## 2017-18 Montreal Analysis Seminar

Seminars are usually held on Mondays or Fridays at Concordia,
McGill or Universite de Montreal

For suggestions, questions etc. please contact Dmitry Jakobson
(jakobson@math.mcgill.ca), Iosif Polterovich
(iossif@dms.umontreal.ca) or
Alina Stancu (alina.stancu@concordia.ca)

## WINTER 2018

** Monday, April 23, 13:30-14:30, McGill, Room 920**

** Sugata Mondal** (Indiana University)

Hot spots conjecture for Euclidean triangles.

** Abstract:**
The hot spots conjecture was made by J. Rauch at a conference
in 1974. One of the (many) versions of the conjecture says the following.
Let D be a domain in a Euclidean space with piece-wise smooth boundary.
Then a second Neumann eigenfunction u for D can not attain its global
maximum at an interior point of D. The conjecture is known to be false for
domains with holes. Positive results are known in many situations due
works of K. Burdzy and his collaborators, D. Jerison-N. Nadirashvilli and
many others. This talk will be focused on the hot spot conjecture for
Euclidean triangles. Obtuse triangles known to satisfy the conjecture,
due to works of Burdzy-Banuelos. A class of acute triangles also known to
satisfy the conjecture, due to works of Miyamoto and Siudeja. In this talk
I will try to explain a proof of the conjecture for all Euclidean triangles.
This a joint work with Chris Judge.

** Monday, March 19, 13:30-14:30, McGill, Room 920**

** Thierry Daude** (Cergy-Pontoise)

On the anisotropic Calderon problem on singular Riemannian manifolds of
Painleve type: the borderline between uniqueness and invisibility.

** Abstract:**
The anisotropic Calderon problem consists in determing the metric of a
Riemannian manifold with boundary from the knowledge of its
Dirichlet-to-Neumann map. I this talk, I will study this type of problem
on Riemannian manifolds equiped with singular metrics, i.e. metrics
whose coefficients are in some L^p spaces. In the particular case of
Riemannian manifolds having certain separability properties of the
geodesic flow (Painlevé property), I shall show what is the borderline
between uniqueness and non-uniqueness results in the corresponding
anisotropic Calderon problem. This is a joint work with Niky Kamran
(McGIll) and Francois Nicoleau (Nantes).

** Friday, March 9, 13:30-14:30, Univ. de Montreal,
Pav. Andre Aisenstadt, Room 5183
**

** Antoine Henrot** (Institut Elie Cartan de Lorraine)

About two shape functionals involving the maximum of the torsion
function

** Abstract:**
In this talk we investigate upper and lower bounds of two shape
functionals involving the maximum of the torsion function.
More precisely, we consider $T(\Omega)/(M(\Omega)|\Omega|)$ and
$M(\Omega)\lambda_1(\Omega)$, where $\Omega$ is a bounded
open set of $\mathbb{R}^N$ with finite Lebesgue measure $|\Omega|$,
$M(\Omega)$ denotes the maximum of the torsion function,
(solution of $-\Delta u=1$ in $\Omega$, $u=0$ on the boundary),
$T(\Omega)=\int_\Omega u$ $ the torsion, and $\lambda_1(\Omega)$
the first Dirichlet eigenvalue. Particular attention is devoted to the
subclass of convex sets.

** Friday, March 2, 13:30-14:30, McGill, Room 920**

** Yulia Bibilo** (Concordia)

Isomonodromic deformations and nonlinear equations

** Abstract:**
We consider monodromy preserving deformations of meromorphic linear
systems of ordinary differential equations over the Riemann sphere.
In particular, we will discuss some results for systems with both
resonant and non-resonant irregular singularities and also applications
to integrable nonlinear differential equations.

** Joint Analysis and Geometric Analysis seminar **

** Friday, February 16, 13:30-14:30, McGill, Room 920
**

** Loredana Lanzani** (Syracuse)

Harmonic Analysis Techniques in Several Complex Variables

** Abstract:** pdf

** Friday, February 9, 13:30-14:30, McGill, Room 920
**

** Jeff Galkowski** (Stanford)

Concentration of Eigenfunctions: Sup-norms and Averages

** Abstract:**
In this talk we relate concentration of Laplace eigenfunctions in
position and momentum to sup-norms and submanifold averages. In particular,
we present a unified picture for sup-norms and submanifold averages which
characterizes the concentration of those eigenfunctions with maximal growth.
We then exploit this characterization to derive geometric conditions under
which such growth cannot occur.

** Friday, Januauary 26, 13:30-14:30, McGill, Room 920**

** Victor Ivrii** (Toronto)

Spectral asymptotics for Steklov’s problem in domains with edges

** Abstract:**
We derive sharp eigenvalue asymptotics for Dirichlet-to-Neumann
operator in the domain with edges and discuss obstacles for deriving
a sharper (two-term) asymptotics.

## FALL 2017

** Friday, December 1, 13:30-14:30, McGill, Room 920**

** Mikhail Panine** (Quebec City)

On Perturbative Methods in Spectral Geometry

** Friday, November 24, 14:30-15:30, Universite de Montreal,
Pav. Andre-Aisenstadt, Room 5448**

** Damir Kinzebulatov** (Laval)

Brownian motion with general drift

** Abstract:**
We construct and study the weak solution to stochastic
differential equation dX_t=-b(X_t)dt+dW_t, X_0=x, for every x \in R^d,
d \geq 3, with b in the class of weakly form-bounded vector fields,
containing, as proper subclasses, a sub-critical class [L^d+L^\infty]^d,
as well as critical classes such as weak the L^d class, the Kato class,
the Campanato-Morrey class, the Chang-Wilson-T. Wolff class.
This is joint work with Yu. A. Semenov
arxiv:1710.06729

** Friday, November 17, 13:30-14:30, McGill, Room 920**

** Mircea Voda** (Toronto)

On the spectrum of multi-frequency quasiperiodic Schrödinger operators
with large coupling

** Abstract:** The spectrum of single-frequency quasiperiodic Schrödinger operators
with analytic potentials is known to be a Cantor set. Chulaevsky and Sinai
conjectured that the spectrum of multi-frequency quasiperiodic Schrödinger
operators is an interval for generic large potentials. I will discuss a
proof of the Chulaevsky-Sinai conjecture based on joint work with M.
Goldstein and W. Schlag.

