[iasmath-semru] [math-ias] Mathematics Seminars-Week of April 9, 2018
Kristina Phillips
kphillips at ias.edu
Fri Apr 6 17:01:38 EDT 2018
INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540
Mathematics Seminars
Week of April 9, 2018
Please note:
* The Workshop on Topology: Identifying Order in Complex Systems
takes place TOMORROW, April 7, 2018 in Simonyi Hall 101 from 9:00am -
5:30pm.
https://www.ias.edu/event-series/workshop-topology-identifying-order-complex
-systems
* The Emerging Topics Working Group takes place April 9 - April 12
in Simonyi Hall 101.
* The April 9th and 10th CSDM Seminars will be held in the West
Building Lecture Hall.
* There will be no Members' Seminar on Monday, April 9.
* A Diophantine Analysis working group seminar will be held at
Princeton University on Monday, April 9.
* There will be no AM or PM Locally Symmetric Spaces Seminar on
Tuesday, April 10.
* Math Conversations will be held in the White-Levy room on
Wednesday, 4/11.
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To view mathematics in titles and abstracts, please click on the talk's
link.
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Monday, April 9
Emerging Topics Working Group
Topic: Arnold diffusion for `complete' families of
perturbations with two or three independent harmonics
Speaker: Amadeu Delshams, UPC
Time/Room: 11:00am - 12:00pm/Simonyi Hall 101
Abstract Link:
http://www.math.ias.edu/seminars/abstract?event=136179
Computer Science/Discrete Mathematics Seminar I
Topic: Large deviations in random graphs
Speaker: Eyal Lubetzky, New York University
Time/Room: 11:00am - 12:15pm/West Building Lecture Hall
Abstract Link:
http://www.math.ias.edu/seminars/abstract?event=128843
Members' Seminar
No Seminar: workshop
Speaker: No seminar: workshop
Time/Room: -
Emerging Topics Working Group
Topic: Symplectic geometry of hyperbolic cylinders and
their homoclinic intersections
Speaker: Jean-Pierre Marco, Pierre and Marie Curie
University - Paris 6
Time/Room: 2:00pm - 3:00pm/Simonyi Hall 101
Abstract Link:
http://www.math.ias.edu/seminars/abstract?event=135831
Princeton/IAS Symplectic Geometry Seminar
Topic: Fukaya categories of Calabi-Yau hypersurfaces
Speaker: Paul Seidel, Massachusetts Institute of Technology;
Member, School of Mathematics
Time/Room: 4:00pm - 5:00pm/Simonyi Hall 101
Abstract Link:
http://www.math.ias.edu/seminars/abstract?event=134640
Diophantine Analysis working group seminar
Topic: Steenrod operations and Tate's Conjecture on the
Brauer group of a surface
Speaker: Tony Feng
Time/Room: 4:45pm - 6:00pm/Fine Hall 1201, Princeton University
Abstract Link:
http://www.math.ias.edu/seminars/abstract?event=136728
Tuesday, April 10
Locally Symmetric Spaces Seminar
Speaker: No Seminar
Time/Room:
Computer Science/Discrete Mathematics Seminar II
Topic: Explicit Binary Tree Codes with Polylogarithmic
Size Alphabet
Speaker: Gil Cohen, Princeton University
Time/Room: 10:30am - 12:30pm/West Building Lecture Hall
Abstract Link:
http://www.math.ias.edu/seminars/abstract?event=129076
Emerging Topics Working Group
Topic: A General Shadowing result for normally
hyperbolic invariant manifolds and its application to Arnold diffusion
Speaker: Tere Seara, UPC
Time/Room: 11:00am - 12:00pm/Simonyi Hall 101
Abstract Link:
http://www.math.ias.edu/seminars/abstract?event=136182
Locally Symmetric Spaces Seminar
Speaker: No Seminar
Time/Room:
Emerging Topics Working Group
Topic: Some geometric mechanisms for Arnold diffusion
Speaker: Rafael de la Llave, Georgia Tech
Time/Room: 2:00pm - 3:00pm/Simonyi Hall 101
Abstract Link:
http://www.math.ias.edu/seminars/abstract?event=135834
Joint IAS/Princeton University Number Theory Seminar
Topic: Non-spherical Poincaré series, cusp forms and
