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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>Mathematics Seminars<o:p></o:p></p><p class=MsoNormal>Week of January 21, 2019<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><b>Please note the following updates:<o:p></o:p></b></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-family:Symbol'><span style='mso-list:Ignore'>ž<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]>Wednesday, January 23<o:p></o:p></p><p class=MsoListParagraph style='margin-left:1.0in;text-indent:-.25in;mso-list:l0 level2 lfo1'><![if !supportLists]><span style='font-family:"Courier New"'><span style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]>Title and abstract added to Math Conversations<o:p></o:p></p><p class=MsoListParagraph style='margin-left:1.0in;text-indent:-.25in;mso-list:l0 level2 lfo1'><![if !supportLists]><span style='font-family:"Courier New"'><span style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]>Speaker added to Working Group on Geometric Applications of the Langlands Correspondence<o:p></o:p></p><p class=MsoListParagraph><o:p> </o:p></p><p class=MsoNormal>--------------<o:p></o:p></p><p class=MsoNormal><b><o:p> </o:p></b></p><p class=MsoNormal><b>Monday, January 21<o:p></o:p></b></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Computer Science/Discrete Mathematics Seminar I<o:p></o:p></p><p class=MsoNormal>Speaker: šššššššššššš no seminar<o:p></o:p></p><p class=MsoNormal>Time/Room: ššššš 11:00am - 12:00pm/no seminar - Dr. Martin Luther King Day<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Members' Seminar<o:p></o:p></p><p class=MsoNormal>Speaker: šššššššššššš no seminar<o:p></o:p></p><p class=MsoNormal>Time/Room: ššššš 2:00pm - 3:00pm/no seminar - Dr. Martin Luther King Day<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><b>Tuesday, January 22<o:p></o:p></b></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Computer Science/Discrete Mathematics Seminar II<o:p></o:p></p><p class=MsoNormal>Topic: šššššššššššššššššš New Results on Projections<o:p></o:p></p><p class=MsoNormal>Speaker: šššššššššššš Guy Moshkovitz, Member, School of Mathematics<o:p></o:p></p><p class=MsoNormal>Time/Room: ššššš 10:30am - 12:30pm/Simonyi Hall 101<o:p></o:p></p><p class=MsoNormal><span lang=FR>Abstract Link:šššš </span><a href="http://www.math.ias.edu/seminars/abstract?event=129124"><span lang=FR>http://www.math.ias.edu/seminars/abstract?event=129124</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>Variational Methods in Geometry Seminar<o:p></o:p></p><p class=MsoNormal>Topic: šššššššššššššššššš Symplectic methods for sharp systolic inequalities<o:p></o:p></p><p class=MsoNormal>Speaker: šššššššššššš Umberto Hryniewicz, Universidade Federal do Rio de Janeiro; Member, School of Mathematics<o:p></o:p></p><p class=MsoNormal>Time/Room: ššššš 1:00pm - 3:00pm/Simonyi Hall 101<o:p></o:p></p><p class=MsoNormal><span lang=FR>Abstract Link:šššš </span><a href="http://www.math.ias.edu/seminars/abstract?event=141176"><span lang=FR>http://www.math.ias.edu/seminars/abstract?event=141176</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>Variational Methods in Geometry Seminar<o:p></o:p></p><p class=MsoNormal>Topic: šššššššššššššššššš (Non)uniqueness questions in mean curvature flow<o:p></o:p></p><p class=MsoNormal>Speaker: šššššššššššš Lu Wang, University of Wisconsin–Madison; Member, School of Mathematics<o:p></o:p></p><p class=MsoNormal>Time/Room: ššššš 3:30pm - 5:30pm/Simonyi Hall 101<o:p></o:p></p><p class=MsoNormal><span lang=FR>Abstract Link:šššš </span><a href="http://www.math.ias.edu/seminars/abstract?event=141179"><span lang=FR>http://www.math.ias.edu/seminars/abstract?event=141179</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>Joint IAS/Princeton