### Do polynomials dream of symmetric curves?

- Series
- Job Candidate Talk
- Time
- Tuesday, March 31, 2015 - 11:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Andrei Martinez-Finkelshtein – Universidad de Almeria, Spain

Polynomials defined either by some type of orthogonality or
satisfying differential equations are pervasive in approximation theory,
random matrix theory, special functions, harmonic analysis, scientific
computing and applications. Numerical simulations show that their zeros
exhibit a common feature: they align themselves along certain curves on the
plane. What are these curves? In some cases we can answer this question, at
least asymptotically. The answer connects fascinating mathematical objects,
such as extremal problems in electrostatics, Riemann surfaces, trajectories
of quadratic differentials, algebraic functions; this list is not complete.
This talk is a brief survey of some ideas related to this problem, from the
breakthrough developments in the 1980-ies to nowadays, finishing with some
recent results and open problems.