Category Archives: cambridge

Crazy Wednesday

Wednesday 4 May is going to be a crazy day in Cambridge (ah, high-class problems). Packing in as much as you can will take Planning. Here’s what is on the menu for geometry seminars and the Birch–Swinnerton-Dyer conference. Scramble as best you can!

1.30–2.30 in MR 2
Bryan Birch (Oxford) and Peter Swinnerton-Dyer (Cambridge).
How It Happened

2.30–3.30 in MR 13
Max Lieblich (Washington).
Derived categories of K3 surfaces in positive characteristic

3.00–4.00 in MR 2
John Cremona (Warwick).
Numerical evidence for the Birch Swinnerton-Dyer Conjecture

4.00–5.00 in MR 13
Francis Bonahon (USC).
Character varieties of surfaces and Kauffman brackets

4.30–5.30 in MR 2
John Tate (University of Texas at Austin).
Old thoughts on elliptic curves, BSD, and algebraic cycles

Actually, Thursday is at least as jam-packed, so pace yourself.

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Turing’s offprints

The (mathematical) headline today is that Turing’s papers have been saved for the British nation. I was puzzled when the papers first came up for sale in November 2010, because upon a bit of investigation it turned out that what was being sold were offprints. I realize that Turing is personally more interesting than most mathematicians, and that there’s been a vast expansion of the “collectables” market, but are people really collecting offprints of mathematical papers now?

Apparently, yes, and they have been for a while. The Scientist wrote about offprints and other scientific collectables in 1996. An offprint of Claude Shannon’s “A Mathematical Theory of Communication” was auctioned at Christie’s NY in 2005 for $9000.

So, if tastes ever turn to interwar algebraic geometry, I’m sitting on a gold mine.

When I came to Cambridge in 1999, I was put into Tim Gowers’ old office (this was when we were still in the converted CUP warehouse in Mill Lane). Tim apologized for the lack of storage space. The cupboards were full of J.A. Todd‘s offprint collection, and he hadn’t had the heart to throw it away.

The collection was an impressive sight — organized alphabetically in special document boxes in elegant, faded colors. I didn’t have any particular need for storage, so I left it alone. When, a year later, I had to pack up to move to the CMS, I found that I too couldn’t bear to throw it out. So I duly packed the collection for carriage to Pavilion B of the CMS, and then packed it again when I moved to the geometry pod (Pavilion E). It’s now arrayed across many feet of shelf space in my office.

I can’t say that I use it. Several years ago, out of curiosity about my predecessors in Cambridge geometry, I extracted a paper by Du Val and I could not make heads or tails of it. It was an astounding reminder of what a difference Weil and Serre and Grothendieck made to algebraic geometry. Igor Dolgachev is only person I know who really understands the old language.

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Eleven years ago at the Centre for Mathematical Sciences

When the two Cambridge math departments moved from Mill Lane to the CMS, the mathematical physicists and a few pure mathematicians were the pioneers, sent in January 2000 to test conditions in the first component of the complex to be “inhabitable,” Pavilion B.

I was one of the DPMMS members sent out to the new site. I remember that we used to get great emails from the long-suffering building manager about the hazards we were facing, but I’d forgotten just how great they were. I think I forwarded this introductory one (from 3rd January 2000) to my mother: MORE


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Past Mordell Lecturers

I’ve reconstructed the history of the Mordell Lectureship, but there are some gaps, which perhaps others can fill. The gap in 1970 might mean that appointment of a lecturer was deferred, but the gap from 1991 to 1997 (if the rules were followed) must have had some lecturers in it. And I’m missing most titles before 1998, when the University Reporter went online.

Update: A source has supplied the missing names of speakers.
Update (2016): Speakers since 2011 now added.

1970   J. W. S. Cassels
1971   C. A. Rogers
1972   Oscar Zariski
1973   Paul Halmos
1974   Michael Atiyah
1975   Fritz Hirzebruch
1976   Kai Lai Chung, Theta functions from Brownian excursions
1977   Gustave Choquet
1978   Jacques Tits, Rigidity
1979   Paul Erdös
1980   Donald J. Lewis
1981   Gilbert Baumslag
1982   Jean Pierre Kahane
1983   S. J. Taylor
1984   André Haefliger
1985   John Coates
1986   Donald Burkholder
1987   Vaughan Jones
1988   Alan Baker
1989   J. A. Green
1990   Alexander Schrijver
1991   Simon Donaldson
1992   Gisbert Wustholz
1993   Nicholas Varopoulos
1994   Jean-Yves Girard
1995   László Lovász
1996   Andrew Wiles
1997   Cliff Taubes
1998   Johan de Jong, Curves over finite fields and Galois representations
1999   Don Zagier, Mock modular forms, Maass modular forms, and true modular forms
2000   Cameron Gordon, The classification of knots
2001   David Aldous, Mathematical probability: some topics we do understand and some we don’t
2002   Yakov Eliashberg, Symplectic field theory: its structure and applications
2003   Mike Hopkins, Algebraic topology and modular forms
2004   Noga Alon, Polynomials in discrete mathematics
2005   Peter Sarnak, The Ramanujan conjecture and its generalizations
2006   Vitaly Bergelson, Ergodic theorems along polynomials: from combinatorial applications to challenges for physicists
2007   Demetrios Christodoulou, Acoustical spacetime geometry and shock formation
2008   Tobias Colding, Geometric PDE
2009   Anatole Katok, KAM and rigidity
2010   Lectureship deferred
2011   Alex Lubotzky, Short presentations of finite groups
2012   Paul Seidel, Categorical dynamics
2014   Alex Eskin, The SL(2,R) action on moduli space
2015   Daniel Spielman, The solution of the Kadison-Singer problem
2016   Dana Scott, Why mathematical proof?

