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Summer Number Theory Day; Session 2

Speaker  Kiran Kedlaya

Affiliation  University of California

Host  Kristin Lauter

Duration  01:06:34

Date recorded  24 July 2012

SPEAKER: Kiran Kedlaya
TITLE: The Robbins phenomenon: unexpected numerical stability in p-adic arithmetic

Since one cannot represent an arbitrary real number on a computer, it is standard to approximate real-number arithmetic using floating-point approximations. The situation is similar for p-adic numbers; we begin by introducing the analogue of floating-point arithmetic for p-adics. We then describe some known and conjectural examples of p-adic numerical stability in which algebraic structures (e.g., cluster algebras) work behind the scenes to keep the loss of numerical precision much lower than one might initially expect. A key example is the Dodgson (Lewis Carroll) condensation algorithm for computing determinants, for which we obtain a partial result towards a conjecture of Robbins. Joint work with Joe Buhler (CCR La Jolla).

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> Summer Number Theory Day; Session 2