Short Mathematical Items

Posted on October 29, 2009 by woit
  • Riemann submitted his paper on the Riemann Hypothesis October 19, 1859, and it was read by Kummer at the meeting of the Berlin academy on November 3. AIM is organizing a celebration of the 150th birthday of the Riemann Hypothesis, with a “Riemann Hypothesis Day” on November 18th. Talks will be given on that day at many institutions around the world, a list is here.
  • The Royal Society in Britain has announced the appointment of six “Royal Society 2010 Anniversary Research Professors”. Two of them are mathematicians: Timothy Gowers, of Cambridge, and Andrew Wiles, who will be leaving Princeton to take up the position at Oxford. Wiles has this comment about his current research:

    Over the last several years my work has focused primarily on the Langlands Program a web of very influential conjectures linking number theory, algebraic geometry and the theory of automorphic forms. I am trying to develop arithmetic techniques that will, I hope, help to resolve some of the fundamental questions in this field. I am delighted to be appointed a Royal Society Research Professor in their anniversary year and I look forward to the opportunities this will give me to further my research.

  • I spent a couple days earlier this week up in New Haven, attending a conference celebrating Gregg Zuckerman’s 60th birthday. Zuckerman’s specialty is representation theory, and he’s well-known in that subject for several ideas that have been important in the modern understanding of infinite dimensional representations of semi-simple Lie groups. He also has done quite a bit of work in mathematical physics, work which includes a classic paper (Proc. Natl. Acad. Sci. U.S.A. 83 (1986), pp. 8442–8446) with his Yale collaborators Howard Garland and Igor Frenkel explaining some aspects of the BRST quantization of the string in terms of semi-infinite cohomology. As far as I know, he was the first person to study (in a 1986 paper “Action principles and global geometry”) the field theory with Chern-Simons action that Witten was to make famous two years later when he worked out its significance as a TQFT giving interesting 3-manifold and knot invariants.
  • An hour or so ago I went out for a walk, stopped at the bookstore, and noticed that there’s a new book out about Grigori Perelman, entitled Perfect Rigor. It looks worth reading, perhaps they’ll be a longer blog post about it sometime soon…
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    5 Responses to Short Mathematical Items

    1. Marcus says:
      October 29, 2009 at 7:27 pm

      I see that slides can be downloaded for 3 out of the 18 talks given at the Group Representations conference you attended at Yale.
      http://www.liegroups.org/zuckerman/slides.html
      In particular Garrett Lisi’s talk is one of those for which the slides are available.

    2. John Armstrong says:
      October 29, 2009 at 8:39 pm

      Unfortunately I couldn’t be there for my advisor’s conference. Unemployment is a harsh and forbidding landscape.

    3. Marcus says:
      October 29, 2009 at 9:09 pm

      J.A. I’ve read your blog and some of the comments re the current math job market. Sounds very tough–as if they are almost forcing pure math PhD’s to go back for applied courses of some type. Sad you were unable to attend your advisor’s 60th-birthday conference. Hope things improve soon.

    4. Sakura-chan says:
      October 29, 2009 at 10:25 pm

      I am going to order that Perelman book right away!

    5. Tim vB says:
      October 30, 2009 at 11:26 am

      The anniversary of the Riemannian hypothesis should be celebrated with a lecture by Allain Connes in Göttingen, but it semms neither Connes nor Göttingen is involved in this? Too bad.
      Just re-read Riemanns original paper (in Edwards, “H. M. Riemann’s Zeta Function”). As you all probably know already, what is called “Riemannian hypothesis” is only a remark in the paper, which is about the “number of primes less than a given magnitude”. At the end of the paper Riemann compares his formula with the known number of primes smaller than 3 million! referencing the work of Gauss and Goldschmidt. Wow, they computed all primes lower than 3 million without a computer! (And he mentions that he himself tried to prove his hypothesis: “One would of course like to have a rigorous proof of this, but I have put aside the search for such a proof after some fleeting vain attemps, because it is not necessary for the immediate objective of my investigation”. What would he have said if someone had told him that this would become one of the most popular open problems of the 21st century?).

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