The Mordell Lectureship was established in honor of Louis Mordell, Sadleirian Professor of Mathematics at Cambridge. He was also an undergraduate at Cambridge, and the New York Times in 1909 had a short item about him:

MORDELL CARRIES HONORS MODESTLY; American Winner of Cambridge Wranglership Admits Being Erratic Student. DECLINED TO HAVE A COACH Only Studied When in the Mood — Believes in Plenty of Exercise and Is Fond of Tennis and Swimming.

Special Cable to THE NEW YORK TIMES.
June 20, 1909,

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Not the Royal Wedding

The list of Cambridge events is kept (somewhat) updated: here.

Save these dates in spring 2011 for scintillating mathematical events in Cambridge:

March 21-25
Emmanuel Candes, the 2011 London Mathematical Society Invited Lecturer, will give an eight-lecture mini-course on compressed sensing at the Centre for Mathematical Sciences. These lectures will be complemented by one-hour lectures by Anders Hansen (Cambridge), Vincent Rivoirard (Paris-Dauphine), Carola Schoenlieb (Cambridge) and Jared Tanner (Edinburgh). More details: here.

April 4-7
The 34th Annual Research Student Conference in Probability and Statistics will be held at the Centre for Mathematical Sciences. The already well populated website is: here.

April 28
Alex Lubotzky will give the 2011 Mordell Lecture of the Department of Pure Mathematics and Mathematical Statistics (DPMMS).

And from January to July, two excellent programs will be running at the Newton Institute: Moduli Spaces and Discrete Analysis. Since this is a geometry blog, I should especially plug the Moduli Spaces program. The people making visits to the UK for this program include some exciting algebraic geometers, such as Valery Alexeev, Kai Behrend, Barbara Fantechi, Gavril Farkas, Daniel Huybrechts, Lothar Goettsche, Rahul Pandharipande, Claire Voisin… I could go on and on.

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Caucher Birkar has been awarded 2010 Philip Leverhulme prize

Caucher Birkar has been awarded one of this year’s Philip Leverhulme prizes. These prizes are intended for “outstanding scholars who have made a substantial and recognised contribution to their particular field of study, recognised at an international level, and where the expectation is that their greatest achievement is yet to come.”

In an earlier post, I said that the abundance conjecture was probably the major open problem in birational geometry. That’s because the obvious major problem in the field, finite generation of the canonical ring, was recently proved by Caucher, with Paulo Cascini, Christopher Hacon and James McKernan (in the paper known as BCHM). Since then he’s been a leader in pushing forward minimal model theory in dimensions 4, 5 and 6.

The other Leverhulme prize winners in mathematics and statistics this year are Tim Browning (Bristol), Tom Coates (Imperial), Radek Erban (Oxford) and Nicolai Meinshausen (Oxford).

Earlier winners are listed: here.

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Post-volcanic COW: 6th May

On Thursday May 6th, Grigory Mikhalkin and Jaroslaw Wlodarczyk will speak in the Cambridge COW algebraic geometry seminar. Talks will be held in Meeting Room 13 in the Centre for Mathematical Sciences, Clarkson Road, Cambridge, with pub/dinner afterward. Everyone is welcome!

More details, including how to claim travel expenses, are available from the COW website: here.

Thursday 6th May
2.30pm: Grigory Mikhalkin (Geneva). Tropical (p,q)-cycles.
3.30pm: Tea.
4.30pm: Jaroslaw Wlodarczyk (Purdue). Resolution algorithm in characteristic zero and its possible extension to positive characteristic.

Mikhalkin’s abstract:
Real 1-parametric families of complex manifolds have limits collapsing to certain polyhedral complexes called tropical varieties. Tropical structure of these limits is responsible for asymptotics of the collapse.

Tropical varieties are simple enough to visualize easily. Yet their homology theories reflect the Hodge structure of the collapsing family. These theories agree with the classical mixed Hodge structures in the case when the real 1-parametric families can be extended to the complex domain.

The talk will review some basic tropical notions and will be illustrated with a few examples.

Wlodarczyk’s abstract:
We discuss the basic ideas of the Hironaka algorithm for the resolution of singularities of algebraic varieties in characteristic zero and its extension to positive characteristic.

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