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<div dir="ltr"><div style="color:rgb(49,49,49);word-spacing:1px"><font size="2">As part of the series of seminars <i>"Insalate di Matematica"</i>, <b>Elena Di Domenico</b>, PhD student at <span style="color:rgb(34,34,34);word-spacing:0px">the Università degli Studi di Trento and at the
University of the Basque Country</span><font style="word-spacing:0px" color="#313131"><span style="word-spacing:1px">, will deliver the first talk of the new year. </span></font></font></div><div style="color:rgb(49,49,49);word-spacing:1px"><font size="2">
The seminar will be held online and, according to the current Covid regulations, it will also be broadcast in room 3014 <b>(more information below)</b>.
</font></div><div style="color:rgb(49,49,49);word-spacing:1px"><font size="2"><br></font></div><div style="color:rgb(49,49,49);word-spacing:1px"><font size="2"><span style="color:rgb(34,34,34)">Here the details:</span></font></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><font size="2"><br></font></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><font size="2"><u>Date and time</u>: <b>13th January 2022, 3:00 pm (CET) </b>
<u>(</u><i>be careful with the change of usual starting time</i><u>)</u></font>
</div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><font size="2"><u><br></u></font></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><font size="2"><u>Title</u>: <i><span style="background-color:rgb(241,194,50)">"<i>p</i>-Basilica groups<span style="color:rgb(34,34,34)">"</span></span><br><span style="color:rgb(34,34,34);background-color:rgb(241,194,50)"></span></i></font></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><font size="2"><br></font></div><div dir="ltr"><font size="2"><u style="color:rgb(49,49,49);word-spacing:1px">Abstract</u><font color="#313131"><span style="word-spacing:1px">:</span></font><font color="#313131"> </font>Groups acting on regular rooted trees provide an answer to many problems in group theory. For example the Gupta-Sidki
<i>p</i>-groups and the Grigorchuk groups are finitely generated infinite
<i>p</i>-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<br></font><div><font size="2">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
<i>p</i>-Basilica groups acting on the
<i>p</i>-adic tree. We will see that the
<i>p</i>-Basilica groups have the
<i>p</i>-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
<i>p</i>-Basilica groups give the first examples of weakly branch, but not branch, groups which are super strongly fractal.</font></div><div><font size="2"><br></font></div><div><font size="2">This is a joint work with Gustavo Fernández Alcober, Marialaura Noce and<br>Anitha Thillaisundaram.</font></div><div><font size="2"><br></font></div>
<font size="2"><span style="color:rgb(0,0,0);font-family:Roboto,-apple-system,BlinkMacSystemFont,"Apple Color Emoji","Helvetica Neue",sans-serif"></span></font></div><div dir="ltr"><font size="2"><span style="color:rgb(0,0,0);font-family:Roboto,-apple-system,BlinkMacSystemFont,"Apple Color Emoji","Helvetica Neue",sans-serif"><br></span></font></div><div dir="ltr"><div dir="auto"><font size="2"><u style="color:rgb(49,49,49);word-spacing:1px">Keywords</u><font color="#313131"><span style="word-spacing:1px">: Groups acting on rooted trees, branch groups, fractal groups, congruence subgroup property.
</span></font><span style="color:rgb(0,0,0);font-family:Roboto,-apple-system,BlinkMacSystemFont,"Apple Color Emoji","Helvetica Neue",sans-serif"></span></font></div><div dir="auto"><font size="2"><br></font></div><div dir="auto" style="word-spacing:1px"><font size="2" color="#313131"><br></font></div>
<div style="word-spacing:1px"><font size="2" color="#313131"><b><u>Information to attend in room 3014<br></u></b></font></div><div style="word-spacing:1px"><font size="2" color="#313131">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, </font><font size="2"><span style="color:rgb(49,49,49)">reservation is mandatory. You can reserve at the following link: </span><a href="https://sites.google.com/view/insalate-di-matematica/reservation?authuser=0" target="_blank">https://sites.google.com/view/insalate-di-matematica/reservation?authuser=0</a></font></div><div style="word-spacing:1px"><font size="2" color="#313131">We also remind that you will be required to exhibit your green pass at the entrance of the building.</font></div>
<div style="word-spacing:1px"><font size="2" color="#313131"><br></font></div><div style="word-spacing:1px"><font size="2"><b style="color:rgb(49,49,49)"><u>Information to attend online</u></b></font></div><div style="word-spacing:1px"><font size="2" color="#313131">The seminar will be streamed via</font><font size="2" color="#313131"> Google Meet platform at the following link: <a href="https://meet.google.com/nxc-abxb-xec" target="_blank">https://meet.google.com/nxc-abxb-xec</a></font><font size="2" color="#313131">
</font><font size="2"><span style="font-family:Roboto,Arial,sans-serif;letter-spacing:0.3px;white-space:nowrap"></span></font></div><div dir="auto"><font size="2"><i><b>** We inform you that the talk will be recorded and uploaded on our website. If you join the talk <u>after the starting time</u>, we kindly ask you to ensure that <u>your microphone and webcam are turned off</u> **</b></i><br></font></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><font size="2"><br></font></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><font size="2">You can find the poster of the event in the attachment. We are looking forward to seeing you! </font></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><font size="2"><br></font></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><font size="2">For further information, please visit our website: <a href="https://sites.google.com/view/insalate-di-matematica" target="_blank">https://sites.google.com/view/insalate-di-matematica</a> or contact us at <a href="mailto:insalate.matematica@unimib.it" target="_blank">insalate.matematica@unimib.it</a>.</font></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><font size="2"><br></font></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><font size="2"><br>The organizers: Luigi Appolloni, Andrea Bisterzo, Alberto Cassella, Francesca Cottini, Ludovico Marini</font></div></div></div>
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