University Number Theory Seminar<o:p></o:p></p><p class=MsoNormal>Topic: šššššššššššššššššš The Eigencurve at Eisenstein weight one points<o:p></o:p></p><p class=MsoNormal>Speaker: šššššššššššš Alice Pozzi, University College London<o:p></o:p></p><p class=MsoNormal>Time/Room: ššššš 4:30pm - 5:30pm/West Building Lecture Hall<o:p></o:p></p><p class=MsoNormal><span lang=FR>Abstract Link:šššš </span><a href="http://www.math.ias.edu/seminars/abstract?event=142554"><span lang=FR>http://www.math.ias.edu/seminars/abstract?event=142554</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><span lang=FR><o:p> </o:p></span></p><p class=MsoNormal><span lang=FR><o:p> </o:p></span></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>BYOP@Lunch Working Group<o:p></o:p></p><p class=MsoNormal>Time/Room: ššššš 12:30pm - 1:30pm/Dilworth Room<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Working Group on Geometric Applications of the Langlands Correspondence<o:p></o:p></p><p class=MsoNormal>Speaker: šššššššššššš Raju Krishnamoorthy, University of Georgia<o:p></o:p></p><p class=MsoNormal>Time/Room: ššššš 3:30pm - 5:30pm/Simonyi Hall 101<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Mathematical Conversations<o:p></o:p></p><p class=MsoNormal>Topic: šššššššššššššššššš Bourgain and the sum-product phenomena<o:p></o:p></p><p class=MsoNormal>Speaker: šššššššššššš Avi Wigderson, Herbert H. Maass Professor, School of Mathematics<o:p></o:p></p><p class=MsoNormal>Time/Room: ššššš 6:00pm - 7:30pm/Dilworth Room<o:p></o:p></p><p class=MsoNormal><span lang=FR>Abstract Link:šššš </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><span lang=FR><o:p> </o:p></span></p><p class=MsoNormal><span lang=FR><o:p> </o:p></span></p><p class=MsoNormal><b>Thursday, January 24<o:p></o:p></b></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Venkatesh Working Group<o:p></o:p></p><p class=MsoNormal>Time/Room: ššššš 10:00am - 12:00pm/Simonyi Hall 101<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Analysis Seminar<o:p></o:p></p><p class=MsoNormal>Topic: šššššššššššššššššš Multiplicity of Eigenvalues for the circular clamped plate problem.<o:p></o:p></p><p class=MsoNormal>Speaker: šššššššššššš Dan Mangoubi, The Hebrew University of Jerusalem<o:p></o:p></p><p class=MsoNormal>Time/Room: ššššš 1:00pm - 2:00pm/Simonyi Hall 101<o:p></o:p></p><p class=MsoNormal><span lang=FR>Abstract Link:šššš </span><a href="http://www.math.ias.edu/seminars/abstract?event=140151"><span lang=FR>http://www.math.ias.edu/seminars/abstract?event=140151</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>1 New Results on Projections <br> Guy Moshkovitz <br><br><br><o:p></o:p></p><p class=MsoNormal>What is the largest number of projections onto k coordinates guaranteed in every family of m binary vectors of length n? This fundamental question is intimately connected to important topics and results in combinatorics and computer science (Turan number, Sauer-Shelah Lemma, Kahn-Kalai-Linial Theorem, and more), and is wide open for most settings of the parameters. We essentially settle the question for linear k and sub-exponential m. <br><br>Based on joint work with Noga Alon and Noam Solomon.<o:p></o:p></p><p class=MsoNormal><a href="http://www.math.ias.edu/seminars/abstract?event=129124">http://www.math.ias.edu/seminars/abstract?event=129124</a><br><br>2 Symplectic methods for sharp systolic inequalities <br> Umberto Hryniewicz <br><br><br><o:p></o:p></p><p class=MsoNormal>In this talk I would like to explain how methods from symplectic geometry can be used to obtain sharp systolic inequalities. I will focus on two applications. The first is the proof of a conjecture due to Babenko-Balacheff on the local systolic maximality of the round 2-sphere. The second is the proof of a perturbative version of Viterbo's conjecture on the systolic ratio of convex energy levels. If time permits I will also explain how to show that general systolic inequalities do not exist in contact geometry. Joint work with Abbondandolo, Bramham and Salomao.