<div dir="ltr"><span style="font-family:arial,sans-serif;font-size:13px">   </span><div><span style="font-family:arial,sans-serif;font-size:13px">   BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR</span><br></div><div><br style="font-family:arial,sans-serif;font-size:13px"><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">   Date: </span><span class="" tabindex="0" style="font-family:arial,sans-serif;font-size:13px"><span class="">Thursday, September 18, 2014</span></span><br style="font-family:arial,sans-serif;font-size:13px"><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">   Time:  </span><span class="" tabindex="0" style="font-family:arial,sans-serif;font-size:13px"><span class="">2.50 pm</span></span><br style="font-family:arial,sans-serif;font-size:13px"><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">   Place: Old Whitney Hall, Room 100E,  followed by coffee/tea in the</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">      Hilton Reading Room. Note the new location of the math department.</span><br style="font-family:arial,sans-serif;font-size:13px"><br style="font-family:arial,sans-serif;font-size:13px"><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">   Speaker: Russell Ricks (University of Michigan)</span><br style="font-family:arial,sans-serif;font-size:13px"><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">   Title: Flat strips in rank one CAT(0) spaces</span><br style="font-family:arial,sans-serif;font-size:13px"><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">Abstract:</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">Let X be a proper, geodesically complete CAT(0) space under a</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">geometric (that is, properly discontinuous, cocompact, and isometric)</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">group action on X; further assume X admits a rank one axis. Using the</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">Patterson-Sullivan measure on the boundary, we construct a generalized</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">Bowen-Margulis measure on the space of geodesics in X. This additional</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">structure allows us to prove some results about the original CAT(0)</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">space X. Here are three such results: First, with respect to the</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">Patterson-Sullivan measure, almost every point in the boundary of X is</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">isolated in the Tits metric. Second, under the Bowen-Margulis measure,</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">almost no geodesic bounds a flat strip of any positive width. Third,</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">we characterize when the length spectrum is arithmetic (that is, the</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">set of translation lengths is contained in a discrete subgroup of the</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">reals). In this talk, we will discuss the constructions and a few of the</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">wrinkles involved for CAT(0) spaces. </span><br style="font-family:arial,sans-serif;font-size:13px"><br style="font-family:arial,sans-serif;font-size:13px"><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">NOTE:  The seminar has a webpage where the semester&#39;s program is listed:</span><br style="font-family:arial,sans-serif;font-size:13px"><br style="font-family:arial,sans-serif;font-size:13px"><a href="http://www2.math.binghamton.edu/p/seminars/topsem" target="_blank" style="font-family:arial,sans-serif;font-size:13px">http://www2.math.binghamton.<u></u>edu/p/seminars/topsem</a><br style="font-family:arial,sans-serif;font-size:13px"><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">It can also be linked from the Department&#39;s Home Page.</span><br></div></div>