<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=iso-8859-1"><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>INSTITUTE FOR ADVANCED STUDY<o:p></o:p></p><p class=MsoNormal>School of Mathematics<o:p></o:p></p><p class=MsoNormal>Princeton, NJ 08540<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><b>Mathematical Conversations<o:p></o:p></b></p><p class=MsoNormal><b>Wednesday, March 6<o:p></o:p></b></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><u>About Mathematical Conversations</u>: We meet in Harry's Bar at 6pm, where free drinks are provided. After 20 minutes, we move to the Dilworth room, where the speaker gives a 20-minute talk, followed by 15 minutes of discussion with the audience. After that we return to the bar for further discussions. Website: <a href="https://www.math.ias.edu/math-conversations">https://www.math.ias.edu/math-conversations</a><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>To view mathematics in titles and abstracts, please click on the talk's link.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Topic: From Celestial Mechanics to the Arnold Conjectures<o:p></o:p></p><p class=MsoNormal>Speaker: Umberto Hryniewicz, Universidade Federal do Rio de Janeiro; von Neumann Fellow, School of Mathematics<o:p></o:p></p><p class=MsoNormal>Time/Room: 6:00pm - 7:30pm/Dilworth Room<o:p></o:p></p><p class=MsoNormal><span lang=FR>Abstract Link: </span><a href="http://www.math.ias.edu/seminars/abstract?event=136645"><span lang=FR>http://www.math.ias.edu/seminars/abstract?event=136645</span></a><span lang=FR><o:p></o:p></span></p><p class=MsoNormal><span lang=FR><o:p> </o:p></span></p><p class=MsoNormal>The study of the planar-circular-restricted 3-body problem led to Poincaré's "last geometric theorem", nowadays known as the Poincaré-Birkhoff theorem. It is a fixed point theorem for certain area-preserving annulus homeomorphisms. Birkhoff's proof did not allow for generalizations, and we had to wait until the 1960's when Arnold realized that the Poincaré-Birkhoff theorem (in the smooth case) is a consequence of a certain conjecture on the number of fixed points of Hamiltonian diffeomorphisms. The conjecture was one among others of the same flavor, and they motivated the invention of Floer theory. In this talk I would like to give more details on this remarkable chain of events.<o:p></o:p></p><p class=MsoNormal><a href="http://www.math.ias.edu/seminars">http://www.math.ias.edu/seminars</a><o:p></o:p></p></div></body></html>