Monthly Archives: June 2015

Ornette Coleman, 1930–2015

OrnetteThe great alto saxophonist Ornette Coleman died on June 11. He had a uniquely emotional style, partly from his background in rhythm and blues, and partly from his willingness to play notes away from any fixed scale. His 1982 album Of Human Feelings is a rich combination of jazz and pop/funk. But the piece to remember him by has to be his magnificent 1959 dirge Lonely Woman.

Photo ©William Claxton.

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Algebraic Geometry 2015: schedule details

cat-watching-clock

Timetables are now available for the afternoon invited talks at the AMS Summer Institute in Algebraic Geometry, taking place in Utah from July 12 to August 1.

The seminar I’m organizing is in Week 3: July 27–31. Speakers are:
Aravind Asok
Joseph Ayoub
Nicolas Bergeron
Patrick Brosnan
Aise Johan de Jong
Moritz Kerz
Bruno Klingler
Max Lieblich
Alena Pirutka
Shuji Saito
Stefan Schreieder
Zhiyu Tian

Photo from www.catster.com.

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New paper: The integral cohomology of the Hilbert scheme of two points

IMG-20140924-00178I’ve posted a new paper on the arXiv. (I haven’t found an apt cat picture, so have just used a photo of Susie the cat, who supervised the writing of the paper closely.)

The Hilbert scheme X^{[a]} of points on a complex manifold X is a compactification of the configuration space of a-element subsets of X. The integral cohomology of X^{[a]} is more subtle than the rational cohomology. In this paper, we compute the mod 2 cohomology of X^{[2]} for any complex manifold X, and the integral cohomology of X^{[2]} when X has torsion-free cohomology.

The results of this paper are used in Voisin’s work on the universal CH_0 group of cubic hypersurfaces, because the crucial point there is to study the 2-torsion in the Chow group.

Photo: Susie the cat in Princeton.

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