First Clay Mathematics Institute Millennium Prize Announced

From the Clay Mathematics Institute website:

The Clay Mathematics Institute hereby awards the Millennium Prize for resolution of the Poincaré conjecture to Grigoriy Perelman.

The Poincaré conjecture is one of the seven Millennium Prize Problems established by CMI in 2000. The Prizes were conceived to record some of the most difficult problems with which mathematicians were grappling at the turn of the second millennium; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; to emphasize the importance of working towards a solution of the deepest, most difficult problems; and to recognize achievement in mathematics of historical magnitude.

For more information, see the page linked from this post's title.

Preprint:"Quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells: the finite-type cases" (arXiv:0912.4397)

A preprint of the paper "Quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells: the finite-type cases", by myself and Stéphane Launois, is now available on the arXiv via the above link. The abstract for this paper is as follows:

We exhibit quantum cluster algebra structures on quantum Grassmannians K_q[Gr(2,n)] and their quantum Schubert cells, as well as on K_q[Gr(3,6)], K_q[Gr(3,7)] and K_q[Gr(3,8)]. These cases are precisely those where the quantum cluster algebra is of finite type and the structures we describe quantize those found by Scott for the classical situation.

Election of new Warden at Keble College, Oxford

The new Warden of Keble College, Oxford, who will succeed Professor Dame Averil Cameron in Michaelmas Term 2010 is Sir Jonathan Phillips KCB, currently Permanent Secretary to the Northern Ireland Executive.

Preprint: "Examples of quantum cluster algebras associated to partial flag varieties" (arXiv:0907.4922)

A preprint of my latest paper is now available on the arXiv via the above link. The abstract for this paper is as follows:

We give several explicit examples of quantum cluster algebra structures, as introduced by Berenstein and Zelevinsky, on quantized coordinate rings of partial flag varieties and their associated unipotent radicals. These structures are shown to be quantizations of the cluster algebra structures found on the corresponding classical objects by Geiß, Leclerc and Schröer, whose work generalizes that of several other authors. We also exhibit quantum cluster algebra structures on the quantized enveloping algebras of the Lie algebras of the unipotent radicals.

Another mathematical blog and podcast

Peter Rowlett of the Institute of Mathematics and its Applications (IMA) has a website travelsinamathematicalworld.co.uk, featuring a blog, a regular podcast and associated show notes. Topics covered are mostly applied and applicable mathematics (which is most of mathematics, after all!) but also include monthly history and news slots, including brief biographies of famous mathematicians and snippets from mathematics on the web and in the media. Podcasts are usually around 15 minutes long and are a great way to hear about the ubiquitous presence of mathematics in modern life. After all, the media player you listen to the podcast on uses lots of mathematics: coding and signal processing for starters, and maybe graphics and encryption too, if it's your phone.