Too Many Topics

Last Friday at the KITP there was a celebration of Stanley Mandelstam’s 80th birthday, with talks available here, and some messages from other physicists here. Geoffrey Chew recalls how Berkeley hired Mandelstam away from Columbia, where no one was very interested in what he was doing, in 1958. The next year the same thing happened with Steven Weinberg…

Recently I’ve noticed two books on a narrow topic not of general interest, but perhaps of interest to readers of this blog: histories of US math departments. They are:

  • Recountings: Conversations with MIT Mathematicians, about MIT.
  • Mathematics at Berkeley, about Berkeley.
  • Perhaps of even more esoteric interest, later this year Princeton University Press will publish Mathematicians: An outer view of the inner world, a book of photographs of mathematicians by Mariana Cook. Some of the photographs are available at her web-site here.

    Via Ars Mathematica: Fulton’s Algebraic Curves is available for free online. It’s a good place to start if you’re looking for a challenging introduction to algebraic geometry at the (quite) advanced undergraduate level.

    Some wonderful expository pieces about areas of mathematics:

  • Ben Webster on higher categories and knot homology.
  • Vaughn Jones on operator algebras and TQFT.
  • Cliff Taubes on Seiberg-Witten Floer homology, in a review of the recent book by Kronheimer and Mrowka.
  • The AMS Notices has an article about the current state of every mathematician’s favorite tool: TeX.

    Les Houches this year will have a summer school devoted to lattice gauge theory.

    For the latest on the question of whether the Tevatron will manage to see the Higgs or rule it out, see excellent postings by Tommaso Dorigo here and here. The bottom line is that by the time the LHC has enough data to start saying something about the Higgs, the Tevatron experiments will have over 10fb-1 of data to analyze, which may, if improvements in their analysis work out, give them a two-thirds chance of seeing the Higgs at 2 sigma level over the entire expected mass range, or a 50/50 chance of seeing it at 3 sigma level over a large range, including a small range just above the 114Gev LEP limit. The Tevatron may remain very competitive with the LHC for some signals far longer than people have been expecting. And, at least for the next 18 months, the US stimulus legislation may make Fermilab better funded than CERN for a change…

    I fear I’ve been remiss about not reporting on the IHES Grothendieck conference that I attended a couple days of when I was in Paris last month. Luckily, there’s a new blog here with a report.

    Protests and strikes in France over Sarkozy’s attacks on the French scientific research system continue, see an English language report here. Some people may have misunderstood my previous mention of this. While it’s not a topic I’m well-informed about, Sarkozy’s argument in favor of moving to something supposedly more American, featuring a market-based, no central government regulation ideology has an obvious problem if you’ve been reading the newspapers.

    Update: Video of the IHES Grothendieck talks is available here.

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    7 Responses to Too Many Topics

    1. Manel says:

      « Fulton’s Algebraic Curves is available for free on-line.»

      It’s been on-line for quite some months now.

      «It’s a good place to start if you’re looking for a challenging introduction to algebraic geometry at the (quite) advanced undergraduate level.»

      Is this really advanced undergraduate? Is it a good place for someone interested into Physics to learn AG from?

      It thing Griffith & Harris is probably more suited for a physicist due to it being more intuitive.

      Does anyone have suggestions of good AG introductions for physicists?

    2. Aaron Bergman says:

      I think G&H is probably the way to go. It stays away from the Zariski topology which I generally think is a distraction for physics applications.

    3. Peter Woit says:


      It’s not really an appropriate book for physicists. You have to realize that a large part of algebraic geometry is commutative algebra, since mathematicians want to do geometry over different fields. not just over the complex numbers. Fulton does the algebraic part of the story seriously, but to follow this you need to have at a minimum a serious course in abstract algebra, which physicists normally don’t.

      Physicists generally are only interested in geometry over the real and complex fields, and often general manifolds, not algebraic varieties. For them, Griffiths and Harris is good, since it approaches algebraic geometry from the point of view of complex manifolds. For something at a more undergraduate level, sticking to complex manifolds, but more along the lines of algebraic geometry, you could try Frances Kirwan’s “Complex Algebraic Curves”.

      Another way to explain the difference in point of view is that, for one complex dimensional spaces, physicists mostly want arbitrary Riemann surfaces, but algebraic geometers are mostly interested in algebraic curves. There’s a big overlap of the two subjects, but physicists rarely care about the algebraic part of it, whereas for mathematicians this is a crucial part of the subject.

    4. Javier says:

      I have just made a blog entry on the subject of algebraic geometry and physic (specifically string theory), concretely tis:

    5. Manel says:

      Peter and Aaron Bergman, thank you for your elucidating explanations.

    6. milkshake says:

      Onion-caliber news: Tom Hanks has been invited to push the button on the repaired LHC. Hanks got that part because of the upcoming Hollywood thriller – where Hanks averts the plans for blowing up Vatican with 250 milligrams of antimatter pilfered from CERN. The movie was filmed at CERN and among other things it also feature the antimatter sinister canister and some CERN people were involved in advising the movie crew so that they get the Pontiff-blowing science right.

    7. Coin says:

      milkshake: That is… odd. Especially given that CERN actually still has up on their website a fun but somewhat testy document talking about all the inaccuracies in the Angels and Demons book…

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