## 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)

## FALL 2016

** Friday, September 16, 13:30-14:30, McGill, Burnside 920**

**Jeff Galkowski** (CRM/McGill)

A Quantitative Vainberg Method for Black Box Scattering

** Abstract: **
We give a quantitative version of Vainbergâ€™s method relating pole
free regions to
propagation of singularities for black box scatterers. In particular, we
show that there is a
logarithmic resonance free region near the real axis of size t with
polynomial bounds on the
resolvent if and only if the wave propagator gains derivatives at rate t.
Next we show that if
there exist singularities in the wave trace at times tending to infinity
which smooth at rate t, then
there are resonances in logarithmic strips whose width is given by t. As
our main application
of these results, we give sharp bounds on the size of resonance free
regions in scattering on
geometrically nontrapping manifolds with conic points. Moreover, these
bounds are generically
optimal on exteriors of nontrapping polygonal domains.

** Monday, October 3, UdeM, 14:00-15:00, U. Montreal,
Pav. Andre Aisenstadt, Room 5448**

**Alexandre Girouard** (Laval University)

Discretization and Steklov eigenvalues of compact manifold with boundary

** Abstract: **
Let M be a compact n-dimensional Riemannian manifolds with cylindrical
boundary, Ricci curvature bounded below by k and injectivity radius bounded
below by r. We introduce a notion of discretization of the manifold M,
leading to a graph with boundary which is roughly isometric to M , with
constant depending only on k, r, n. In this context, we prove a uniform
spectral comparison inequality between the Steklov eigenvalues of the
manifold M and those of its discretization. Some applications to the
construction of sequences of surfaces with boundary of fixed length and
with large Steklov eigenvalues are given. In particular, we obtain such a
sequence for surfaces with connected boundary. These applications are based
on the construction of graph-like surfaces which are modeled using
sequences of graphs with good expansion properties. This talk is based on
joint work with Bruno Colbois (Neuchatel) and Binoy Raveendran.

** Friday, October 28, Concordia, 14:00, LB 921-4**

**Scott Rodney** (Cape Breton university)

The Poincare Inequality and the $p$-Laplacian

** Abstract: **
In this talk I will explore a necessary and sufficient condition for the
validity of a Poincar\'e - type inequality.
This work will be presented in the context of the degenerate Sobolev
spaces $W^{1,p}_Q(\Omega)$ and the Degenerate
$p$-Laplacian given by $\Delta_p u =
\text{Div}\Big( \Big|\sqrt{Q(x)}\nabla u(x)\Big|^{p-2} Q(x)
\nabla u\Big)$ where
$Q(x)$ is a non-negative definite $L^1_{\text{loc}}$ matrix valued function.

** Special Analysis/Applied seminar**

** Friday, October 28, McGill, 15:30-16:30, Burnside 1120**

** Daniel Han-Kwan** (Ecole Polytechnique)

Title TBA

** Friday, November 4, Time and Room TBA**

**Carlos Perez** (BCAM, Bilbao)

Title TBA

** Monday, November 7, Time and Room TBA**

**Steve Lester** (CRM and McGill)

Title TBA

** Friday, November 11, Burnside 920, 13:00-14:00**

**Michael Hitrik** (UCLA)

Title TBA

** Friday, November 11, Burnside 920, 14:00-15:00**

**Katya Krupchyk** (UC Irvine)

Title TBA

## WINTER 2017

** Wednesday, March 15, Time and Room TBA**

**Alexander Olevskii** (Tel Aviv)

Title TBA

## SUMMER 2016

** Thursday, June 2, 13:30-14:30, Concordia, Room LB 921-04
**

**Vlad Yaskin** (University of Alberta, Edmonton)

Stability results for sections of convex bodies

** Abstract:**
(pdf)
Let $K$ be a convex body in $\mathbb R^n$.
The parallel section function of $K$ in the direction $\xi\in S^{n-1}$ is
defined by
$$
A_{K,\xi}(t)=\mathrm{vol}_{n-1}(K\cap \{\xi^{\perp}+t\xi\}), \quad
t\in \mathbb R.
$$
If $K$ is origin-symmetric (i.e. $K=-K$), then Brunn's theorem implies
$$
A_{K,\xi}(0) =\max_{t\in \mathbb R} A_{K,\xi}(t)
$$
for all $\xi\in S^{n-1}$.
The converse statement was proved by Makai, Martini and \'Odor.
Namely, if $A_{K,\xi}(0) =\max_{t\in \mathbb R} A_{K,\xi}(t)$ for all
$\xi\in S^{n-1}$, then $K$ is origin-symmetric.
We provide a stability version of this result. If $A_{K,\xi}(0)$ is
close to $\max_{t\in \mathbb R} A_{K,\xi}(t)$ for all $\xi\in
S^{n-1}$, then $K$ is close to $-K$.
Joint work with Matthew Stephen.

** Monday, August 1, 13:30-14:30, McGill, Burnside 920 (room
to be confirmed) **

**Fedor Pakovich** (Ben Gurion University)

On semiconjugate Rational Functions

** Abstract: ** pdf

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