XL Workshop on Geometric Methods in Physics Białowieża, 2-8.07.2023 XII School on Geometry and Physics Białystok, 26-30.06.2023

Marco Bertola

Orthogonal polynomials, some of their applications and asymptotic analysis

The course provides an overview to the theory and applications of orthogonal polynomials (OPs). The undergraduate student most likely encounters OPs when discussing separation of variables in solutions of important PDEs, notably the harmonic oscillator in quantum mechanics (i.e. Hermite polynomials). However, their applications cover a much wider range of topics, whose list includes (but is not limited to): elements of combinatorics, number theory (e.g. the proof that the Euler constant is transcendental); integrable systems (e.g. the Toda lattice equations); stochastic models (random matrices); special equations (Painlevé equations).

The topics covered in the course will be:

The course is aimed at graduate students (or advanced undergraduate) with a solid grasp of complex analysis (contour integration, conformal properties of holomorphic functions, Cauchy theorem(s)), linear algebra and elementary measure theory.
Event sponsored by
University of Białystok
University of Białystok
Doskonala Nauka