<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=us-ascii"><meta name=Generator content="Microsoft Word 15 (filtered medium)"><style><!--
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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><b><span style='font-size:12.0pt'>Please be advised that today’s 2<sup>nd</sup> Variational Methods Seminar will begin at 3:15pm instead of 3:30pm. <o:p></o:p></span></b></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Variational Methods in Geometry Seminar<o:p></o:p></p><p class=MsoNormal>Topic: Multiplicity One Conjecture in Min-max theory<o:p></o:p></p><p class=MsoNormal>Speaker: Xin Zhou, University of California, Santa Barbara; Member, School of Mathematics<o:p></o:p></p><p class=MsoNormal>Time/Room: 3:15pm /Simonyi Hall 101<o:p></o:p></p><p class=MsoNormal>Abstract Link: <a href="http://www.math.ias.edu/seminars/abstract?event=141227">http://www.math.ias.edu/seminars/abstract?event=141227</a><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I will present a proof with some substantial details of the Multiplicity One Conjecture in Min-max theory, raised by Marques and Neves. It says that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves are all two-sided and have multiplicity one. <br><br>In particular, I will discuss three main parts of the proof, including: the formulation of multiple-parameter min-max construction for hypersurfaces with prescribed mean curvature (PMC), an approximation scheme (by PMC min-max theory) of min-max construction of minimal hypersurfaces for relative homotopy class of boundaries, and a topological argument to reduce min-max construction for free homotopy class of mod-2 cycles to that for relative homotopy class of boundaries.<o:p></o:p></p></div></body></html>