*Title: *Introduction to Random Geometry
*Abstract:* This course wants to give an overview of active research topics
in the field of Random Geometry, with a focus on growth models. We will
start by discussing discrete growth models such as the Eden model,
Diffusion Limited Aggregation and Internal DLA. We will then move to the
continuum for the remaining part of the course. After discussing conformal
invariance of Brownian motion, we will focus on the class of randomly
growing domains on the complex plane which can be described via Loewner
dynamics. We will introduce several random aggregation models on the
complex plane, which go under the name of Hastings-Levitov models and
Aggregate Loewner Evolutions, of which we will study the large-scale
features, presenting existing results and several open questions.
*Keywords:* Random growth models, Diffusion Limited Aggregation,
Schramm-Loewner Evolutions, Hastings-Levitov, Aggregate Loewner Evolutions.
*Prerequisites:* The course will be as self-contained as possible. However,
basic notions of Probability and Analysis are necessary. Some knowledge of
complex analysis, martingale theory and stochastic calculus is desirable
but not required.
*Duration:* 20 hours (10 lectures of 2 hours each)
*Class schedule:* The lectures will take place in Room G, Dipartimento di
Matematica G. Castelnuovo, 13:00-15:00 in the following dates:
Monday 18/3
Wednesday 20/3
Friday 22/3
Monday 25/3
Wednesday 27/3
Tuesday 2/4
Wednesday 3/4
Monday 8/4
Wednesday 10/4
Friday 12/4