<div dir="ltr"><br><div><p dir="ltr" style="font-size:12.8px">BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR</p><p dir="ltr" style="font-size:12.8px">   Date: Thursday, October 15th, 2015</p><p dir="ltr" style="font-size:12.8px">   Time:  2.50 pm</p><p dir="ltr" style="font-size:12.8px">   Place: Whitney Hall, Room 100E,  followed by coffee/tea in the<br>      Hilton Reading Room. Note the new location of the math department (<a href="http://www2.math.binghamton.edu/p/directions" target="_blank">http://www2.</a><a href="http://www2.math.binghamton.edu/p/directions" target="_blank">math.binghamton.edu</a><a href="http://www2.math.binghamton.edu/p/directions" target="_blank">/p/directions</a>).</p><p dir="ltr"><span style="font-size:12.8px">   </span>Speaker:  <strong style="color:rgb(51,51,51);font-family:Arial,sans-serif;line-height:16.8px">Andrew Geng</strong><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;line-height:16.8px"> (University of Chicago)</span><span style="color:rgb(51,51,51);font-family:Arial,sans-serif;line-height:16.8px"> </span> </p><p dir="ltr"><font color="#333333">   Title: </font> <strong style="color:rgb(51,51,51);font-family:Arial,sans-serif;line-height:16.8px">Classification and examples of 5-dimensional geometries</strong></p><p style="line-height:16.8px;color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px"><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;line-height:normal">    Abstract:<span style="background-color:rgb(243,243,243)"> </span></span><span style="line-height:16.8px;background-color:rgb(243,243,243)">Thurston's eight homogeneous geometries formed the building blocks of 3-manifolds in the Geometrization Conjecture. Filipkiewicz classified the 4-dimensional geometries in 1983, finding 18 and one countably infinite family. I have recently classified the 5-dimensional geometries. I will review what a geometry in the sense of Thurston is, survey related ideas, and outline the classification in 5 dimensions. Salient features, especially those first occurring in dimension 5, will be illustrated using particular geometries from the list. The classification touches a number of topics including foliations, fiber bundles, representations of compact Lie groups, Lie algebra cohomology, Galois theory in algebraic number fields, and conformal transformation groups. I hope to give some indication of how all of these come into play.</span><br></p><p style="line-height:16.8px;color:rgb(51,51,51);font-family:Arial,sans-serif;font-size:15px"><span style="font-size:12.8px;font-family:arial,sans-serif;line-height:normal;color:rgb(34,34,34)">NOTE:  The seminar has a webpage where the semester's program is listed:</span><br></p><p dir="ltr" style="font-size:12.8px"><a href="http://www2.math.binghamton.edu/p/seminars/topsem" target="_blank">http://www2.math.binghamton.edu/p/seminars/topsem</a></p></div></div>