Published on *Max-Planck-Institut für Mathematik* (http://www.mpim-bonn.mpg.de)

Posted in

- Vortrag [1]

Speaker:

Peter Zograf
Zugehörigkeit:

Steklov Math. Institute, St. Petersburg
Datum:

Don, 2018-04-26 15:00 - 16:00 A meander is a topological configuration of a line and a simple closed curve in the plane (or a pair of simple closed curves on the 2-sphere) intersecting transversely. In physics, meanders provide a model of polymer folding, and their enumeration is directly related to the entropy of the associated dynamical systems. We combine recent results on Masur-Veech volumes of the moduli spaces of meromorphic quadratic differentials in genus zero with a fact that horizontal and vertical separatrix diagrams of integer quadratic differentials are asymptotically uncorrelated to study asymptotic enumeration of meanders. As a result, we get an explicit asymptotic formula for the number of closed meanders with fixed number of minimal arcs when the number of crossings goes to infinity.

**Links:**

[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/de/node/3444

[3] http://www.mpim-bonn.mpg.de/de/node/158