On Recent Progress in Solving Polynomial Equations - Part 1

I will review some recently developed algorithms for real and complex root finding, which are simple and practical and whose worst-case bit complexity matches that of the best methods in theory.
Combining our techniques with a classical approach that considers so-called fractional derivatives, we can further derive a polynomial-time algorithm to compute approximations of all real roots of a sparse polynomial with arbitrary real coefficients. For very sparse polynomials with integer coefficients, the method performs near-optimal.