Title: On graphs, arithmetic progressions and communication

Abstract:

Tools from Extremal Graph Theory are helpful in the study of problems in Additive Number Theory, Theoretical Computer Science, and Information Theory. I will illustrate this fact by several closely related examples focusing on a recent one in a joint paper with Moitra and Sudakov.

Speaker: Persi Diaconis

Title: "An Introduction to additive combinatorics via 'carries'"

Abstract

When numbers are added in the usual way, "carries" occur.  The chance of a carry is about .45 (base 10).  There are other choices of digits that lead to fewer carries (balanced digits).  These balanced systems turn out to be best (fewest carries).  Showing this requires an excursion into additive combinatorics a la Gowers-Green-Szemeredi-Tao.  This is joint work with Shao and Soundarajan.

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Program

Schedule

• 9:00 am - Breakfast (Klaus atrium)
• 9:30 am - Keynote: Noga Alon
• 10:30 am - Break
• 10:45 am - Talks (25 min each) by:
  • Greg Blekherman (Math)
  • Frank Dellaert (CoC)
  • Justin Romberg (ECE)
• 12:15 pm - Lunch (Klaus atrium, with the student poster session for viewing)
• 1:30 pm - Keynote: Persi Diaconis