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<p>Hi everyone,</p><p>This week our speaker is Ignat Soroko of Louisiana State University. Links and details are below.<br></p><p>Zoom link for the seminar, 2:50 - 3:50:<br>
<a href="https://binghamton.zoom.us/j/94057178271" rel="noreferrer" target="_blank">https://binghamton.zoom.us/j/94057178271</a><br>
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Zoom link for the coffee, 12:30 - 1:30:<br>
<a href="https://binghamton.zoom.us/j/96674397432" rel="noreferrer" target="_blank">https://binghamton.zoom.us/j/96674397432</a></p>
<i>Title: </i>Groups of type FP: their quasi-isometry classes and homological Dehn functions<br><br><i>Abstract: </i>There
are only countably many isomorphism classes of finitely presented
groups, i.e. groups of type $F_2$. Considering a homological analog of
finite presentability, we get the class of groups $FP_2$. Ian Leary
proved that there are uncountably many isomorphism classes of groups of
type $FP_2$ (and even of finer class FP). R.Kropholler, Leary and I
proved that there are uncountably many classes of groups of type FP even
up to quasi-isometries. Since `almost all' of these groups are
infinitely presented, the usual Dehn function makes no sense for them,
but the homological Dehn function is well-defined. In an on-going
project with N.Brady, R.Kropholler and myself, we show that for any
integer $k\ge4$ there exist uncountably many quasi-isometry classes of
groups of type FP with a homological Dehn function $n^k$. In this talk I
will give the relevant definitions and describe the construction of
these groups. Time permitting, I will describe the connection of these
groups to the Relation Gap Problem.<br><span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline"></span><p><br></p><p>See you on Thursday!</p><p>Best,</p><p>Matt</p>
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