• 254B, Notes 6: The inverse conjecture for the Gowers norm II. The integer case

    Updated: 2010-05-29 23:15:10
    In Notes 5, we saw that the Gowers uniformity norms on vector spaces in high characteristic were controlled by classical polynomial phases . Now we study the analogous situation on cyclic groups . Here, there is an unexpected surprise: the polynomial phass (classical or otherwise) are no longer sufficient to control the Gowers norms once [...]

  • Locus of the midpoints of concurrent chords - from the 1991 Canadian MO

    Updated: 2010-05-28 04:51:57
    Locus of the midpoints of concurrent chords - from the 1991 Canadian MO

  • Squares and Cubes - from the 1978 Canadian MO

    Updated: 2010-05-28 04:51:57
    Squares and Cubes - from the 1978 Canadian MO

  • Sum of 1984 consecutive squares - from the 1984 Canadian MO

    Updated: 2010-05-28 04:51:56
    Sum of 1984 consecutive squares - from the 1984 Canadian MO

  • 1986 Canadian MO, Problem 1

    Updated: 2010-05-28 04:51:55
    1986 Canadian MO, Problem 1

  • Areas in a quadrilateral - from the 1978 Canadian MO

    Updated: 2010-05-28 04:51:55
    Areas in a quadrilateral - from the 1978 Canadian MO

  • 1980 Canadian MO, Problem 3

    Updated: 2010-05-27 18:58:08
    1980 Canadian MO, Problem 3

  • Gonz Vector Drawings « Four Fifths Design

    Updated: 2010-05-21 03:37:27
    Designer: Gonz

  • Higher order Hilbert spaces

    Updated: 2010-05-20 00:54:22
    A (complex, semi-definite) inner product space is a complex vector space equipped with a sesquilinear form which is conjugate symmetric, in the sense that for all , and non-negative in the sense that for all . By inspecting the non-negativity of for complex numbers , one obtains the Cauchy-Schwarz inequality if one then defines , [...]

  • Create an Awesome Funky Text Effect | Design.CreativeFan

    Updated: 2010-05-13 02:49:45
    Funky, abstract text effects can yield incredibly stunning results.  Whether they're fiery and explosive, cool and sleek, retro, or intricate vector

  • Approximate subgroups of linear groups

    Updated: 2010-05-12 22:30:27
    Emmanuel Breuillard, Ben Green, and I have just uploaded to the arXiv our paper “Approximate subgroups of linear groups“, submitted to GAFA. This paper contains (the first part) of the results announced previously by us; the second part of these results, concerning expander groups, will appear subsequently. The release of this paper has been coordinated [...]

  • i.Ge Studio Vector Collection

    Updated: 2010-05-12 06:17:59
    i.Ge Studio Vector Collection Download Movies Music Applications TV Shows

  • 254B, Lecture Notes 4: Equidistribution of polynomials over finite fields

    Updated: 2010-05-08 22:47:33
    In the previous lectures, we have focused mostly on the equidistribution or linear patterns on a subset of the integers , and in particular on intervals . The integers are of course a very important domain to study in additive combinatorics; but there are also other fundamental model examples of domains to study. One of [...]

  • Suzuki groups as expanders

    Updated: 2010-05-06 17:33:20
    Emmanuel Breuillard, Ben Green, and I have just uploaded to the arXiv the paper “Suzuki groups as expanders“, to be submitted. The purpose of this paper is to finish off the last case of the following theorem: Theorem 1 (All finite simple groups have expanders) For every finite simple non-abelian group , there exists a [...]

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