Talks' abstracts > Perales Anaya Daniel

Finite free probability lies in the intersection of studying the geometry of polynomials and non-commutative probability. The main objects are expected characteristic polynomials of randomly rotated matrices. These operations can be understood using some classical operations on (deterministic) polynomials studied a century ago.
We will briefly survey the areas of free probability and finite free probability. Then we will go over some selected applications:
-Understanding the limiting distribution of roots of polynomials under repeated differentiation.
-Characterizing the limiting distribution of the roots in terms of ratios of consecutive coefficients.