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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal style='background:white'><span style='color:black'><a href="https://statistics.yale.edu/" title="Department of Statistics and Data Science
"><span style='font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#286DC0;text-decoration:none'><img border=0 width=150 height=49 style='width:1.5625in;height:.5069in' id=logo src="cid:image001.jpg@01D8FE3E.C35D9FF0" alt="Department of Statistics and Data Science
"></span></a></span><span style='color:black'> <a href="https://statistics.yale.edu/" title=Home><b><span style='font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#286DC0'>Department of Statistics and Data Science </span></b></a></span><b><i><u><span style='font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#286DC0'> <o:p></o:p></span></u></i></b></p><p class=MsoNormal style='background:white'><span class=date-display-single><u><span style='font-size:16.0pt;font-family:"Arial",sans-serif;color:black'>We invite you to participate in our virtual seminar</span></u></span><u><span style='font-size:16.0pt;font-family:"Arial",sans-serif;color:#286DC0'><o:p></o:p></span></u></p><p class=MsoNormal style='background:white'><span style='font-size:16.0pt;font-family:"Arial",sans-serif;color:#00356B'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:16.0pt;font-family:"Arial",sans-serif;color:#00356B'><a href="https://statistics.yale.edu/seminars/tselil-schramm"><span style='color:black;text-decoration:none'>Tselil Schramm</span></a>, </span><span style='font-size:16.0pt;font-family:"Arial",sans-serif;color:#222222'>Stanford University<o:p></o:p></span></p><p class=MsoNormal><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
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</v:shape><![endif]--><![if !vml]><img width=165 height=199 style='width:1.7222in;height:2.0694in' src="cid:image003.jpg@01D8FE3F.12DAE600" align=left hspace=12 v:shapes="Picture_x0020_3"><![endif]><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Date: Monday, November 28, 2022<o:p></o:p></span></span></p><p class=MsoNormal><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Time: </span></span><span class=date-display-start><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>4:00PM</span></span><span class=date-display-range><span style='font-size:12.0pt;font-family:"Arial",sans-serif'> to </span></span><span class=date-display-end><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>5:00PM</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#003C76'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Via Zoom: <a href="https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09">https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09</a> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Password: 24<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><a href="https://tselilschramm.org/"><span style='color:#003C76'>Website</span></a><o:p></o:p></span></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal><b><span style='font-size:14.0pt;font-family:"Arial",sans-serif'>Title: Testing thresholds in high-dimensional random geometric graphs<o:p></o:p></span></b></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Information and Abstract: <o:p></o:p></span></b></p><p style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:0in;box-sizing: inherit'><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>We study random geometric graphs in the high-dimensional setting, where the dimension grows to infinity with the number of vertices. Our central question is: given such a graph, when is it possible to identify the underlying geometry? As the dimension grows relative to the number of vertices, the edges in the graph become increasingly independent, and the underlying geometry becomes less apparent. In this talk I will present recent progress on this question: we show that in sparse geometric random graphs on the unit sphere, if the dimension is at least polylogarithmic in the number of vertices, then the graphs are statistically indistinguishable from Erdos-Renyi graphs, and the underlying geometry disappears.<o:p></o:p></span></p><p style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:0in;box-sizing: inherit'><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Based on joint work with Siqi Liu, Sidhanth Mohanty, and Elizabeth Yang.<o:p></o:p></span></p><p class=MsoNormal style='line-height:18.0pt;background:white'><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'><a href="x-apple-data-detectors://10/"><span style='color:black;text-decoration:none'>3:30pm</span></a> - Pre-talk meet and greet via Zoom</span></b><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></b></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Zoom Link: </span></b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Via Zoom: Join from PC, Mac, Linux, iOS or Android: <a href="https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09"><span style='color:#0563C1'>https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09</span></a> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'> Password: 24<br> Or Telephone</span><span style='font-size:12.0pt;font-family:"MS Mincho"'>：</span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>203-432-9666 (2-ZOOM if on-campus) or 646 568 7788<br> Meeting ID: 924 1107 7917<o:p></o:p></span></p><p class=MsoNormal style='line-height:18.0pt;background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>For more details and upcoming events visit our website at <a href="http://statistics.yale.edu/"><span style='color:black'>http://statistics.yale.edu/</span></a></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></p><h2 style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:6.0pt;margin-left:0in'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;font-weight:normal'><o:p> </o:p></span></h2><h2 style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:6.0pt;margin-left:0in'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;font-weight:normal'><o:p> </o:p></span></h2><h2 style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:6.0pt;margin-left:0in'><span style='font-family:"Georgia",serif;font-weight:normal'><o:p> </o:p></span></h2><h2 style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:6.0pt;margin-left:0in'><span style='font-family:"Georgia",serif;font-weight:normal'>Department of Statistics and Data Science<o:p></o:p></span></h2><p style='margin:0in;box-sizing: inherit'><span style='font-size:9.0pt;color:black'>Yale University<br>24 Hillhouse Avenue<br>New Haven, CT 06511<o:p></o:p></span></p><p style='margin:0in;box-sizing: inherit'><span style='font-size:9.0pt;color:black'>t 203.432.0666<br>f 203.432.0633<o:p></o:p></span></p><p class=MsoNormal style='margin-top:.1in'><span style='font-size:13.0pt;font-family:"Arial",sans-serif;background:white'><o:p> </o:p></span></p></div></body></html>