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 (firstname.lastname@example.org), Alexandre Girouard
(email@example.com), Dmitry Jakobson
(firstname.lastname@example.org), Damir Kinzebulatov
(email@example.com) or Iosif Polterovich
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
Friday, September 11, 9:00 Eastern Time, zoom seminar
Jose Maria Martell (ICMAT)
Uniform rectifiability and elliptic operators satisfying a Carleson
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
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
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
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
Friday, October 16, 14:30 Eastern Time,
Guangyu Xi (University of Maryland)
On the Smoluchowski-Kramers approximation of infinite dimensional systems
with state-dependent damping
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,
Mohammad Shirazi (McGill)
Schiffer operator corresponding to Riemann surfaces with finitely many
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),
Hien Nguyen (Iowa State)
Friday, November 20, (date and time to be confirmed),
Daniel Peralta-Salas (ICMAT)
Optimal domains for the first curl eigenvalue
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
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),
Alex Brudnyi (Calgary)
2020 Zoom Seminars
Fall 2013 Seminars
Winter 2014 Seminars
2005/2006 Analysis Seminar
2004/2005 Seminar in Nonlinear Analysis and Dynamical Systems
2003/2004 Working Seminar in Mathematical Physics