Partitions Compositions and the Excitement of Ramanujan
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Partitions, Compositions, and the Excitement of Ramanujan

Özet (Abstract): The theory of partitions concerns the representation of
        integers as distinct sums of integers.  For example, the
        five partitions of 4 are 4, 3 + 1, 2 + 2, 2 + 1 + 1,
        1 + 1 + 1 + 1.

          Compositions take order into account.  Thus there are 8
        compositions of 4, namely 4, 3 + 1, 1 + 3, 2 + 2, 2 + 1 + 1,
        1 + 2 + 1, 1 + 1 + 2, 1 + 1 + 1 + 1.  Although seemingly more
        complicated, compositions are much easier to study as we
        shall see.

           Euler was the first to study partitions seriously, and
        many of his discoveries are still fundamental in the subject.
        In this talk we introduce the basic ideas of partitions and
        compositions.  We limit the necessary background to arithmetic
        and a little algebra.

           The talk begins with an account of compositions.  The ideas
        turn out to be easily understood, and the scope of the subject
        is easily comprehended.  We then turn to partitions, the subject
        that the Indian genius Ramanujan revolutionized.  We note several
        themes from Ramanujan's work suggested by our study of compositions.
        In each instance, we gain some appreciation of the depth and
        surprise of Ramanujan's insights.

Tarih (Date): Mayıs (May) 18 Cumartesi (Saturday)

Zaman (Time): 13:00-14:00 (1:00 p.m. - 2:00 p.m.)

seminerden önce çay-kahve-kurabiye ikramı olacaktır
(tea-coffee-pastries will be served before the talk)


Yer (Loc'n): Sabancı Üniv. Karaköy İletişim Merkezi Giriş katı
    (Sabancı Univ. Karaköy Communications Center Ground Floor)