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<p>Hi everyone,</p><p>This week our speaker is Rylee Lyman of Rutgers 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>
<br>
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><p><i>Title: 
</i><span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">Nielsen realization for infinite-type surfaces</span><i>



</i></p><p>
<em>Abstract: </em>
<span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">We learn the classification of surfaces early in our</span><br style="font-family:Arial,sans-serif;white-space:pre-wrap">
<span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">mathematical careers: the homeomorphism type of an orientable surface</span><br style="font-family:Arial,sans-serif;white-space:pre-wrap">
<span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">with finitely generated fundamental group is determined by genus,</span><br style="font-family:Arial,sans-serif;white-space:pre-wrap">
<span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">punctures and boundary components. Without the finite generation</span><br style="font-family:Arial,sans-serif;white-space:pre-wrap">
<span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">assum</span><span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">ption, there is still a classification, due to Kerékjártó and</span><br style="font-family:Arial,sans-serif;white-space:pre-wrap">
<span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">Richards. These surfaces are of infinite type. Associated to any</span><br style="font-family:Arial,sans-serif;white-space:pre-wrap">
<span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">surface is its mapping class group. A famous theorem of Kerckhoff from</span><br style="font-family:Arial,sans-serif;white-space:pre-wrap">
<span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">1983 solves the "Nielsen realization" problem posed in 1932: finite</span><br style="font-family:Arial,sans-serif;white-space:pre-wrap">
<span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">subgroups of the mapping class group of a finite-type surface of</span><br style="font-family:Arial,sans-serif;white-space:pre-wrap">
<span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">negative Euler characteristic are exactly the groups of isometries of</span><br style="font-family:Arial,sans-serif;white-space:pre-wrap">
<span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">some hyperbolic metric on the surface. Recently, joint with Santana</span><br style="font-family:Arial,sans-serif;white-space:pre-wrap">
<span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">Afton, Danny Calegari and Lvzhou Chen, I extended Kerckhoff's theorem to</span><br style="font-family:Arial,sans-serif;white-space:pre-wrap">
<span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">orientable, infinite-type surfaces. I'd like to introduce infinite-type</span><br style="font-family:Arial,sans-serif;white-space:pre-wrap">
<span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">su</span><span style="font-family:Arial,sans-serif;font-size:small;white-space:pre-wrap;background-color:rgb(255,255,255);display:inline">rfaces and discuss the theorem and some of its consequences.</span>

</p><p><br></p><p>See you on Thursday!</p><p>Best,</p><p>Matt</p>

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