Jeffrey Shallit, David R. Cheriton School of Computer Science, University of Waterloo
"Waring's theorem for binary k'th powers and palindromes"
In this talk I will discuss some recent results about palindromes in bases 2, 3, 4 and binary k'th powers. (A binary k'th power is an integer whose base-2 expansion consists of k consecutive identical blocks.) In particular, I'll show that for all k ≥ 1 there exists a constant W(k) such that every sufficiently large multiple of gcd(k,2k - 1)$ is the sum of W(k) binary k'th powers.
This is joint work with Aayush Rajasekaran, Dirk Nowotka, Parthasarathy Madhusudan, Tim Smith, Daniel Kane, and Carlo Sanna.