L-functions for GL(3)
Speaker: Jack Buttcane, University of Buffalo
Time/Room: 4:45pm - 5:45pm/Simonyi Hall 101
Abstract Link:
http://www.math.ias.edu/seminars/abstract?event=135900
Wednesday, April 11
Emerging Topics Working Group
Topic: Diffusion along chains of normally hyperbolic
cylinders
Speaker: Marian Gidea, Yeshiva University
Time/Room: 11:00am - 12:00pm/Simonyi Hall 101
Abstract Link:
http://www.math.ias.edu/seminars/abstract?event=136188
Emerging Topics Working Group
Topic: Arnold diffusion and Mather theory
Speaker: Ke Zhang, University of Toronto
Time/Room: 2:00pm - 3:00pm/Simonyi Hall 101
Abstract Link:
http://www.math.ias.edu/seminars/abstract?event=135837
Mathematical Conversations
Topic: Ordinary points mod p of hyperbolic 3-manifolds
Speaker: Mark Goresky, Visitor, School of Mathematics
Time/Room: 6:00pm - 7:00pm/White Levy Room
Abstract Link:
http://www.math.ias.edu/seminars/abstract?event=136523
Thursday, April 12
Emerging Topics Working Group
Time/Room: 10:00am - 12:00pm/Simonyi Hall 101
Emerging Topics Working Group
Topic: Growth of Sobolev norms for the cubic NLS near 1D
quasi-periodic solutions
Speaker: Marcel Guardia, UPC
Time/Room: 11:00am - 12:00pm/Simonyi Hall 101
Abstract Link:
http://www.math.ias.edu/seminars/abstract?event=136191
Seminar on Theoretical Machine Learning
Topic: To Be Announced
Speaker: To Be Announced
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: Xinwen Zhu, California Institute of Technology
Time/Room: 4:30pm - 5:30pm/Fine Hall 214, Princeton University
1 Arnold diffusion for `complete' families of perturbations with two or
three independent harmonics
Amadeu Delshams
Abstract: We prove that for any non-trivial perturbation depending on any
two independent harmonics of a pendulum and a rotor there is global
instability. The proof is based on the geometrical method and relies on the
concrete computation of several scattering maps. A complete description of
the different kinds of scattering maps taking place as well as the existence
of piecewise smooth global scattering maps is also provided. Similar results
apply for any non-trivial perturbation depending on any three independent
harmonics of a pendulum and two rotors. This is a joint work with Rodrigo G.
Schaefer.
http://www.math.ias.edu/seminars/abstract?event=136179
2 Large deviations in random graphs
Eyal Lubetzky
What is the probability that the number of triangles in the
Erd\H{o}s-R\'enyi random graph with edge density $p$, is at least twice its
mean? What is the typical structure of the graph conditioned on this rare
event? For instance, when $p=o(1)$, already obtaining the order of log of
this probability was a longstanding open problem finally settled by
Chatterjee and by DeMarco and Kahn, whereas the latter problem remains
largely open. I will review some recent progress on these questions and
related ones, in both the dense and sparse regimes of the random graph.
http://www.math.ias.edu/seminars/abstract?event=128843
3 Symplectic geometry of hyperbolic cylinders and their homoclinic
intersections
Jean-Pierre Marco
Abstract: We first examine the existence, uniqueness, regularity, twist and
symplectic properties of compact invariant cylinders with boundary, located
near simple or double resonances in perturbations of action-angle systems on
the annulus $A^3$. We then prove they satisfy sufficient compatibility
conditions on their dynamics and their homoclinic intersections, in order to
prove the existence of drifting orbits along them, shadowing pseudo-orbits
of inner-homoclinic polysystems. This provides us with a good control of the
local behavior of the drifting orbits near essential hyperbolic
2-dimensional tori located inside the cylinders.
