<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>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, January 23<o:p></o:p></b></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><b>About Mathematical Conversations: </b>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><b><u>*Please note that Harry's Bar is closed tonight, but drinks will be available in the Dilworth Room.<o:p></o:p></u></b></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: Bourgain and the sum-product phenomena<o:p></o:p></p><p class=MsoNormal>Speaker: Avi Wigderson, Herbert H. Maass Professor, 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=136627"><span lang=FR>http://www.math.ias.edu/seminars/abstract?event=136627</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>In 2004 Jean Bourgain proved, with Netz Katz and Terry Tao, the "sum-product theorem in finite fields". He referred to this result (and proof technique) as a "goose which lays golden eggs". Indeed, in subsequent years, he has published a couple of dozen papers on consequences and applications to numerous areas: Analysis, Number Theory, Group Theory, Dynamical Systems, Combinatorial Geometry, Graph expansion, Randomness extractors and more. His works were naturally followed by many others, creating what Jean liked calling "the sum-product phenomena", and making clear how fundamental this initial work was. <br><br>I will only have time to explain what is a "sum-product theorem", talk about the history of the problem, perhaps give a couple of applications. These may change your view on the interaction of the two operations we all learn in grade school and take for granted since: addition and multiplication.<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><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><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>