The Stokes Phenomenon: Introduction (Nikita Nikolaev, UNIGE)

14.10.2019 14:00 – 16:00

There is an interesting and surprising phenomenon in complex analysis: the asymptotic behaviour of some functions in the complex plane at (say) infinity depends on the direction of approach towards infinity; moreover, matching asymptotic expansions with functions comes with abrupt discontinuities at specific discrete directions. This phenomenon was first discovered by Sir George Stokes in 1847 in the study of geometric optics, and it is now known as the Stokes Phenomenon.

We now know that the Stokes phenomenon occurs in the analysis of solutions to meromorphic differential equations with an irregular singular point. In the last few decades, it was recognised that similar phenomena appear in a wide range of subjects in mathematics and physics, from the study of stability conditions in the geometry of moduli spaces of sheaves to counting black holes in string theory. These and many other phenomena are now more generally known as Wall-Crossing Phenomena.

In this introductory lecture, I want to demonstrate the Stokes phenomenon through a very explicit example. The prerequisites will be kept at a minimum, so this talk is especially suitable for students and non-experts.

Lieu

Bâtiment: Battelle

Séminaire "The Stokes seminar"

entrée libre