2010 Abel Prize awarded to John T. Tate

From the Abel Prize website:

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2010 to John Torrence Tate, University of Texas at Austin, for his vast and lasting impact on the theory of numbers. The President of the Norwegian Academy of Science and Letters, Nils Christian Stenseth, announced the name of the 2010 Abel Laureate at the Academy in Oslo today, 24. March. John Tate will receive the Abel Prize from His Majesty King Harald at an award ceremony in Oslo, Norway, May 25.

The Abel Prize recognizes contributions of extraordinary depth and influence to the mathematical sciences and has been awarded annually since 2003. It carries a cash award of NOK 6,000,000 (close to € 730,000 or US$ 1 mill.)

The theory of numbers stretches from the mysteries of prime numbers to the ways in which we store, transmit, and secure information in modern computers. Over the past century it has developed into one of the most elaborate and sophisticated branches of mathematics, interacting profoundly with other key areas. John Tate is a prime architect of this development.

John Tate's scientific accomplishments span six decades. A wealth of essential mathematical ideas and constructions were initiated by Tate and later named after him, such as the Tate module, Tate curve, Tate cycle, Hodge-Tate decompositions, Tate cohomology, Serre-Tate parameter, Lubin-Tate group, Tate trace, Shafarevich-Tate group, Néron-Tate height, to mention just a few.

According to the Abel committee, "Many of the major lines of research in algebraic number theory and arithmetic geometry are only possible because of the incisive contributions and illuminating insights of John Tate. He has truly left a conspicuous imprint on modern mathematics".

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: "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.

Lifetime Achievement prize for George Lusztig

From the American Mathematical Society web pages:

George Lusztig of the Massachusetts Institute of Technology has received the 2008 AMS Leroy P. Steele Prize for Lifetime Achievement. Presented annually by the American Mathematical Society, the Steele Prize is one of the highest distinctions in mathematics. The prize was awarded today [7th January 2008] at the Joint Mathematics Meetings in San Diego, California.

"The work of George Lusztig has entirely reshaped representation theory, and in the process changed much of mathematics," the prize citation states. "His work has touched widely separated parts of mathematics, reshaping them and knitting them together. He has built new bridges to combinatorics and algebraic geometry, solving classical problems in those disciplines and creating exciting new ones. This is a remarkable career, and as exciting to watch today as it was at the beginning more than thirty years ago."

The full citation may be found in the prize booklet (PDF), from page 46 onwards.

Many congratulations to Prof. Lusztig. I have personally been inspired by his work, especially on quantum groups. Indeed, my whole research career would likely not exist without him.

Two Lots of mathematical blogs

This blog now has its own blogroll (see sidebar), along with two new entries: the Secret Blogging Seminar and the n-Category Café. The first of these is mainly mathematical in content, the latter covering mathematics, physics and philosophy.

Update: (13/07/07, 11:21) I've added lots more blogs to the blogroll. Enjoy!

Plus Magazine

Plus Magazine is a project of the Millennium Mathematics Project, which aims to increase the public awareness of mathematics, particularly among young people. The magazine appears four times a year and the website is updated regularly with news from the world of mathematics, together with a blog. It is highly recommended for anyone who is interested in mathematics, professionally or not.

The introduction to quantum geometry described in a recent post is from the latest edition of Plus.

An introduction to quantum geometry

Quantum geometry describes attempts to find new versions of classical geometry suited one of the major tasks in modern physics: finding a model of the universe that describes both quantum mechanics and gravity. In the linked article, this subject is introduced and explained for the non-specialist, by means of an interview with Prof. Shahn Majid, of Queen Mary, University of London, who has contributed several of the mathematical and physical ideas involved.

Note: Prof. Majid was my doctoral supervisor; my work with him was on the structure of algebraic objects related to quantum geometry, in the field colloquially known as the theory of "quantum groups".

Preprint: "On the inductive construction of quantized enveloping algebras" (arXiv:0706.0455)

A preprint of my latest paper is now available on the arXiv (the mathematical preprint repository) via the above link. The subject of this paper is a construction for a class of Hopf algebras called quantized enveloping algebras. The construction is a way of encoding in the algebraic structure the idea of adding nodes to the associated Dynkin diagrams.

A new mathematical celebrity: E8

Towards the end of last month, the popular media across the world covered a story about pure mathematics research. While this is not unheard of, it was rather surprising - though not in a bad way! The story in question was about a calculation carried out by a group of mathematicians, investigating the structure of an object called "E₈". (Actually, many different objects can be reasonably labelled E₈ but the one they were interested in is the split real form of the Lie group. Don't worry if you don't know what that is! The links below will help explain.)

For those interested in knowing more, I suggest starting with the original information put out by the group or the BBC's report of it. These also include some "pretty pictures" (they're mathematical, so they do mean something, rather than simply being decorative!) There's a more in-depth discussion in comments posted by John Baez and others on the n-Category Cafe blog. This is aimed at the semi-knowledgeable and could be considered a warm-up for the full technical details.

This story highlights several features of modern pure mathematical research:

• even the explicit calculations often take substantial computing power;
• the calculations provide glimpses of more general theory (they're not the end of the story, just the beginning);
• it's hard to convey in layperson's language what's actually being done (if you're not a mathematician, please don't take it personally when we say it's hard to explain!);
• sometimes you get very pretty pictures: it's all about symmetry! And finally
  
• representation theory is cool*
  

(* OK, I'm biased. But really, it is!)

Happy Birthday, Leonhard Euler!

The 15th of April 2007 is the 300th anniversary of the birth of Leonhard Euler, almost certainly the greatest mathematician who ever lived. Happy Birthday, Euler!