2021 Winter School in Mathematical Physics

20 Jan 2021, 09:00 → 22 Jan 2021, 19:00 Europe/Zurich

Les Diablerets

Anton Alekseev (University of Geneva), Maria Podkopaeva (IHES)

Organized by

• Anton Alekseev (UNIGE)
• Alberto Cattaneo (UZH)
• Giovanni Felder (ETH Zürich)
• Maria Podkopaeva (IHES)
• Thomas Strobl (U. Lyon 1)
• Andras Szenes (UniGe).

Marcos Marino, Lecture notes on resurgence

Wednesday, 20 January

10:30 → 12:30 A. Alekseev, "Coadjoint orbits and equivariant localisation in finite and infinite dimensions"

17:00 → 19:00 M.Mariño, "Resurgence in mathematics and physics"

Thursday, 21 January

09:30 → 12:30 Student talks

09:30 Weronika Czerniawska, "What is Arakelov geometry and what does it have to do with Physics?"

10:00 Raphaël Ducatez, "A forward-backward random process for the spectrum of 1D Anderson operator"

Anderson's model in 1 dimension has been studied since the 80's and the location is well understood. Here I propose a new formula for the construction of the eigenvectors which makes the link with the products of independent random matrices. In particular, I show that, with a adapted scaling, eigenvectors behave as the exponential of a Brownian process with a drift, the drift corresponding to the classical localization result. This result is known for the product of independent random matrices but at our knowledge had not been generalized to Anderson's model.

10:30 Matthias Kloeckner, "A new characterization of conformal maps in (pseudo-)Euclidean spaces"

11:15 Donald Youmans, "BF, Schwarzian theory and Drinfeld-Sokolov reduction"

11:45 Danilo Lewanski, "Resurgent Topological Recursion"

Topological recursion (TR) arose from random matrix models and was promoted to a mathematical theory in 2007. It can be thought as an implementable algorithm which takes as input an object called spectral curve and produces as output the infinite list of numbers which are solution to some enumerative problem. TR is by now applied to Mirror Symmetry, String Theory, Gromov-Witten theory, Hurwitz theory, WKB analysis, Painleve equations, polynomial invariants of knots, Hitchin systems, and more. We will give some accessible example of how it works and what can generate. If time allows, we’ll dive into some conjectural connection with resurgence.

17:00 → 19:00 M.Mariño, "Resurgence in mathematics and physics"

Friday, 22 January

10:30 → 12:30 A. Alekseev, "Coadjoint orbits and equivariant localisation in finite and infinite dimensions"