[Csdmsemo] Updates to Mathematics Seminars--Week of January 21, 2019

Tue Jan 22 13:47:56 EST 2019

INSTITUTE FOR ADVANCED STUDY

School of Mathematics

Princeton, NJ 08540

Mathematics Seminars

Week of January 21, 2019

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Please note the following updates:

·         Wednesday, January 23

o   Title and abstract added to Math Conversations

o   Speaker added to Working Group on Geometric Applications of the
Langlands Correspondence

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Monday, January 21

Computer Science/Discrete Mathematics Seminar I

Speaker:              no seminar

Time/Room:       11:00am - 12:00pm/no seminar - Dr. Martin Luther King Day

Members' Seminar

Speaker:              no seminar

Time/Room:       2:00pm - 3:00pm/no seminar - Dr. Martin Luther King Day

Tuesday, January 22

Computer Science/Discrete Mathematics Seminar II

Topic:                    New Results on Projections

Speaker:              Guy Moshkovitz, Member, School of Mathematics

Time/Room:       10:30am - 12:30pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=129124>
http://www.math.ias.edu/seminars/abstract?event=129124

Variational Methods in Geometry Seminar

Topic:                    Symplectic methods for sharp systolic inequalities

Speaker:              Umberto Hryniewicz, Universidade Federal do Rio de
Janeiro; Member, School of Mathematics

Time/Room:       1:00pm - 3:00pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=141176>
http://www.math.ias.edu/seminars/abstract?event=141176

Variational Methods in Geometry Seminar

Topic:                    (Non)uniqueness questions in mean curvature flow

Speaker:              Lu Wang, University of Wisconsin-Madison; Member,
School of Mathematics

Time/Room:       3:30pm - 5:30pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=141179>
http://www.math.ias.edu/seminars/abstract?event=141179

Joint IAS/Princeton University Number Theory Seminar

Topic:                    The Eigencurve at Eisenstein weight one points

Speaker:              Alice Pozzi, University College London

Time/Room:       4:30pm - 5:30pm/West Building Lecture Hall

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=142554>
http://www.math.ias.edu/seminars/abstract?event=142554

Wednesday, January 23

BYOP at Lunch Working Group

Time/Room:       12:30pm - 1:30pm/Dilworth Room

Working Group on Geometric Applications of the Langlands Correspondence

Speaker:              Raju Krishnamoorthy, University of Georgia

Time/Room:       3:30pm - 5:30pm/Simonyi Hall 101

Mathematical Conversations

Topic:                    Bourgain and the sum-product phenomena

Speaker:              Avi Wigderson, Herbert H. Maass Professor, School of
Mathematics

Time/Room:       6:00pm - 7:30pm/Dilworth Room

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=136627>
http://www.math.ias.edu/seminars/abstract?event=136627

Thursday, January 24

Venkatesh Working Group

Time/Room:       10:00am - 12:00pm/Simonyi Hall 101

Analysis Seminar

Topic:                    Multiplicity of Eigenvalues for the circular
clamped plate problem.

Speaker:              Dan Mangoubi, The Hebrew University of Jerusalem

Time/Room:       1:00pm - 2:00pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=140151>
http://www.math.ias.edu/seminars/abstract?event=140151

1 New Results on Projections 
   Guy Moshkovitz 

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. 

Based on joint work with Noga Alon and Noam Solomon.

http://www.math.ias.edu/seminars/abstract?event=129124

2 Symplectic methods for sharp systolic inequalities 
   Umberto Hryniewicz 

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.

http://www.math.ias.edu/seminars/abstract?event=141176

3 (Non)uniqueness questions in mean curvature flow 
   Lu Wang 

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.

http://www.math.ias.edu/seminars/abstract?event=141179

4 The Eigencurve at Eisenstein weight one points 
   Alice Pozzi 

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. 

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.

http://www.math.ias.edu/seminars/abstract?event=142554

5 Bourgain and the sum-product phenomena 
   Avi Wigderson 

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. 

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.

http://www.math.ias.edu/seminars/abstract?event=136627

6 Multiplicity of Eigenvalues for the circular clamped plate problem. 
   Dan Mangoubi 

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. 

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. 

The talk is based on a joint work with Yuri Lvovski.

http://www.math.ias.edu/seminars/abstract?event=140151

IAS Math Seminars Home Page:
http://www.math.ias.edu/seminars

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