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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>INSTITUTE FOR ADVANCED STUDY<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>School of Mathematics<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Princeton, NJ 08540<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><b><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Mathematics Seminars<o:p></o:p></span></b></pre><pre><b><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Week of April 16, 2018<o:p></o:p></span></b></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre style='margin-bottom:6.0pt'><b><u><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Request</span></u></b><b><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>:<o:p></o:p></span></b></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Please help us preserve our White Levy Room privileges by maintaining the Idea Board (DaLite markers only; clean when finished).<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>--------------<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>To view mathematics in titles and abstracts, please click on the talk's link.<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>--------------<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><b><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Monday, April 16<o:p></o:p></span></b></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Computer Science/Discrete Mathematics Seminar I<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Topic: Sums of Squares Over k-Subset Hypercubes<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Speaker: Annie Raymond, University of Massachusetts, Amherst<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Time/Room: 11:00am - 12:15pm/Simonyi Hall 101<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Abstract Link: <a href="http://www.math.ias.edu/seminars/abstract?event=128840">http://www.math.ias.edu/seminars/abstract?event=128840</a><o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Princeton/IAS Symplectic Geometry Seminar<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Topic: The wrapped Fukaya category of a Weinstein manifold is generated by the Lagrangian cocore discs<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Speaker: Georgios Dimitroglou Rizell, Uppsala University<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Time/Room: 4:00pm - 5:00pm/Fine Hall 322, Princeton University<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Abstract Link: <a href="http://www.math.ias.edu/seminars/abstract?event=135645">http://www.math.ias.edu/seminars/abstract?event=135645</a><o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><b><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Tuesday, April 17<o:p></o:p></span></b></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Computer Science/Discrete Mathematics Seminar II<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Topic: A simple proof of a reverse Minkowski inequality<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Speaker: Noah Stephens-Davidowitz, Visitor, School of Mathematics<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Time/Room: 10:30am - 12:30pm/Simonyi Hall 101<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Abstract Link: <a href="http://www.math.ias.edu/seminars/abstract?event=136796">http://www.math.ias.edu/seminars/abstract?event=136796</a><o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Joint IAS/Princeton University Number Theory Seminar<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Topic: A New Northcott Property for Faltings Height<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Speaker: Lucia Mocz, Princeton University<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Time/Room: 4:45pm - 5:45pm/Simonyi Hall 101<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Abstract Link: <a href="http://www.math.ias.edu/seminars/abstract?event=136736">http://www.math.ias.edu/seminars/abstract?event=136736</a><o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><b><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Thursday, April 19<o:p></o:p></span></b></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Seminar on Theoretical Machine Learning<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Topic: To be announced<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Speaker: Zhiyuan Li, Princeton University<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Time/Room: 12:15pm - 1:45pm/White-Levy Room<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Working Group on Algebraic Number Theory<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Speaker: To Be Announced<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Time/Room: 2:00pm - 4:00pm/1201 Fine Hall, Princeton University<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Joint IAS/Princeton University Number Theory Seminar<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Topic: To Be Announced<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>Speaker: Rong Zhou, Member, School of Mathematics<o:p></o:p></span></pre><pre><span style='font-size:12.0pt;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:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></pre><p class=MsoNormal style='margin-bottom:12.0pt'><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:12.0pt'><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:12.0pt'><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>1 Sums of Squares Over k-Subset Hypercubes <br> Annie Raymond <o:p></o:p></span></p><p>Polynomial optimization over hypercubes has important applications in combinatorial optimization. We develop a symmetry-reduction method that finds sums of squares certificates for non-negative symmetric polynomials over k-subset hypercubes that improves on a technique due to Gatermann and Parrilo. For every symmetric polynomial that has a sos expression of a fixed degree, our method finds a succinct sos expression whose size depends only on the degree and not on the number of variables. Our results relate naturally to Razborov's flag algebra calculus for solving problems in extremal combinatorics. This leads to new results involving flags and their power in finding sos certificates. This is joint work with James Saunderson, Mohit Singh and Rekha Thomas.<o:p></o:p></p><p class=MsoNormal style='margin-bottom:12.0pt'><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><a href="http://www.math.ias.edu/seminars/abstract?event=128840">http://www.math.ias.edu/seminars/abstract?event=128840</a><br><br><br><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:12.0pt'><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>2 The wrapped Fukaya category of a Weinstein manifold is generated by the Lagrangian cocore discs <br> Georgios Dimitroglou Rizell <o:p></o:p></span></p><p>In a joint work with B. Chantraine, P. Ghiggini, and R. Golovko we decompose any object in the wrapped Fukaya category as a twisted complex built from the cocores of the critical (i.e. half-dimensional) handles in a Weinstein handle decomposition. The main tools used are the Floer homology theories of exact Lagrangian immersions, of exact Lagrangian cobordisms in the SFT sense (i.e. between Legendrians), as well as relations between these theories. Note that exact Lagrangians admit Legendrian lifts, and that appropriate Lagrange surgeries can be seen to give rise to an exact Lagrangian cobordism of the aforementioned type.<o:p></o:p></p><p class=MsoNormal style='margin-bottom:12.0pt'><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><a href="http://www.math.ias.edu/seminars/abstract?event=135645">http://www.math.ias.edu/seminars/abstract?event=135645</a><br><br><br><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:12.0pt'><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>3 A simple proof of a reverse Minkowski inequality <br> Noah Stephens-Davidowitz <o:p></o:p></span></p><p>We consider the following question: how many points with bounded norm can a "non-degenerate" lattice have. Here, by a "non-degenerate" lattice, we mean an n-dimensional lattice with no surprisingly dense lower-dimensional sublattices.<br> <br>Dadush and Regev conjectured an upper bound on this quantity (which they called a "reverse Minkowski-type inequality") and showed a number of applications---from cryptography to Brownian motion on flat tori. In joint work with Regev in 2016, we proved this conjecture via a rather tedious proof using two heavy hammers from convex geometry.<br> <br>Recently, Eldan showed how to remove the tedium from the proof, and even more recently, Dadush showed how to remove the heavy hammers (to prove a slightly different result). The resulting (still unpublished) streamlined proof is quite nice, and we present it more-or-less in full.<o:p></o:p></p><p class=MsoNormal style='margin-bottom:12.0pt'><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><a href="http://www.math.ias.edu/seminars/abstract?event=136796">http://www.math.ias.edu/seminars/abstract?event=136796</a><br><br><br><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:12.0pt'><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>4 A New Northcott Property for Faltings Height <br> Lucia Mocz <o:p></o:p></span></p><p>The Faltings height is a useful invariant for addressing questions in arithmetic geometry. In his celebrated proof of the Mordell and Shafarevich conjectures, Faltings shows the Faltings height satisfies a certain Northcott property, which allows him to deduce his finiteness statements. In this work we prove a new Northcott property for the Faltings height. Namely we show, assuming the Colmez Conjecture and the Artin Conjecture, that there are finitely many CM abelian varieties of a fixed dimension which have bounded Faltings height. The technique developed uses new tools from integral p-adic Hodge theory to study the variation of Faltings height within an isogeny class of CM abelian varieties. In special cases, we are able to use these techniques to moreover develop new Colmez-type formulas for the Faltings height.<o:p></o:p></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><a href="http://www.math.ias.edu/seminars/abstract?event=136736">http://www.math.ias.edu/seminars/abstract?event=136736</a><br><br><br><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>-------------------------------------------<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman",serif'>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></span></p></div></body></html>