<div dir="ltr"><font face="arial, helvetica, sans-serif" style="font-size:13px">  BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR<br><br><br>   Date: Thursday, March 26th, 2015<br><br>   Time:  2.50 pm<br><br>   Place: Whitney Hall, Room 100E,  followed by coffee/tea in the<br>      Hilton Reading Room. Note the new location of the math department (</font><a href="http://www2.math.binghamton.edu/p/directions" target="_blank" style="font-size:12.8000001907349px">http://www2.math.binghamton.edu/p/directions</a><span style="font-size:12.8000001907349px">)</span><font face="arial, helvetica, sans-serif" style="font-size:13px">.<br><br><br> </font><font face="arial, helvetica, sans-serif" style="font-size:12.7272720336914px">  </font><font face="arial, helvetica, sans-serif" style="font-size:12.8000001907349px">Speaker: </font><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px;line-height:21px">Jim Belk (Bard College) </span><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px;line-height:21px"> </span><div style="font-size:12.8000001907349px"><div style="font-size:12.8000001907349px"><font face="arial, helvetica, sans-serif"><font color="#333333"><span style="line-height:21px">   Title: </span></font></font><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px;line-height:21px"> </span><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px;line-height:21px">Rearrangement Groups of Fractals</span></div><div style="font-size:12.8000001907349px"><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px;line-height:21px"><br></span></div><div><span style="font-size:15px;color:rgb(51,51,51);font-family:Arial,sans-serif;line-height:21px">   </span><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;line-height:21px">Abstract:</span><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;line-height:21px"> </span><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px;line-height:21px">The definition of Thompson&#39;s group</span><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px;line-height:21px"> </span><span class="" id="MathJax-Element-17-Frame" style="display:inline;font-size:15px;word-wrap:normal;white-space:nowrap;float:none;direction:ltr;border:0px;padding:0px;margin:0px;color:rgb(51,51,51);font-family:Arial,sans-serif"><span class="" id="MathJax-Span-61" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0.947em"><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0.781em;height:0px;font-size:18px"><span style="border:0px;padding:0px;margin:0px;vertical-align:0px"><span class="" id="MathJax-Span-62" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px"><span class="" id="MathJax-Span-63" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px"><img src="https://www2.math.binghamton.edu/js/mathjax-MathJax-727332c/fonts/HTML-CSS/TeX/png/Math/Italic/400/0046.png" style="border: 0px; vertical-align: 0px; color: rgb(102, 102, 102); font-style: italic; height: 13px; max-width: none; padding: 0px; margin: 0px -0.108em 0px 0px; max-height: none; width: 14px; display: inline !important; float: none !important; background-color: transparent;"><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;overflow:hidden;height:1px;width:0.114em"></span></span></span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0px;height:1.725em"></span></span></span><span style="display:inline-block;border-width:0px 0px 0px 0.003em;border-left-style:solid;padding:0px;margin:0px;vertical-align:-0.063em;overflow:hidden;width:0px;height:1.003em"></span></span></span><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px;line-height:21px"> depends crucially on the self-similar structure of the unit interval. In this talk, I will describe a family of Thompson-like groups that act on a variety of self-similar structures. Each of these groups has an associated CAT(0) cubical complex, analogous to the Farley complexes for </span><span class="" style="color:rgb(136,136,136);font-family:Arial,sans-serif;font-size:15px;line-height:21px"></span><span class="" id="MathJax-Element-18-Frame" style="display:inline;font-size:15px;word-wrap:normal;white-space:nowrap;float:none;direction:ltr;border:0px;padding:0px;margin:0px;color:rgb(51,51,51);font-family:Arial,sans-serif"><span class="" id="MathJax-Span-64" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0.947em"><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0.781em;height:0px;font-size:18px"><span style="border:0px;padding:0px;margin:0px;vertical-align:0px"><span class="" id="MathJax-Span-65" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px"><span class="" id="MathJax-Span-66" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px"><img src="https://www2.math.binghamton.edu/js/mathjax-MathJax-727332c/fonts/HTML-CSS/TeX/png/Math/Italic/400/0046.png" style="border: 0px; vertical-align: 0px; color: rgb(102, 102, 102); font-style: italic; height: 13px; max-width: none; padding: 0px; margin: 0px -0.108em 0px 0px; max-height: none; width: 14px; display: inline !important; float: none !important; background-color: transparent;"><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;overflow:hidden;height:1px;width:0.114em"></span></span></span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0px;height:1.725em"></span></span></span><span style="display:inline-block;border-width:0px 0px 0px 0.003em;border-left-style:solid;padding:0px;margin:0px;vertical-align:-0.063em;overflow:hidden;width:0px;height:1.003em"></span></span></span><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px;line-height:21px">, </span><span class="" style="color:rgb(136,136,136);font-family:Arial,sans-serif;font-size:15px;line-height:21px"></span><span class="" id="MathJax-Element-19-Frame" style="display:inline;font-size:15px;word-wrap:normal;white-space:nowrap;float:none;direction:ltr;border:0px;padding:0px;margin:0px;color:rgb(51,51,51);font-family:Arial,sans-serif"><span class="" id="MathJax-Span-67" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0.892em"><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0.725em;height:0px;font-size:18px"><span