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

Posted in

- Vortrag [1]

Speaker:

Jeanne Scott
Zugehörigkeit:

Universidad de los Andes
Datum:

Die, 2019-09-24 14:00 - 15:00 The theory of random Delaunay triangulations of the plane has been proposed by

David-Eynard and others as a discrete model for 2-dimensional quantum gravity: In this model

the role of a continuous metric is played by a Delaunay triangulation while flat metrics

correspond to isoradial triangulations (on which one can define a theory of discrete analyticity).

Like the continuous case, the partition function for this discrete theory is given by a suitably

normalized determinant of a Beltrami-Laplace operator which varies with the choice of

triangulation. An elegant formula of Richard Kenyon expresses this determinant as a finite sum

of local contributions when the triangulation is both isoradial and periodic. In joint work with

François David we consider smooth perturbations of a periodic isoradial triangulation and obtain

an asymptotic expansion for the second variation of the log-determinant of the discrete

Beltrami-Laplace operator. This result can be interpreted as a discretization of the formula for

the second variation (of the logarithm) of the continuous partition function know from conformal

field theory; using this interpretation we can identify the central charge in this discrete setting.

**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/5312