[iasmath-seminars] Mathematics Seminars-Week of March 25, 2019
Kristina Phillips
kphillips at ias.edu
Fri Mar 22 17:32:33 EDT 2019
INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540
Mathematics Seminars
Week of March 25, 2019
--------------
Please note:
. There will be no Seminar on Theoretical Machine Learning on
Monday, March 25.
. Emerging Topic Working Group sessions will be held in the West
Building Lecture Hall on Tuesday (March 26) and Wednesday (March 27).
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Monday, March 25
Computer Science/Discrete Mathematics Seminar I
Topic: On the Approximation Resistance of Balanced Linear
Threshold Functions
Speaker: Aaron Potechin, University of Chicago
Time/Room: 11:00am - 12:00pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=128915>
http://www.math.ias.edu/seminars/abstract?event=128915
Seminar on Theoretical Machine Learning
Speaker: No Seminar
Time/Room: 12:15pm - 1:45pm/No Seminar
Members' Seminar
Topic: To Be Announced
Speaker: Amie Wilkinson, University of Chicago
Time/Room: 2:00pm - 3:00pm/Simonyi Hall 101
Symplectic Dynamics/Geometry Seminar
Topic: To be announced
Speaker: To be announced
Time/Room: 3:30pm - 5:00pm/Simonyi Hall 101
Joint IAS/Princeton University Algebraic Geometry Seminar
Topic: Singular Hodge theory of matroids
Speaker: Jacob Matherne, Member, School of Mathematics
Time/Room: 5:00pm - 6:00pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142001>
http://www.math.ias.edu/seminars/abstract?event=142001
Tuesday, March 26
Computer Science/Discrete Mathematics Seminar II
Topic: Factors of sparse polynomials: structural results
and some algorithms
Speaker: Shubhangi Saraf, Member, School of Mathematics
Time/Room: 10:30am - 12:30pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=129151>
http://www.math.ias.edu/seminars/abstract?event=129151
Emerging Topics working group
Topic: Coherence, planar boundaries, and the geometry of
subgroups
Speaker: Genevieve Walsh, Tufts University
Time/Room: 11:00am - 12:00pm/West Building Lecture Hall
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142986>
http://www.math.ias.edu/seminars/abstract?event=142986
Variational Methods in Geometry Seminar
Topic: $\alpha-harmonic$ maps between spheres
Speaker: Tobias Lamm, Karlsruhe Institute of Technology
Time/Room: 1:00pm - 3:00pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=141233>
http://www.math.ias.edu/seminars/abstract?event=141233
Variational Methods in Geometry Seminar
Topic: A mountain pass theorem for minimal hypersurfaces
with fixed boundary
Speaker: Rafael Montezuma, Princeton University
Time/Room: 3:30pm - 5:30pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=141230>
http://www.math.ias.edu/seminars/abstract?event=141230
Emerging Topics working group
Topic: One-relator groups, non-positive immersions and
coherence
Speaker: Henry Wilton, Cambridge University
Time/Room: 4:00pm - 5:00pm/West Building Lecture Hall
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142989>
http://www.math.ias.edu/seminars/abstract?event=142989
Wednesday, March 27
BYOP at Lunch Working Group
Time/Room: 12:30pm - 1:30pm/Dilworth Room
Working Group on Geometric Applications of the Langlands Correspondence
Speaker: Kiran Kedlaya, University of California, San Diego
Time/Room: 3:30pm - 5:30pm/Simonyi Hall Classroom 114
Emerging Topics working group
Topic: Coherence and lattices
Speaker: Matthew Stover, Temple University
Time/Room: 4:00pm - 5:00pm/West Building Lecture Hall
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142992>
http://www.math.ias.edu/seminars/abstract?event=142992
Mathematical Conversations
Topic: The general case?
Speaker: Amie Wilkinson, University of Chicago
Time/Room: 6:00pm - 7:30pm/Dilworth Room
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=136654>
http://www.math.ias.edu/seminars/abstract?event=136654
Thursday, March 28
Venkatesh Working Group
Time/Room: 10:00am - 12:00pm/Simonyi Hall 101
Analysis Seminar
Speaker: No Seminar
Time/Room: 1:00pm - 2:00pm/No Seminar
Working Seminar in Algebraic Number Theory
Topic: Hida theory and Ohta's canonical comparison map
Speaker: Giada Grossi, University College London
Time/Room: 2:15pm - 4:15pm/Princeton University, Fine 1201
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=140061>
http://www.math.ias.edu/seminars/abstract?event=140061
Joint IAS/Princeton University Number Theory Seminar
Topic: Stronger Arithmetic Equivalence
Speaker: Andrew Sutherland, MIT
Time/Room: 4:30pm - 5:30pm/Princeton University, Fine Hall 214
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=139918>
http://www.math.ias.edu/seminars/abstract?event=139918
1 On the Approximation Resistance of Balanced Linear Threshold Functions
Aaron Potechin
Constraint satisfaction problems (CSPs) are a central topic of study in
computer science. A fundamental question about CSPs is as follows. Given a
CSP where each constraint has the form of some predicate P and almost all of
the constraints can be satisfied, is there a randomized polynomial time
algorithm which is guaranteed to do significantly better in expectation than
a random assignment? If so, then we say that the predicate P is
approximable. If not, then we say that P is approximation resistant.
