2020-21 CRM/MONTREAL/QUEBEC ANALYSIS ZOOM SEMINARS

Seminars are usually held on Mondays or Fridays. In person seminars in Montreal are held at Concordia, McGill or Universite de Montreal; in person seminars in Quebec City are held at Laval.
To attend a zoom session, and for suggestions, questions etc. please contact Galia Dafni (galia.dafni@concordia.ca), Alexandre Girouard (alexandre.girouard@mat.ulaval.ca), Dmitry Jakobson (dmitry.jakobson@mcgill.ca), Damir Kinzebulatov (damir.kinzebulatov@mat.ulaval.ca) or Iosif Polterovich (iossif@dms.umontreal.ca)


After a break due to COVID-19, Montreal Analysis seminar has resumed on zoom, organized jointly with Laval University in Quebec City. Please, contact one of the organizers for the seminar zoom links.

The talks are recorded and posted on the CRM Youtube channel, on Mathematical Analysis Lab playlist

FALL 2020

Friday, September 11, 9:00 Eastern Time, zoom seminar
Jose Maria Martell (ICMAT)
Uniform rectifiability and elliptic operators satisfying a Carleson measure condition
Abstract: In this talk I will study the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of whether (quantitative) absolute continuity of the elliptic measure with respect to the surface measure and uniform rectifiability of the boundary are equivalent, in an optimal class of divergence form elliptic operators satisfying a suitable Carleson measure condition. Our setting is that of domains having an Ahlfors regular boundary and satisfying the so-called interior Corkscrew and Harnack chain conditions (these are respectively scale-invariant/quantitative versions of openness and path-connectivity) and we show that for the class of Kenig-Pipher uniformly elliptic operators (operators whose coefficients have controlled oscillation in terms of a Carleson measure condition) the solvability of the $L^p$-Dirichlet problem with some finite $p$ is equivalent to the quantitative openness of the exterior domains or to the uniform rectifiablity of the boundary. Joint work with S. Hofmann, S. Mayboroda, T. Toro, and Z. Zhao.
Friday, October 9, 13:00 Eastern time, zoom seminar
Arick Shao (Queen Mary university)
On Controllability of Waves and Geometric Carleman Estimates
Abstract: We consider the question of exact (boundary) controllability of wave equations: whether one can steer their solutions from any initial state to any final state using appropriate boundary data. In particular, we discuss new and fully general results for linear wave equations on time-dependent domains with moving boundaries. We also discuss the novel geometric Carleman estimates that are the main tools for proving these controllability results.
Friday, October 16, 14:30 Eastern Time, zoom seminar
Guangyu Xi (University of Maryland)
On the Smoluchowski-Kramers approximation of infinite dimensional systems with state-dependent damping
Abstract: We study a class of stochastic nonlinear damped wave equations endowed with Dirichlet boundary conditions. We show that the Smoluchowski-Kramers approximation describes the convergence of solutions of the stochastic wave equations to the solution of a quasilinear stochastic parabolic equation endowed with Dirichlet boundary conditions. This is a joint work with Sandra Cerrai from UMD.
Friday, October 23, 14:30 Eastern time, zoom seminar
Mohammad Shirazi (McGill)
Schiffer operator corresponding to Riemann surfaces with finitely many borders
Abstract: In this talk, a brief history of the Schiffer operator on the complex plane, on the Riemann sphere, and (some type of) Riemann surfaces will be reviewed. Some of my thesis' results concerning the development of this operator on Riemann surfaces (open, with finitely many borders, each homeomorphic to S^1) will be presented. We will see when the Schiffer operator is a bounded isomorphism.
Friday, November 13, 14:30 Eastern time (to be confirmed), zoom seminar
Hien Nguyen (Iowa State)
Title TBA

Friday, November 20, (date and time to be confirmed), zoom seminar
Daniel Peralta-Salas (ICMAT)
Optimal domains for the first curl eigenvalue
Abstract: The classical Faber-Krahn inequality for the first eigenvalue of the Dirichlet Laplacian shows that the ball is the unique optimal domain. In this talk I will explore the analogous problem for the curl operator: for a fixed volume, what is the optimal domain for the first positive (or negative) eigenvalue of curl? In spite of being one of the most important vector-valued operators, this question is rather unexplored and remains wide open. In this talk I will show that, even taking into account that the first eigenvalue is uniformly lower bounded in terms of the volume, there are no axisymmetric smooth optimal domains for the curl that satisfy a mild technical assumption. In particular, this rules out the existence of optimal axisymmetric domains with a convex section. This is based on joint work with Alberto Enciso.
Friday, November 27, 14:30 Eastern time (to be confirmed), zoom seminar
Alex Brudnyi (Calgary)
Title TBA

2020 Zoom Seminars

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