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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><pre><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>INSTITUTE FOR ADVANCED STUDY<o:p></o:p></span></pre><pre><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>School of Mathematics<o:p></o:p></span></pre><pre><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>Princeton, NJ 08540<o:p></o:p></span></pre><pre><span style='font-size:11.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></b></pre><pre><b><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>Mathematics Seminars<o:p></o:p></span></b></pre><pre><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>Week of April 16, 2018<o:p></o:p></span></pre><p class=MsoNormal><span style='font-family:"Times New Roman",serif'><o:p> </o:p></span></p><pre><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></b></pre><pre><b><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>Thursday, April 19<o:p></o:p></span></b></pre><pre><span style='font-size:11.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre style='margin-bottom:6.0pt'><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>Joint IAS/Princeton University Number Theory Seminar<o:p></o:p></span></pre><pre><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>Topic: Mod$p$ points on Shimura varieties with parahoric level structure<o:p></o:p></span></pre><pre><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>Speaker: Rong Zhou, Member, School of Mathematics<o:p></o:p></span></pre><pre><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>Time/Room: 4:30pm - 5:30pm/Fine Hall 214, Princeton University<o:p></o:p></span></pre><pre><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>Abstract Link: <a href="http://www.math.ias.edu/seminars/abstract?event=136739">http://www.math.ias.edu/seminars/abstract?event=136739</a><o:p></o:p></span></pre><p class=MsoNormal><span style='font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif'>The Langlands-Rapoport conjecture gives a description of the mod $p$ points of suitable integral models of Shimura varieties. Such results are of use, for example, in computing the local factor of the (semi-simple) Hasse-Weil zeta function of the Shimura variety. In this talk, we show that the points in each of the isogeny classes on the special fiber of the integral models of Shimura varieties with parahoric level constructed by Kisin and Pappas have the form predicted by the above conjecture, when the group is residually split at p. Along the way, we verify some of the He-Rapoport axioms which allow us to deduce the non-emptiness of Newton strata for these models.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif'>---------------------------------<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif'>IAS Math Seminars Home Page:<br><a href="http://www.math.ias.edu/seminars">http://www.math.ias.edu/seminars</a><o:p></o:p></span></p></div></body></html>