http://www.math.ias.edu/seminars/abstract?event=135831
4 Fukaya categories of Calabi-Yau hypersurfaces
Paul Seidel
Consider a Calabi-Yau manifold which arises as a member of a Lefschetz
pencil of anticanonical hypersurfaces in a Fano variety. The Fukaya
categories of such manifolds have particularly nice properties. I will
review this (partly still conjectural) picture, and how it constrains the
field of definition of the Fukaya category.
http://www.math.ias.edu/seminars/abstract?event=134640
5 Steenrod operations and Tate's Conjecture on the Brauer group of a surface
Tony Feng
There is a canonical pairing on the Brauer group of a surface over a finite
field, which is the analogue of the Cassels-Tate pairing on the
Tate-Shafarevich group of a Jacobian variety. An old conjecture of Tate
predicts that this pairing is alternating. In this talk I will present a
proof of Tate's conjecture. The key new ingredient is a circle of ideas
originating in algebraic topology, centered around the Steenrod operations,
that is imported to algebraic geometry on the ships of eětale homotopy
theory. The talk will advertise these new tools (while assuming minimal
background in algebraic topology).
http://www.math.ias.edu/seminars/abstract?event=136728
6 Explicit Binary Tree Codes with Polylogarithmic Size Alphabet
Gil Cohen
In this talk, we consider the problem of explicitly constructing a binary
tree code with constant distance and constant alphabet size. We present an
explicit binary tree code with constant distance and alphabet size
polylog(n), where n is the depth of the tree. This is the first improvement
over a two-decade-old construction that has an exponentially larger alphabet
of size poly(n). For analyzing our construction, we prove a bound on the
number of integral roots a real polynomial can have in terms of its sparsity
with respect to the Newton basis - a result of independent interest.
Joint work with Bernhard Haeupler and Leonard Schulman.
http://www.math.ias.edu/seminars/abstract?event=129076
7 A General Shadowing result for normally hyperbolic invariant manifolds and
its application to Arnold diffusion
Tere Seara
Abstract: In this talk we present a general shadowing result for normally
hyperbolic invariant manifolds. The result does not use the existence of
invariant objects like tori inside the manifold and works in very general
settings. We apply this result to establish the existence of diffusing
orbits in a large class of nearly integrable Hamiltonian systems. Our
approach relies on successive applications of the so called `scattering map'
along homoclinic orbits to a normally hyperbolic invariant manifold. The
main idea is that we can closely follow any path of the scattering map. This
gives the existence of diffusing orbits. The method applies to perturbed
integrable Hamiltonians of arbitrary degrees of freedom (not necessarily
convex) which present some hyperbolicity without any assumption about the
inner dynamics. Joint work with Marian Gidea and Rafael de la Llave.
http://www.math.ias.edu/seminars/abstract?event=136182
8 Some geometric mechanisms for Arnold diffusion
Rafael de la Llave
Abstract: We consider the problem whether small perturbations of integrable
mechanical systems can have very large effects. It is known that in many
cases, the effects of the perturbations average out, but there are
exceptional cases (resonances) where the perturbations do accumulate. It is
a complicated problem whether this can keep on happening because once the
instability accumulates, the system moves out of resonance. V. Arnold
discovered in 1964 some geometric structures that lead to accumulation in
carefuly constructed examples. We will present some other geometric
structures that lead to the same effect in more general systems and that can
be verified in concrete systems. In particular, we will present an
application to the restricted 3 body problem. We show that, given some
conditions, for all sufficiently small (but non-zero) values of the
eccentricity, there are orbits near a Lagrange point that gain a fixed
amount of energy. These conditions (amount to the non-vanishing of an
integral) are verified numerically. Joint work with M. Capinski, M. Gidea,
T. M-Seara
http://www.math.ias.edu/seminars/abstract?event=135834
9 Non-spherical Poincaré series, cusp forms and L-functions for GL(3)
Jack Buttcane
The analytic theory of Poincaré series and Maass cusp forms and their
L-functions for $SL(3,Z)$ has, so far, been limited to the spherical Maass
forms, i.e. elements of a spectral basis for
$L^2(SL(3,Z)\PSL(3,R)/SO(3,R))$. I will describe the Maass cusp forms of
$L^2(SL(3,Z)\PSL(3,R))$ which are minimal with respect to the action of the
Lie algebra and give a (relatively) simple method for constructing
Kuznetsov-type trace formulas by considering Fourier coefficients of certain
Poincaré series. In recent work with Valentin Blomer, we have extended our
proof of spectral-aspect subconvexity for L-functions of $SL(3,Z)$ Maass
forms to the non-spherical case, and I will discuss the structure of that
proof, as well.
