[iasmath-semru] [math-ias] Mathematics Seminars_Week of April 16, 2018

Fri Apr 13 16:50:58 EDT 2018

INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540

Mathematics Seminars
Week of April 16, 2018

Request:
Please help us preserve our White Levy Room privileges by maintaining the
Idea Board (DaLite markers only; clean when finished).

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To view mathematics in titles and abstracts, please click on the talk's
link.
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Monday, April 16

Computer Science/Discrete Mathematics Seminar I
Topic:                    Sums of Squares Over k-Subset Hypercubes
Speaker:                 Annie Raymond, University of Massachusetts, Amherst
Time/Room:          11:00am - 12:15pm/Simonyi Hall 101
Abstract Link:        http://www.math.ias.edu/seminars/abstract?event=128840

Princeton/IAS Symplectic Geometry Seminar
Topic:                    The wrapped Fukaya category of a Weinstein
manifold is generated by the Lagrangian cocore discs
Speaker:                 Georgios Dimitroglou Rizell, Uppsala University
Time/Room:          4:00pm - 5:00pm/Fine Hall 322, Princeton University
Abstract Link:        http://www.math.ias.edu/seminars/abstract?event=135645

Tuesday, April 17

Computer Science/Discrete Mathematics Seminar II
Topic:                    A simple proof of a reverse Minkowski inequality
Speaker:                 Noah Stephens-Davidowitz, Visitor, School of
Mathematics
Time/Room:          10:30am - 12:30pm/Simonyi Hall 101
Abstract Link:        http://www.math.ias.edu/seminars/abstract?event=136796

Joint IAS/Princeton University Number Theory Seminar
Topic:                    A New Northcott Property for Faltings Height
Speaker:                 Lucia Mocz, Princeton University
Time/Room:          4:45pm - 5:45pm/Simonyi Hall 101
Abstract Link:        http://www.math.ias.edu/seminars/abstract?event=136736

Thursday, April 19

Seminar on Theoretical Machine Learning
Topic:                    To be announced
Speaker:                 Zhiyuan Li, Princeton University
Time/Room:          12:15pm - 1:45pm/White-Levy Room

Working Group on Algebraic Number Theory
Speaker:                 To Be Announced
Time/Room:          2:00pm - 4:00pm/1201 Fine Hall, Princeton University

Joint IAS/Princeton University Number Theory Seminar
Topic:                    To Be Announced
Speaker:                 Rong Zhou, Member, School of Mathematics
Time/Room:          4:30pm - 5:30pm/Fine Hall 214, Princeton University

1 Sums of Squares Over k-Subset Hypercubes 
   Annie Raymond 

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.

http://www.math.ias.edu/seminars/abstract?event=128840

2 The wrapped Fukaya category of a Weinstein manifold is generated by the
Lagrangian cocore discs 
   Georgios Dimitroglou Rizell 

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.

http://www.math.ias.edu/seminars/abstract?event=135645

3 A simple proof of a reverse Minkowski inequality 
   Noah Stephens-Davidowitz 

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.

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.

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.

http://www.math.ias.edu/seminars/abstract?event=136796

4 A New Northcott Property for Faltings Height 
   Lucia Mocz 

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.

http://www.math.ias.edu/seminars/abstract?event=136736

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

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