** Joint Analysis + Geometric Analysis seminar**

** Friday, November 10, 13:30-14:30, McGill, Room 920**

** Dan Pollack** (U. Washington)

On the geometry and topology of initial data sets with horizons

** Friday, November 3, 13:30-14:30, McGill, Room 920**

** Niko Laaksonen** (McGill)

Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space

** Abstract:**
On hyperbolic manifolds the lengths of primitive closed geodesics
(prime geodesics)
have many similarities with the usual prime numbers. In particular,
they obey
an asymptotic distribution analogous to the Prime Number Theorem.
The error in
this estimation is well-studied in two dimensions. In three dimensions the
only unconditional non-trivial estimate is by Sarnak. In this talk we show
how to improve on Sarnak's
pointwise bound for the error term. We also investigate the second
moment of the error term and highlight
some of the difficulties compared to the two dimensional case.

** Monday, October 16, 13:30-14:30, McGill, Room 920**

** Frederic Naud** (Avignon)

Sharp resonances and large covers of hyperbolic surfaces

** Abstract:**
(joint With D. Jakobson and L. Suares)
In this talk we will look at the spectral properties of infinite area
hyperbolic surfaces in families
of covers. Depending on the structure of the covering groups we
establish several asymptotic results on the distribution
of resonances in the large degree limit.

** Friday, October 6, 13:30-14:30, McGill, Room 920**

** Kay Kirkpatrick** (University of Illinois at Urbana-Champaign)

Free Araki-Woods Factors and a Calculus for Moments in Quantum Groups.

**Abstract:**
We will discuss a central limit theorem for quantum groups: that the joint
distributions with respect to the Haar state of the generators of free
orthogonal quantum groups converge to free families of generalized
circular elements in the large (quantum) dimension limit. We also discuss
a connection to almost-periodic free Araki-Woods factors. This is joint
work with Michael Brannan.

** Spectral Theory seminar**

** Monday, September 25, 14:00-15:00, UdeM, Room 5340/5380**

** Lise Turner** (McGill)

Distribution of coefficients of rank polynomials for
random sparse graphs

** Abstract:**
We study the distribution of coefficients of rank polynomials of
random sparse graphs. We first discuss the limiting distribution for
general graph sequences that converge in the sense of Benjamini-Schramm.
Then we compute the limiting distribution and Newton polygons of the
coefficients of the rank polynomial of random d-regular graphs.
This is joint work with S. Norin and D. Jakobson

** Monday, September 18, 13:00-14:00, McGill, Burnside 920**

** Alexander Olevskii** (Tel Aviv University)

Around uncertainty principle

** Abstract:**
How "small" the support and the spectrum of a function
in R^d can be?
I'll present an introduction to the subject and discuss new results
joint with Fedor Nazarov and with my student T.Amit.

** Monday, September 18, 14:00-15:00, Burnside 920**

** Alex Iosevich** (Rochester University)

Finite point configuration in continuous, discrete and
arithmetic settings

** Abstract:**
The basic question we ask is, how "large" does a subset of a vector space
need to be to ensure that it contains a given geometric configurations, or
a positive proportion of congruence classes of a given geometric
configuration? This problem is connected with many interesting questions
in analysis, number theory and combinatorics, including the sum-product
phenomenon, the local smoothing conjecture for the wave equation and
various notions of rigidity in classical geometry. We will survey some
recent results in a variety of settings and describe the ideas behind them.

** Friday, September 15, 13:30-14:30, McGill, Burnside 920**

** Eli Liflyand** (Bar Ilan University)

Asymptotic relations for the Fourier transform of a function of bounded
variation

** Abstract:**
Earlier and recent one-dimensional estimates and asymptotic relations for the
cosine and sine Fourier transform of a function of bounded variation
are refined
in such a way that become applicable for obtaining multidimensional asymptotic
relations for the Fourier transform of a function with bounded Hardy variation.

** Monday, August 28, Univ. de Montreal,
13:30-14:30, Room 5183**

** Alexei Penskoi** (Moscow State University
and Higher School of Economics)

An isoperimetric inequality for Laplace eigenvalues on the sphere and
the projective plane

** Abstract:**
The ﬁrst subject of this talk is an isoperimetric inequality for the
second non-zero eigenvalue of the Laplace-Beltrami operator on the real
projective plane (based on a joint paper with N. Nadirashvili). For a metric
of area 1
this eigenvalue is not greater than 20\pi. This value could be attained as a
limit on a sequence of metrics of area 1 on the projective plane converging to
a singular metric on the projective plane and the sphere with standard metrics
touching in a point such that the ratio of the areas of the projective plane
and the sphere is 3:2. The second subject of this talk is a very recent
result (joint paper with M. Karpukhin, N. Nadirashvili and I. Polterovich)
about
an isoperimetric inequality for Laplace eigenvalues on the sphere. For a
metric
of area 1 the k-th eigenvalue is not greater than 8\pi k. This value could
be attained as a limit on a sequence of metrics of area 1 on the sphere
converging to a singular metric on k spheres with standard metrics of equal
radius touching in a point.

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