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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