Summer Number Theory Day; Session 2

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

ABSTRACT:
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).

Speaker Details

Dr. Kedlaya received his Ph.D. in Mathematics from MIT in 2000. For the next three years, he held postdoctoral positions at the Mathematical Sciences Research Institute in Berkeley, at the University of California at Berkeley, and at the Institute for Advanced Study in Princeton. Since then, Dr. Kedlaya has been a faculty member at MIT, first as Assistant Professor and then as Associate Professor. Dr. Kedlaya is an expert on a broad range of topics related to arithmetic algebraic geometry and number theory, especially p-adic cohomology, p-adic Hodge theory, and computational number theory. He is the author of 49 research papers, and his research has been recognized with a highly prestigious five year Presidential Early Career Award for Scientists and Engineers (PECASE) from the NSF. In addition, he has been awarded a Sloan Research Fellowship, and a Clay Liftoff Fellowship.

Dr. Kedlaya has an outstanding record of dedicated teaching, has served as a mentor to numerous undergraduate and graduate students, and has been active in nurturing talented high school students in mathematics, with active involvement in organizational aspects for the International Mathematics Olympiad and as the author of a Putnam Exam problem book. At UCSD, Dr. Kedlaya will teach a range of courses, ranging from lower division calculus to research-level courses in algebra and number theory.

Dr. Kedlaya’s research is in the area of number theory and arithmetic algebraic geometry. His specialties include p-adic analytic methods, p-adic Hodge theory, algorithms, and applications in computer science (including cryptography).

Date:
Speakers:
Kiran Kedlaya
Affiliation:
University of California