[Dottorcomp] Insalate di Matematica - E. Di Domenico (Thursday 13/01)

[Mbs Insalate Di Matematica]

 As part of the series of seminars *"Insalate di Matematica"*, *Elena Di
Domenico*, PhD student at the Università degli Studi di Trento and at the
University of the Basque Country, will deliver the first talk of the new
year.
The seminar will be held online and, according to the current Covid
regulations, it will also be broadcast in room 3014 *(more information
below)*.

Here the details:

*Date and time*: *13th January 2022, 3:00 pm (CET) * *(**be careful with
the change of usual starting time**)*

*Title*:
*"p-Basilica groups"*

*Abstract*: Groups acting on regular rooted trees provide an answer to many
problems in group theory. For example the Gupta-Sidki *p*-groups and the
Grigorchuk groups are finitely generated infinite *p*-groups so they give a
negative answer to the General Burnside Problem. The First Grigorchuk group
is also the first example of a group with intermediate growth. In this talk
we will give an introduction to the theory of the groups of automorphisms
of regular rooted
trees, providing examples and interesting properties of these groups. The
Basilica group is a famous group acting on the binary tree. It is weakly
branch but not branch, is torsion-free, is of exponential growth, and is
not subexponentially amenable. We will focus on a generalization of the
Basilica group to all odd primes: the *p*-Basilica groups acting on
the *p*-adic
tree. We will see that the *p*-Basilica groups have the *p*-congruence
subgroup property but not the congruence subgroup property nor the weak
congruence subgroup property. This provides the first examples of weakly
branch groups with such properties. In addition, the *p*-Basilica groups
give the first examples of weakly branch, but not branch, groups which are
super strongly fractal.

This is a joint work with Gustavo Fernández Alcober, Marialaura Noce and
Anitha Thillaisundaram.


*Keywords*: Groups acting on rooted trees, branch groups, fractal groups,
congruence subgroup property.



*Information to attend in room 3014*
The seminar will also be broadcast in room 3014, at the building U5-Ratio,
Università degli Studi di Milano Bicocca. For the traceability of persons
present in the department, reservation is mandatory. You can reserve at the
following link:
https://sites.google.com/view/insalate-di-matematica/reservation?authuser=0
We also remind that you will be required to exhibit your green pass at the
entrance of the building.

*Information to attend online*
The seminar will be streamed via Google Meet platform at the following
link: https://meet.google.com/nxc-abxb-xec
*** We inform you that the talk will be recorded and uploaded on our
website. If you join the talk after the starting time, we kindly ask you to
ensure that your microphone and webcam are turned off ***

You can find the poster of the event in the attachment. We are looking
forward to seeing you!

For further information, please visit our website:
https://sites.google.com/view/insalate-di-matematica or contact us at
insalate.matematica a unimib.it.


The organizers: Luigi Appolloni, Andrea Bisterzo, Alberto Cassella,
Francesca Cottini, Ludovico Marini
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