In 2008, Raghavendra proved a dichotomy theorem for the hardness of CSPs.
Either a standard semidefinite program (SDP) gives a better approximation
ratio than a random assignment or it is unique games hard to do so. However,
for any given CSP it may be extremely hard to decide which case holds. In
fact, it is not even known whether it is decidable!
The main result of this work is that there exists a balanced linear
threshold function (LTF) which is unique games hard to approximate, refuting
a conjecture of Austrin, Benabbas, and Magen. This work also shows that the
almost monarchy predicate on k variables is approximable for sufficiently
large k.
In this talk, I will describe Raghavendra's dichotomy theorem and illustrate
it with two important examples, 3-SAT and the majority predicate. I will
then describe how to construct a predicate which is a balanced LTF and is
unique games hard to approximate.
http://www.math.ias.edu/seminars/abstract?event=128915
2 Singular Hodge theory of matroids
Jacob Matherne
Kazhdan-Lusztig (KL) polynomials for Coxeter groups were introduced in the
1970s, providing deep relationships among representation theory, geometry,
and combinatorics. In 2016, Elias, Proudfoot, and Wakefield defined
analogous polynomials in the setting of matroids. In this talk, I will
compare and contrast KL theory for Coxeter groups with KL theory for
matroids. I will also associate to any matroid a certain ring whose Hodge
theory can conjecturally be used to establish the positivity of the KL
polynomials of matroids as well as the "top-heavy conjecture" of Dowling and
Wilson from 1974 (a statement on the shape of the poset which plays an
analogous role to the Bruhat poset). Examples involving the geometry of
hyperplane arrangements will be given throughout. This is joint work with
Tom Braden, June Huh, Nick Proudfoot, and Botong Wang.
http://www.math.ias.edu/seminars/abstract?event=142001
3 Factors of sparse polynomials: structural results and some algorithms
Shubhangi Saraf
Are factors of sparse polynomials sparse? This is a really basic question
and we are still quite far from understanding it in general.
In this talk, I will discuss a recent result showing that this is in some
sense true for multivariate polynomials when the polynomial has each
variable appearing only with bounded degree. Our sparsity bound uses
techniques from convex geometry, such as the theory of Newton polytopes and
an approximate version of the classical Caratheodory's Theorem. Using our
sparsity bound, we then show how to devise efficient deterministic factoring
algorithms for sparse polynomials of bounded individual degree. Along the
way we will see many of the ideas used in the classical randomized blackbox
factoring algorithm of Kaltofen and Trager, which we will show to
derandomize in our setting.
The talk is based on joint work with Vishwas Bhargav and Ilya Volkovich.
http://www.math.ias.edu/seminars/abstract?event=129151
4 Coherence, planar boundaries, and the geometry of subgroups
Genevieve Walsh
Abstract: This will be a broad talk about coherence of groups, and how it
relates to conjectures about hyperbolic groups with planar boundaries. A
group is coherent if every finitely generated subgroup is finitely
presented. This is a property enjoyed by the fundamental groups of
3-manifolds. A natural stepping stone to proving that certain hyperbolic
groups are 3-manifold groups is to prove that they are coherent. A stronger
property that some hyperbolic groups possess is "local quasi-convexity", in
that every finitely generated subgroup is quasi-convex. It is conjectured
that a hyperbolic group whose Gromov boundary is a Sierpinski carpet is
locally quasi-convex. I'll also discuss several examples of coherent and
incoherent groups that have 3-manifold like properties.
http://www.math.ias.edu/seminars/abstract?event=142986
5 $\alpha-harmonic$ maps between spheres
Tobias Lamm
In a famous paper, Sacks and Uhlenbeck introduced a perturbation of the
Dirichlet energy, the so-called $\alpha$-energy $E_\alpha$, $\alpha > 1$, to
construct non-trivial harmonic maps of the two-sphere in manifolds with a
non-contractible universal cover. The Dirichlet energy corresponds to
$\alpha = 1$ and, as $\alpha$ decreases to 1, critical points of $E_\alpha$
are known to converge to harmonic maps in a suitable sense.
