• 254A, Notes 0 – Hilbert’s fifth problem and related topics

    Updated: 2011-08-27 20:34:32
    This fall (starting Friday September 23), I will be teaching a graduate topics course which I have entitled “Hilbert’s fifth problem and related topics.” The course is going to focus on three related topics: Hilbert’s fifth problem on the topological description of Lie groups, as well as the closely related (local) classification of locally compact [...]

  • Notes on local groups

    Updated: 2011-08-18 04:00:46
    One of the fundamental structures in modern mathematics is that of a group. Formally, a group is a set equipped with an identity element , a multiplication operation , and an inversion operation obeying the following axioms: (Closure) If , then and are well-defined and lie in . (This axiom is redundant from the above [...]

  • The Hilbert-Smith conjecture

    Updated: 2011-08-14 04:51:20
    The classical formulation of Hilbert’s fifth problem asks whether topological groups that have the topological structure of a manifold, are necessarily Lie groups. This is indeed, the case, thanks to following theorem of Gleason and Montgomery-Zippin: Theorem 1 (Hilbert’s fifth problem) Let be a topological group which is locally Euclidean. Then is isomorphic to a [...]

  • Identities with Triangular Numbers

    Updated: 2011-08-11 01:34:16
    Identities with Triangular Numbers

  • Involution on the Projective Line

    Updated: 2011-08-11 01:34:15
    Involution on the Projective Line

  • A geometric proof of the impossibility of angle trisection by straightedge and compass

    Updated: 2011-08-10 23:25:34
    One of the most well known problems from ancient Greek mathematics was that of trisecting an angle by straightedge and compass, which was eventually proven impossible in 1837 by Pierre Wantzel, using methods from Galois theory. Formally, one can set up the problem as follows. Define a configuration to be a finite collection of points, [...]

Current Feed Items | Previous Months Items

Jul 2011 | Jun 2011 | May 2011 | Apr 2011 | Mar 2011 | Feb 2011