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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><b><span style='font-family:"Times New Roman",serif'>Mathematics Seminars<o:p></o:p></span></b></p><p class=MsoNormal><b><span style='font-family:"Times New Roman",serif'>Week of May 14, 2018<o:p></o:p></span></b></p><p class=MsoNormal><b><span style='font-family:"Times New Roman",serif'><o:p> </o:p></span></b></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'>Tuesday, May 15<o:p></o:p></span></b></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><pre style='margin-bottom:6.0pt'><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Special Mathematics Physics Seminar<o:p></o:p></span></pre><pre><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>Topic: An Introduction to Liouville Theory<o:p></o:p></span></pre><pre><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>Speaker: Antti Kupiainen, University of Helsinki<o:p></o:p></span></pre><pre><span style='font-size:11.0pt;font-family:"Times New Roman",serif'>Time/Room: 2:00pm - 3:00pm/Simonyi Hall 101<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=137389">http://www.math.ias.edu/seminars/abstract?event=137389</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'>Liouville Conformal Field Theory (LCFT) is an essential building block of Polyakov’s formulation of non critical string theory. Moreover, scaling limits of statistical mechanics models on random lattices (planar maps) are believed to be described by LCFT as well as partition functions of certain 4-dimensional Yang-Mills theories. I will give an introduction to a rigorous probabilistic construction of LCFT (joint work with F. David, R. Rhodes and V. Vargas) and sketch a proof (jointly with R. Rhodes and V. Vargas) of the remarkable explicit expression of the three point functions of LCFT conjectured by Dorn, Otto, Zamolodchicov and Zamolodchikov.<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'><o:p> </o:p></span></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'><span style='font-family:"Times New Roman",serif'><o:p> </o:p></span></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><span style='font-family:"Times New Roman",serif'><o:p></o:p></span></p></div></body></html>