# A strange space with wormholes

Università degli Studi Trento

38123 Povo (TN)

Tel +39 04 61/281508-1625-1701-3898-1980.

dept.math [at] unitn.it

**Luogo: **l'evento si terrà in via telematica attraverso collegamento alla piattaforma Zoom. Per informazioni sull'accesso contattare lo Staff di Dipartimento

**Ore: **16.00

**“Doc in Progress” and #iorestoacasa** are pleased to introduce you to:

**Marco Capolli**- PhD in Mathematics, University of Trento

**Abstract:**

Laakso spaces were first introduced in 2000 by the Finnish mathematician T.J. Laakso. The motivation behind their construction was to provide an example of a space with classical properties, like the existence of geodesics or a weak (1; 1)-Poincare inequality, but that can not be biLipschitz embedded in any n-dimensional Euclidean space.

The main characteristic that makes working in Laakso spaces so peculiar is the fact that they have fractional dimension and do not possess a group structure. Properties that are used when working in classical settings may not make sense in a Laakso space. One of these properties is the existence of a family of dilatations and its absence causes the standard approach to many problems to fail. For this reason new methodologies must be employed and the validity of classical results must be checked.

In this talk I will give an overview on how a Laakso space is constructed, trying to emphasize where the difficulties arise. I will also give some insights about the work that I have done so far in the study of related problems.