Seminars are usually held on Friday afternoon.
The seminar is currently held in hybrid mode, organized jointly with Laval University in Quebec City. In-person seminars in Montreal are held at Concordia, McGill or the CRM/Université de Montréal; in person seminars in Quebec City are held at Laval.
To be added to the mailing list, attend a zoom session, and for suggestions, questions etc. please contact one of the organizers.
Some of the past talks are recorded and posted on the CRM Youtube channel, on the Mathematical Analysis Lab playlist.
Friday, November 6, 1:30 pm (note earlier time), hybrid seminar at Université Laval, Pavillon Alexandre-Vachon, VCH-3840
Joe Ghafari (University of Ottawa)
Local existence and uniqueness of the stochastic Cahn–Hilliard equation in dimensions four and five
The Cahn–Hilliard equation is a fourth-order nonlinear evolution equation motivated by phase separation. When driven by space–time white noise in four and five spatial dimensions, its solutions are too irregular for the cubic nonlinearity to be defined through ordinary multiplication.
I will present local existence and uniqueness results in dimensions one through five, emphasizing the analytical challenges in dimensions four and five. In four dimensions, the Da Prato–Debussche decomposition separates the singular random component from a more regular remainder. In five dimensions, a paracontrolled expansion describes additional interactions between singular components.
The main focus will be the resulting deterministic analysis: smoothing and Schauder estimates in Besov spaces, paraproduct and commutator estimates, and the fixed-point arguments used to construct solutions. The construction and renormalization of the stochastic terms will be outlined briefly to explain the analytical framework.
The talk is based on my PhD work:
Joe Ghafari, Paracontrolled approach to the stochastic Cahn–Hilliard equation (2026), arXiv:2609.02197.
Friday, November 13, 2:25pm, hybrid seminar at UdeM, Pavillon André-Aisenstadt, room 5183
Mikhail Karpukhin (University College London)
Spectral group theory and index of minimal surfaces.
Consider a Schrödinger-type operator that is invariant under the action of a symmetry group. The underlying function space can be decomposed into operator-invariant isotypic components according to the irreducible representations of the symmetry group. It was shown by Helffer et al. (2002) that, for the action of a dihedral group on planar domains, there are universal inequalities that relate the lowest eigenvalues in different isotypic components, independently of the choice of invariant potential. In this talk, I will show that this phenomenon is much more general and is not specific to planar domains, dihedral groups or the lowest eigenvalues. I will also discuss applications to Morse index computations for symmetric minimal surfaces. Based on joint works with D. Cao, J. Lagacé-Taylor and M. Schulz.
Tuesday, November 17, 11am, hybrid seminar at UdeM, Pavillon André-Aisenstadt, room 4186 (note unusual day, time and location)
Romain Petrides (IMJ-PRG)
TBA
Other activities of interest:
Nirenberg Lectures in Geometric Analysis, November 16 - 20, 2026
CRM Workshop in Convex and Geometric Analysis, December 9 - 11, 2026
Friday, October 2, 2:30 pm, hybrid seminar at Université Laval, Pavillon Alexandre-Vachon, VCH-3840
Karol Szczypkowski (Politechnika Wroclawska)
Towards a General Invariance Principle for Schrödinger Perturbations
We study how a heat kernel changes after adding a Schrödinger potential. Our aim is to find functions that remain invariant, or become supermedian, for the perturbed evolution. We present a general method based on Duhamel’s formula and perturbation series, and illustrate it with Hardy-type potentials. The examples also show that different solutions of the same Duhamel equation may have different invariance properties.
Friday, September 25, 2:30pm, hybrid seminar at Université Laval, Pavillon Alexandre-Vachon, VCH-3840
Tomasz Jakubowski (Wrocław University of Science and Technology)
Fractional Burgers equation with singular initial condition
We consider a multidimensional fractional Burgers equation with singular initial data. Previous results in this area usually required integrable initial conditions. I will present a broader framework that allows strongly singular, non-integrable data, including functions with power-type singularities. The talk will focus on the existence of solutions and their main qualitative properties, including self-similar behavior and pointwise estimates.
Friday, September 18, 2:25pm, hybrid seminar at UdeM, Pavillon André-Aisenstadt, room 5183
Lawford Hatcher, CRM-ISM (Concordia, Laval, UdeM)
The no-flux Laplacian and its applications
We present some results on eigenvalues of the Laplacian with "no-flux" boundary conditions, under which eigenfunctions have constant Dirichlet data and mean-zero Neumann data. It was established by Greco-Lucia in 2008 that the disjoint union of two balls uniquely minimizes the first positive eigenvalue of this problem among Euclidean domains of a fixed volume. We will discuss a new stability result for this inequality. We will also present applications of this eigenvalue problem to two problems in spectral geometry: the existence of large hyperbolic surfaces with conical singularities and a spectral gap greater than ¼ (based on joint work with Bram Petri) and the minimization of curl eigenvalues on domains in a certain geometric setting (based on joint work with Willi Kepplinger and David Perrella).
Alexandre Girouard (Université Laval)
Galia Dafni (Concordia University)
Dmitry Faifman (Université de Montréal)
Dmitry Jakobson (McGill University)
Maria Ntekoume (Concordia University)