However, in a joint work with Andrea Malchiodi and Mario Micallef, we show
that not every harmonic map can be approximated by critical points of such
perturbed energies. Indeed, we prove that constant maps and the rotations of
$S^2$ are the only critical points of $E_\alpha$ for maps from $S^2$ to
$S^2$ whose $\alpha$-energy lies below some threshold, which is independent
of $\alpha$ (sufficiently close to 1). In particular, nontrivial dilations
(which are harmonic) cannot arise as strong limits of $\alpha$-harmonic
maps. We also show the optimality of our threshold assumption.
http://www.math.ias.edu/seminars/abstract?event=141233
6 A mountain pass theorem for minimal hypersurfaces with fixed boundary
Rafael Montezuma
In this talk, we will be concerned with the existence of a third embedded
minimal hypersurface spanning a closed submanifold B contained in the
boundary of a compact Riemannian manifold with convex boundary, when it is
known a priori the existence of two strictly stable minimal hypersurfaces
that bound B. For this purpose, we will study min-max methods similar to
those of the work of De Lellis and Ramic, adapted to the discrete setting of
Almgren and Pitts. It is expected that these methods can be applied in the
construction of unbounded minimal surfaces in certain asymptotically flat
3-manifolds. We give some evidence that this can actually be done by
analyzing related aspects in the case of the exact Riemannian Schwarzschild
metric.
http://www.math.ias.edu/seminars/abstract?event=141230
7 One-relator groups, non-positive immersions and coherence
Henry Wilton
Abstract: There seems to be an analogy between the classes of fundamental
groups of compact 3-manifolds and of one-relator groups. (Indeed, many
3-manifold groups are also one-relator groups.) For instance, Dehn's Lemma
for 3-manifolds (proved by Papakyriakopoulos) can be seen as analogous to
Magnus' Freiheitssatz for one-relator groups. But the analogy is still very
incomplete, and since there are deep results on each side that have no
analogue on the other, there is a strong incentive to flesh it out.
Coherence is one property for which the analogy remains unknown. A group is
*coherent* if every finitely generated subgroup is finitely presented. A
famous theorem of Scott asserts that 3-manifold groups are coherent;
Baumslag asked in 1974 if one-relator groups are coherent, and the question
remains open.
In this talk, I'll describe some recent progress towards Baumslag's problem,
which centres around Wise's notion of *non-positive immersions*. We will
see that one-relator groups are homologically coherent, that one-relator
groups with torsion are coherent, and that low-rank subgroups of one-relator
groups are always free.
http://www.math.ias.edu/seminars/abstract?event=142989
8 Coherence and lattices
Matthew Stover
Abstract: I will survey (in)coherence of lattices in semisimple Lie groups,
with a view toward open problems and connections with the geometry of
locally symmetric spaces. Particular focus will be placed on rank one
lattices, where I will discuss connections with reflection groups,
"algebraic" fibrations of lattices, and analogies with classical
low-dimensional topology.
http://www.math.ias.edu/seminars/abstract?event=142992
9 The general case?
Amie Wilkinson
In the early 1930's, the Ergodic theorems of von Neumann and Birkhoff put
Boltzmann's Ergodic Hypothesis in mathematical terms, and the natural
question was born: is ergodicity the "general case" among conservative
dynamical systems? Oxtoby and Ulam tackled this question early on and showed
that the answer to this question is "yes" for continuous dynamical systems.
The work of Kolmogorov Arnol'd and Moser beginning in the 1950's showed that
the answer to this question is "no" for C^infty dynamical systems. I will
discuss recent work with Artur Avila and Sylvain Crovisier that addresses
what happens for C^1 dynamical systems.
http://www.math.ias.edu/seminars/abstract?event=136654
10 Hida theory and Ohta's canonical comparison map
Giada Grossi
>From Romyar's AWS notes:
* Sections 4.1 and 4.2.
Regarding the proof of Ohta's comparison isomorphism:
* Discuss Fukaya-Kato Section 1.7, which explains some p-adic Hodge
theory background.
* Discuss some elements of Ohta's proof, from Sections 3.3-3.4 of "On
p-adic Eichler-Shimura".
http://www.math.ias.edu/seminars/abstract?event=140061
11 Stronger Arithmetic Equivalence
Andrew Sutherland
Number fields with the same Dedekind zeta function are said to be
arithmetically equivalent. Such number fields necessarily have the same
degree, discriminant, signature, Galois closure, and isomorphic unit groups,
but may have different regulators, class groups, rings of adeles, and idele
class groups. Motivated by a recent result of Prasad, I will discuss three
stronger notions of arithmetic equivalence that force isomorphisms of some
or all of these invariants without forcing an isomorphism of number fields,
along with explicit examples and some open questions. These results also
have applications to the construction of curves with isomorphic Jacobians
(due to Prasad), isospectral Riemannian manifolds (due to Sunada), and
isospectral graphs (due to Halbeisen and Hungerbuhler).
http://www.math.ias.edu/seminars/abstract?event=139918
IAS Math Seminars Home Page:
http://www.math.ias.edu/seminars
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