<o:p></o:p></p><p class=MsoNormal><a href="http://www.math.ias.edu/seminars/abstract?event=141176">http://www.math.ias.edu/seminars/abstract?event=141176</a><br><br>3 (Non)uniqueness questions in mean curvature flow <br> Lu Wang <br><br><br><o:p></o:p></p><p class=MsoNormal>Mean curvature flow is the negative gradient flow of the volume functional which decreases the volume of (hyper)surfaces in the steepest way. Starting from any closed surface, the flow exists uniquely for a short period of time, but always develops singularities in finite time. In this talk, we discuss some non-uniqueness problems of the mean curvature flow passing through singularities. The talk is mainly prepared for non-specialists of geometric flows.<o:p></o:p></p><p class=MsoNormal><a href="http://www.math.ias.edu/seminars/abstract?event=141179">http://www.math.ias.edu/seminars/abstract?event=141179</a><br><br>4 The Eigencurve at Eisenstein weight one points <br> Alice Pozzi <br><br><br><o:p></o:p></p><p class=MsoNormal>In 1973, Serre observed that the Hecke eigenvalues of Eisenstein series can be p-adically interpolated. In other words, Eisenstein series can be viewed as specializations of a p-adic family parametrized by the weight. The notion of p-adic variations of modular forms was later generalized by Hida to include families of ordinary cuspforms. In 1998, Coleman and Mazur defined the eigencurve, a rigid analytic space classifying much more general p-adic families of Hecke eigenforms parametrized by the weight. The local nature of the eigencurve is well-understood at points corresponding to cuspforms of weight k ≥ 2, while the weight one case is far more intricate. <br><br>In this talk, we discuss the geometry of the eigencurve at weight one Eisenstein points. In particular, we focus on the unusual phenomenon in which cuspidal Hida families specialize to Eisenstein series at weight one. Our approach consists in studying the deformation rings of certain (deceptively simple!) Artin representations. We discuss how this Galois-theoretic method yields some new insight on Gross’s formula relating the leading term of the p-adic L-function to p-adic logarithms of units of certain number fields.<o:p></o:p></p><p class=MsoNormal><a href="http://www.math.ias.edu/seminars/abstract?event=142554">http://www.math.ias.edu/seminars/abstract?event=142554</a><br><br>5 Bourgain and the sum-product phenomena <br> Avi Wigderson <br><br><br><o:p></o:p></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><a href="http://www.math.ias.edu/seminars/abstract?event=136627">http://www.math.ias.edu/seminars/abstract?event=136627</a><br><br>6 Multiplicity of Eigenvalues for the circular clamped plate problem. <br> Dan Mangoubi <br><br><br><o:p></o:p></p><p class=MsoNormal>A celebrated theorem of C.L. Siegel from 1929 shows that the multiplicity of eigenvalues for the Laplace eigenfunctions on the unit disk is at most two. More precisely, Siegel shows that positive zeros of Bessel functions are transcendental. <br><br>We study the fourth order clamped plate problem, showing that the multiplicity of eigenvalues is uniformly bounded (by not more than six). Our method is based on Siegel-Shidlovskii theory and new recursion formulas. <br><br>The talk is based on a joint work with Yuri Lvovski.<o:p></o:p></p><p class=MsoNormal><a href="http://www.math.ias.edu/seminars/abstract?event=140151">http://www.math.ias.edu/seminars/abstract?event=140151</a><br><br>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></p></div></body></html>