-
Sir Michael is appointed to the Legion d'honneur (July 2011)
- Interview of
Sir Michael by Nigel Hitchin and Rob Kirby,
at the Simons Center for Geometry and Physics, 7 November, 2011
-
Mod 2 indices Slides of lecture
at Heilbronn Conference
Celebration of the 70th birthday of Elmer Rees, 20-21 April, 2012
- Topology:
Mathematics, a beautiful elsewhere Discussion with Cedric Villani, Tate Modern Art Gallery, London, 2 June 2012
- Sir Michael is a member of the Order of Merit.
He regularly attends the Annual Service and Lunch, most recently on 14th May 2013.
Photo and video
-
Advice to a Young Mathematician Video of lecture at the Heidelberg Laureate Forum (24th September 2013)
- Interview with John D. Cook
(24th September, 2013)
- Selbstzweifel eines Genies,
by George Szpiro, Neue Züricher Zeitung (1st December, 2013)
- The experience of mathematical beauty and its neural correlates
Joint paper with S.Zeki, J.P.Romaya and D.M.T.Benincasa (Frontiers in Human Neuroscience, 13th February 2014).
- Unlocking the startling truth about beautiful mathematical minds by Magnus Linklater
(The Times, 29th March 2014)
- The Impact of Physics on Mathematics:
Past, Present and Future, Video of lecture given by video-conference
to the British Mathematical Colloquium, QMU, London (8th April, 2014)
- Atiyah85
Conference in Oxford to celebrate Sir Michael's 85th birthday on 22nd April, 2014
- Publication of Volume 7 of the
Collected Works (22nd April, 2014)
- Reflections on time in Oxford: interview with Paul Tod
(22nd April 2014)
- "'Yes' vote will free us from nuclear reliance" (The Times, 10th July 2014)
- Atiyah adds voice to Yes campaign over Trident
by Magnus Linklater (The Times, 10th July 2014)
- Im Zweifel für die Schönheit by George Szpiro (Neue Züricher Zeitung, 1.10.2014)
- The Beauty of Mathematics
Lecture to University of Edinburgh mathematics students (6th November, 2014)
- Clerk Maxwell's Influence on Mathematics, Video of lecture at the Royal Society of Edinburgh meeting
Inspiring Brilliance:
Celebrating Maxwell's Genius and Legacy (9th November, 2015)
- The Role of Beauty in Mathematics, Video of lecture at the Royal Society of Edinburgh
meeting The Science of Beauty (10-11th November, 2015)
- Geometry and Physics, Video of lecture at the University of Edinburgh (7th December, 2015)
- Biology, logic and imagination, Video of lecture at the University of Edinburgh (7th December, 2015)
- Michael Atiyah's imaginative state of mind,
by Siobhan Roberts, QUANTA Magazine (March, 2016)
- A conversation between Michael Atiyah and Roger Penrose
(on the occasion of Honorary Degree awarded to Penrose, Edinburgh, 10th July 2017)
- Mathematician, 88, hopes to prove himself again with new solution by Magnus Linklater, The Times (12th August 2017).
©2009-17 Andrew Ranicki
Last updated: 12 August 2017