Colorado State University   Mathematical

Root Separation Bound

By  Hoon Hong
From  North Carolina State University
When  Monday, November 13, 2017
4:00 pm
Where  Weber 237

Let f be a square-free polynomial. The root separation of f is the minimum of the pair-wise distance between the complex roots of f. Finding a lower bound on the root separation is a fundamental problem, arising in numerous disciplines. Due to its importance, there has been extensive research on this problem, resulting in various bounds. In this talk, we present another bound, which is "nicer" than the previous bounds in that

  1. It is bigger (hence better) than the previous bounds.
  2. It is covariant under the scaling of the roots, unlike the previous bounds.
If time allows, we will also describe a generalization to multivariate polynomials systems. This is a joint work with Aaron Herman and Elias Tsigaridas.

Dan Bates