http://www.math.ias.edu/seminars/abstract?event=135900
10 Diffusion along chains of normally hyperbolic cylinders
Marian Gidea
Abstract: We consider a geometric framework that can be applied to prove the
existence of drifting orbits in the Arnold diffusion problem. The main
geometric objects that we consider are 3-dimensional normally hyperbolic
invariant cylinders with boundary, which admit well-defined stable and
unstable manifolds. These enable us to define chains of cylinders i.e.,
finite, ordered families of cylinders in which each cylinder admits
homoclinic connections, and any two consecutive cylinders admit heteroclinic
connections. We show the existence of orbits drifting along such chains,
under precise conditions on the dynamics on the cylinders, and on their
homoclinic and heteroclinic connections. Our framework applies to both the a
priori stable setting, once the preliminary geometric reductions are
preformed, and to the a priori unstable setting, rather directly. This is
joint work with J.-P. Marco.
http://www.math.ias.edu/seminars/abstract?event=136188
11 Arnold diffusion and Mather theory
Ke Zhang
Abstract: Arnold diffusion studies the problem of topological instability in
nearly integrable Hamiltonian systems. An important contribution was made my
John Mather, who announced a result in two and a half degrees of freedom and
developed deep theory for its proof. We describe a recent effort to better
conceptualize the proof for Arnold diffusion. Combining Mather's theory and
classical hyperbolic methods, we define special cohomology classes called
Aubry-Mather type, where each such cohomology is connected to a nearby one
for a "residue perturbation" of the Hamiltonian. The question of Arnold
diffusion then reduces to the question of finding large connected components
of such cohomologies. This is a joint work with Vadim Kaloshin.
http://www.math.ias.edu/seminars/abstract?event=135837
12 Ordinary points mod p of hyperbolic 3-manifolds
Mark Goresky
Hyperbolic 3-manifolds with arithmetic fundamental group exhibit many
remarkable number theoretic properties. Is it possible that such manifolds
live over finite fields (whatever that means)? In this talk I will give some
evidence for this possibility.
http://www.math.ias.edu/seminars/abstract?event=136523
13 Growth of Sobolev norms for the cubic NLS near 1D quasi-periodic
solutions
Marcel Guardia
Abstract: Consider the defocusing cubic Schrödinger equation defined in the
2 dimensional torus. It has as a subsystem the one dimension cubic NLS (just
considering solutions depending on one variable). The 1D equation is
integrable and admits global action angle coordinates. Therefore, all its
solutions are either periodic, quasi-periodic or almost-periodic. Consider
one of the finite dimensional quasiperiodic invariant tori that the 1D
equation possesses. Under certain assumptions on the torus (smallness,
Diophantine frequency), we show that there exist solutions of the 2D
equation which start arbitrarily close to this invariant torus in the H^s
topology (with 0<s<1) and whose H^s Sobolev norm can grow by any given
factor. This is a joint work with Z. Hani, E. Haus, A. Maspero and M.
Procesi.
http://www.math.ias.edu/seminars/abstract?event=136191
---------------------------------
IAS Math Seminars Home Page:
http://www.math.ias.edu/seminars
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