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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal><span style='font-family:"Times New Roman",serif'>INSTITUTE FOR ADVANCED STUDY<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif'>School of Mathematics<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif'>Princeton, NJ 08540<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'>Mathematics Seminars<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif'>Week of May 14, 2018<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><b><span style='font-family:"Times New Roman",serif'><o:p> </o:p></span></b></p><pre><b><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>Thursday, May 17<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><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: A new <i>p</i>-adic Maass-Shimura operator and supersingular Rankin-Selberg <i>p</i>-adic <i>L</i>-functions<o:p></o:p></span></pre><pre><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>Speaker: Daniel Kriz, Princeton University<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=137231">http://www.math.ias.edu/seminars/abstract?event=137231</a><o:p></o:p></span></pre><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>We introduce a new $p$-adic Maass-Shimura operator acting on a space of "generalized $p$-adic modular forms" (extending Katz's notion of $p$-adic modular forms) defined on the $p$-adic (preperfectoid) universal cover of Shimura curves. Using this operator, we construct new $p$-adic $L$-functions in the style of Katz, Bertolini-Darmon-Prasanna and Liu-Zhang-Zhang for Rankin-Selberg families over imaginary quadratic fields $K$ in the case where $p$ is inert or ramified in $K$. We also establish new $p$-adic Waldspurger formulas, relating $p$-adic logarithms of elliptic units and Heegner points to special values of these $p$-adic $L$-functions.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><div style='mso-element:para-border-div;border:none;border-bottom:double windowtext 2.25pt;padding:0in 0in 1.0pt 0in'><p class=MsoNormal style='border:none;padding:0in'><o:p> </o:p></p></div><p class=MsoNormal>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></p></div></body></html>