Ian agol mathematics quotes

  • “No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game.” He seemed to.
  • Apparently he used both "the trash cans of science" and "a pure mathematician's wastebasket".
  • Www.youtube.com › watch.

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    The Virtually Haken Conjecture

    A Haken 3-manifold is a compact 3-dimensional manifold M which is irreducible (in a certain strong sense) but contains an incompressible surface S. (An embedded surface S is incompressible if the embedding indices an injection of its fundamental group to the fundamental group of M. A 3-manifold is virtually  Haken  if it has a finite cover which is Haken. (This is a typical way how the word “virtually” occurs in algebra and topology.)

    The virtually Haken conjecture states that every compact, orientable, irreducible 3-dimensional manifold with infinite fundamental group is virtually Haken. The big news is that Ian Agol has just announced the proof of the virtually Haken conjecture!

    Danny Calegary have just wrote three detailed posts about it over his blog “Geometry and the Imagination”:  Agol’s Virtual Haken Theorem (part 1), Agol’s Virtual Haken Theorem (part 2): Agol-Groves-Manning strike back, and Agol’s Virtual Haken Theorem (part 3): return of the hierarchies. (Everything I say is taken from there.)

    To quote Danny:

    I think it is no overstatement to say that this marks the end of an era in 3-manifold topology, since the proof ties up just about every loose end left over on the list of problems in 3-manifold to

  • ian agol mathematics quotes

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    Strings 2011

    Strings 2011 started today in Uppsala, with attendance quite a bit lower than in the past (259 registered participants, versus 500 or so at some of the past such conferences). One reason for this may be the high conference cost (discussed here), another may be that excellent video of the talks is available, so why bother traveling to Uppsala?

    The opening talk was by David Gross, who tried to address the question “Where do we stand?” for string theory. He claimed the field is “extremely healthy”, “vibrant and exciting”, “making enormous progress in a variety of areas'”, with “stupendous progress” in N=4 planar SYM. At the same time, he acknowledged that it was “very sobering” that string theory was 43 years old.

    In the past, Strings XXXX conferences often featured a call for progress towards making predictions that could be tested at the LHC. With LHC data now coming in, Gross acknowledged that this had been a failure: there are no string theory LHC predictions. He put a positive spin on this by noting that the lack of any BSM signal at the LHC so far is not a worry for string theory, since string theory can’t be tested at the LHC. As for the lack of any supersymmetry signal so far, he

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