A univariate polynomial of degree n has n complex roots, which form a multiset in the complex plane. This article discusses the geometry of these points, such as upper and lower bounds on the absolute values of the roots and the expected number of real roots for a random polynomial. It also considers properties related to a single polynomial, such as the distance between two roots.
Stanford University
Autumn 2022
The course addresses both classic and recent developments in counting and sampling. It covers counting complexity, exact counting via determinants, sampling via Markov chains, and high-dimensional expanders.
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