## 2019-20 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
(dmitry.jakobson@mcgill.ca), Iosif Polterovich
(iossif@dms.umontreal.ca) or
Galia Dafni (galia.dafni@concordia.ca)

## FALL 2019

** Friday, September 6, 13:30-14:30, McGill, Burnside Hall, Room 1104**

**Reem Yassawi** (Open University)

Measure non-rigidity for linear cellular automata

**Abstract:**
pdf

** Friday, September 20, 13:30-14:30, McGill, Burnside Hall, Room 1104
**

**Damir Kinzebulatov** (Laval)

Heat kernel bounds and desingularizing weights for non-local
operators

**Abstract:**
In 1998, Milman and Semenov introduced the method of desingularizing
weights in order to obtain sharp two-sided bounds on the heat kernel of
the Schroedinger operator with a potential having critical-order
singularity at the origin. In this talk, I will discuss the method of
desingularizing weights in a non-symmetric, non-local situation. In
particular, I will talk about sharp two-sided bounds on the heat kernel
of the fractional Laplacian perturbed by a Hardy drift.
The crucial ingredient of the desingularization method is a weighted
L^1->L^1 estimate on the semigroup, leading to the weighted Nash initial
estimate. Milman and Semenov established this estimate appealing to the
Stampacchia criterion in L^2. These arguments becomes quite problematic
in the non-local non-symmetric situation (e.g. for a strong enough
singularity of the drift, there is only L^p theory of the operator
for p>2). The core of the talk will be the discussion of a new approach
to the proof of this estimate.
Joint with Yu.A.Semenov and K.Szczypkowsi (arxiv:1904.07363)

** Monday, November 4, 13:30-14:30, McGill, Burnside Hall, Room 1104**

**Stephane Sabourau** (U. Paris-Est)

Systolically extremal metrics on nonpositively curved surfaces

** Abstract:**
The regularity of systolically extremal surfaces (i.e., surfaces of
minimal area with fixed systole) is a delicate problem already discussed
by M. Gromov in the 80's. We propose to study the problem of
systolically extremal metrics in the context of generalized metrics of
nonpositive curvature. A natural approach would be to work in the class
of Alexandrov surfaces of finite total curvature, where one can exploit
the tools of the completion provided in the context of Radon measures as
studied by Reshetnyak and others. However the generalized metrics in
this sense still don't have enough regularity. Instead, we develop a
more hands-on approach and show that, for each genus, every systolically
extremal nonpositively curved surface is piecewise flat with finitely
many conical singularities. Joint work with M. Katz.

** Friday, November 15, 14:30-15:30, Universite de Montreal,
Pavillon Andre-Aisenstadt, Room 5183. **

**Almaz Butaev** (U. Calgary)

Extension problem on subspaces of BMO on domains

** Abstract:**
In joint work with Galia Dafni, we discuss the extension problem for some
subspaces of functions of bounded mean oscillation (BMO). Based on the
extension operator of Jones we construct a universal extension in the sense
that it simultaneously extends certain natural subspaces of BMO. The
presented results will show an interplay between approximation, extension
and geometric properties of the domain.

** Friday, November 29, 14:00-15:00, Concordia, Library Building,
Room LB921-4. **

**Ritva Hurri-Syrjanen** (U. of Helsinki)

On the John-Nirenberg inequalities

** Abstract:**
The goal of my talk is to address some inequalities which Fritz John
and Louis
Nirenberg proved to be valid for certain functions defined in a cube.
I will discuss the
validity of similar inequalities for functions dened in an arbitrary
bounded domain.
My talk is based on joint work with Niko Marola and Antti
Vahakangas.

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