style="border:0px;padding:0px;margin:0px;vertical-align:0px"><span class="" id="MathJax-Span-68" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px"><span class="" id="MathJax-Span-69" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px"><img src="https://www2.math.binghamton.edu/js/mathjax-MathJax-727332c/fonts/HTML-CSS/TeX/png/Math/Italic/400/0054.png" style="border: 0px; vertical-align: 0px; color: rgb(102, 102, 102); font-style: italic; height: 13px; max-width: none; padding: 0px; margin: 0px -0.108em 0px 0px; max-height: none; width: 13px; display: inline !important; float: none !important; background-color: transparent;"><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;overflow:hidden;height:1px;width:0.114em"></span></span></span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0px;height:1.725em"></span></span></span><span style="display:inline-block;border-width:0px 0px 0px 0.003em;border-left-style:solid;padding:0px;margin:0px;vertical-align:-0.063em;overflow:hidden;width:0px;height:1.003em"></span></span></span><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px;line-height:21px">, and </span><span class="" style="color:rgb(136,136,136);font-family:Arial,sans-serif;font-size:15px;line-height:21px"></span><span class="" id="MathJax-Element-20-Frame" style="display:inline;font-size:15px;word-wrap:normal;white-space:nowrap;float:none;direction:ltr;border:0px;padding:0px;margin:0px;color:rgb(51,51,51);font-family:Arial,sans-serif"><span class="" id="MathJax-Span-70" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0.947em"><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0.781em;height:0px;font-size:18px"><span style="border:0px;padding:0px;margin:0px;vertical-align:0px"><span class="" id="MathJax-Span-71" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px"><span class="" id="MathJax-Span-72" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px"><img src="https://www2.math.binghamton.edu/js/mathjax-MathJax-727332c/fonts/HTML-CSS/TeX/png/Math/Italic/400/0056.png" style="border: 0px; vertical-align: -1px; color: rgb(102, 102, 102); font-style: italic; height: 14px; max-width: none; padding: 0px; margin: 0px -0.164em 0px 0px; max-height: none; width: 14px; display: inline !important; float: none !important; background-color: transparent;"><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;overflow:hidden;height:1px;width:0.169em"></span></span></span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0px;height:1.781em"></span></span></span><span style="display:inline-block;border-width:0px 0px 0px 0.003em;border-left-style:solid;padding:0px;margin:0px;vertical-align:-0.063em;overflow:hidden;width:0px;height:1.003em"></span></span></span><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px;line-height:21px">. By analyzing descending links on these complexes, I will show that some of these groups have type </span><span class="" style="color:rgb(136,136,136);font-family:Arial,sans-serif;font-size:15px;line-height:21px"></span><span class="" id="MathJax-Element-21-Frame" style="display:inline;font-size:15px;word-wrap:normal;white-space:nowrap;float:none;direction:ltr;border:0px;padding:0px;margin:0px;color:rgb(51,51,51);font-family:Arial,sans-serif"><span class="" id="MathJax-Span-73" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:1.781em"><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:1.447em;height:0px;font-size:18px"><span style="border:0px;padding:0px;margin:0px;vertical-align:0px"><span class="" id="MathJax-Span-74" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px"><span class="" id="MathJax-Span-75" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px"><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:1.447em;height:0px"><span style="border:0px;padding:0px;margin:0px;vertical-align:0px"><span class="" id="MathJax-Span-76" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px"><img src="https://www2.math.binghamton.edu/js/mathjax-MathJax-727332c/fonts/HTML-CSS/TeX/png/Math/Italic/400/0046.png" style="border: 0px; vertical-align: 0px; color: rgb(102, 102, 102); font-style: italic; height: 13px; max-width: none; padding: 0px; margin: 0px -0.108em 0px 0px; max-height: none; width: 14px; display: inline !important; float: none !important; background-color: transparent;"><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;overflow:hidden;height:1px;width:0.114em"></span></span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0px;height:1.725em"></span></span><span style="border:0px;padding:0px;margin:0px;vertical-align:0px"><span class="" id="MathJax-Span-77" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;font-size:12.7259998321533px"><img src="https://www2.math.binghamton.edu/js/mathjax-MathJax-727332c/fonts/HTML-CSS/TeX/png/Main/Regular/283/221E.png" style="border: 0px; vertical-align: 0px; color: rgb(102, 102, 102); font-style: italic; height: 6px; max-width: none; padding: 0px; margin: 0px 0.058em 0px 0px; max-height: none; width: 12px; display: inline !important; float: none !important; background-color: transparent;"></span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0px;height:1.336em"></span></span></span></span></span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;width:0px;height:1.003em"></span></span></span><span style="display:inline-block;border-width:0px 0px 0px 0.003em;border-left-style:solid;padding:0px;margin:0px;vertical-align:-0.263em;overflow:hidden;width:0px;height:1.203em"></span></span></span><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px;line-height:21px">. This is joint work with Bradley Forrest.</span></div><div><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px;line-height:21px"><br></span></div><div><br></div><div><font face="arial, helvetica, sans-serif">NOTE:  The seminar has a webpage where the semester&#39;s program is listed:<br><br><a href="http://www2.math.binghamton.edu/p/seminars/topsem" target="_blank" style="font-size:13px">http://www2.math.binghamton.<u></u>edu/p/seminars/topsem</a></font></div></div></div>