Sum of Square Roots of Polynomials and of Integers

Neeraj Kayal Microsoft Research Lab., “Scientia” 196/36 2nd Main Sadashivnagar Bangalore 560 080
Tuesday, 19 Apr 2011 (all day)
A-212 (STCS Seminar Room)
Let a_1, a_2, ..., a_n and b_1, b_2, ..., b_n be positive integers each of which is at most n bits long. Let S be the difference between the sum of square roots of a_i's and the sum of square roots of the b_j's. If S is nonzero how small can it be in absolute value? It is conjectured that in absolute absolue value S must be at least 1/(2^{poly(n)}). In this talk we will see the solution of a polynomial analog of this conjecture.