• Associativity of the Baker-Campbell-Hausdorff formula

    Updated: 2011-10-29 20:25:13
    Let be a finite-dimensional Lie algebra (over the reals). Given two sufficiently small elements of , define the right Baker-Campbell-Hausdorff-Dynkin law where , is the adjoint map , and is the function , which is analytic for near . Similarly, define the left Baker-Campbell-Hausdorff-Dynkin law where . One easily verifies that these expressions are well-defined [...]

  • 254A, Notes 7: Models of ultra approximate groups

    Updated: 2011-10-28 05:37:01
    In the previous set of notes, we introduced the notion of an ultra approximate group – an ultraproduct of finite -approximate groups for some independent of , where each -approximate group may lie in a distinct ambient group . Although these objects arise initially from the “finitary” objects , it turns out that ultra approximate [...]

  • Infinitude of Primes Via Lower Bounds

    Updated: 2011-10-27 07:17:24
    Infinitude of Primes Via Lower Bounds: the lower bound on pi(x) shows that as xgrows, so does pi(x)

  • The structure of approximate groups

    Updated: 2011-10-25 03:45:29
    Emmanuel Breuillard, Ben Green, and I have just uploaded to the arXiv our paper “The structure of approximate groups“, submitted to Pub. IHES. We had announced the main results of this paper in various forums (including this blog) for a few months now, but it had taken some time to fully write up the paper [...]

  • October 2011 issue of symmetry available

    Updated: 2011-10-19 15:38:25
    This month marks the 50th issue of symmetry magazine, which published its first issue in Oct/Nov 2004. It quickly established its own quirky style with a cover of a little girl in jammies dragging an Einstein bear.

  • 254A, Notes 6: Ultraproducts as a bridge between hard analysis and soft analysis

    Updated: 2011-10-15 19:58:18
    Roughly speaking, mathematical analysis can be divided into two major styles, namely hard analysis and soft analysis. The precise distinction between the two types of analysis is imprecise (and in some cases one may use a blend the two styles), but some key differences can be listed as follows. Hard analysis tends to be concerned [...]

  • 254A, Notes 5: The structure of locally compact groups, and Hilbert’s fifth problem

    Updated: 2011-10-08 21:57:29
    In the previous notes, we established the Gleason-Yamabe theorem: Theorem 1 (Gleason-Yamabe theorem) Let be a locally compact group. Then, for any open neighbourhood of the identity, there exists an open subgroup of and a compact normal subgroup of in such that is isomorphic to a Lie group. Roughly speaking, this theorem asserts the “mesoscopic” [...]

  • Executive coaching: The effect of working alliance discrepancy on the development of coachees' self-efficacy

    Updated: 2011-10-07 13:58:15
    : . Contact us Help Shopping cart Home About us Article title , keywords or abstract Article title Publication title Author Advanced search Subject Publisher Publication Browse : by Home The Journal of Management Development Volume 30, Number 9 Executive coaching : The effect of working alliance discrepancy on the development of coachees' self-efficacy Authors : Baron , Louis Morin , Lucie Morin , Denis : Source The Journal of Management Development Volume 30, Number 9, 2011 pp . 847-864(18 Publisher : Emerald Group Publishing Limited view table of contents next article Buy download fulltext : article OR Pressing the buy now button more than once may result in multiple purchases Price : 38.00 plus tax Refund Policy : Abstract : Keywords Coaching relationship Discrepancy Executive coaching

  • The Jordan-Schur theorem

    Updated: 2011-10-06 00:36:18
    Jordan’s theorem is a basic theorem in the theory of finite linear groups, and can be formulated as follows: Theorem 1 (Jordan’s theorem) Let be a finite subgroup of the general linear group . Then there is an abelian subgroup of of index , where depends only on . Informally, Jordan’s theorem asserts that finite [...]

  • 254A, Notes 4: Building metrics on groups, and the Gleason-Yamabe theorem

    Updated: 2011-10-04 21:58:29
    In this set of notes we will be able to finally prove the Gleason-Yamabe theorem from Notes 0, which we restate here: Theorem 1 (Gleason-Yamabe theorem) Let be a locally compact group. Then, for any open neighbourhood of the identity, there exists an open subgroup of and a compact normal subgroup of in such that [...]

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