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 talks are recorded and posted on the CRM Youtube channel, on the Mathematical Analysis Lab playlist.
Friday, January 23, 2pm, hybrid seminar at UdeM, Pavillon André-Aisenstadt, room 5183
Luca Iffland (Goethe-Universität Frankfurt)
The local logarithmic Brunn-Minkowski inequality for bodies of revolution
The conjectured logarithmic Brunn-Minkowski inequality is a stronger
version of the classical Brunn-Minkowski inequality, that has many
applications in convex geometry, stochastis and other fields of
mathematics. In my recent work, I prove a local version of the
logarithmic Brunn-Minkowski inequality for one body of revolution and
one arbitrary body. Equality cases are discussed and some consequences
such as the logarithmic Minkowski inequality and the uniqueness of the
cone volume measure for bodies of revolution are deduced. The proof uses
an operator theoretic approach together with the decomposition of
spherical functions into isotypical components with respect to rotations
around a fixed axis.
Friday, March 20, time and location TBA
Katja Vassilev (Chicago)
Friday, January 16, 2pm, hybrid seminar at UdeM, Pavillon André-Aisenstadt, room 5183
Yvonne Alama Bronsard (MIT)
Numerical approximations to nonlinear dispersive equations, from short to long times
The first part of this talk deals with the numerical approximation to nonlinear dispersive equations, such as the prototypical nonlinear Schrödinger or Korteweg-deVries equations. We introduce integration techniques allowing for the construction of schemes which preserve the geometric structure and qualitative behavior of the equation on the discrete level. Higher order extensions will be presented, following techniques based on decorated trees series inspired by singular stochastic PDEs via the theory of regularity structures.
In the second part, we introduce a new approach for designing and analyzing schemes for some nonlinear and nonlocal integrable PDEs. This work is based upon recent theoretical breakthroughs on explicit formulas for nonlinear integrable equations. It opens the way for studying the asymptotic behavior of the solutions, with applications to the soliton resolution conjecture, and in wave turbulence theory.
Friday, September 19, 1:30 pm, hybrid seminar at McGill, Burside Hall, room 1104
Marta Lewicka (Pittsburgh)
Tug-of-War games for nonlinear PDEs
The lecture will present an overview of the probabilistic interpretation of the nonlinear potential theory, relying on the notion of tug-of-war games with noise, and the asymptotic expansions of averages. We will explore constructions pertaining to the p-laplacian, the non-local setting, and the various boundary conditions.
Friday, October 10, 1pm *Note earlier time*, hybrid seminar at UdeM, Pavillon André-Aisenstadt, room 5183
Lukas Bundrock (Alabama)
Behavior of Absorbing and Generating p-Robin Eigenvalues in Bounded and Exterior Domains
The spectrum of the Laplace operator with Robin boundary conditions has been studied extensively, with deep connections to physical models including heat flow, fluid dynamics, and wave propagation. Its nonlinear counterpart, the p-Laplacian, also plays a central role in modeling complex media, particularly non-Newtonian fluids.
In this talk, we investigate the principal eigenvalue of the p-Laplacian under Robin boundary conditions, with a focus on its asymptotic behavior depending on the boundary parameter. For bounded domains, we establish quantitative inequalities valid for all p, which in particular improve known results in the classical case (p=2). In the setting of exterior domains, we address questions of existence, derive general bounds for the first eigenvalue of the complement of a ball, and prove sharp geometric inequalities for the complement of convex domains in two dimensions.
Friday, October 24, 2pm, hybrid seminar at Concordia, Library Building, room 921-4
Timo Takala (Aalto)
An introduction to John-Nirenberg spaces and recent results featuring vanishing subspaces and maximal functions
The space of functions of bounded mean oscillation BMO was first defined by John and Nirenberg in 1961, and it is an essential function space in harmonic analysis. The John-Nirenberg space JNp was first defined in the same paper and it is also related to oscillations, but it has not been studied as much as BMO. In this talk I will first present the definition and some of
the basic properties of JNp functions.
The spaces VMO and CMO are well-known vanishing subspaces of BMO. Corresponding vanishing subspaces of JNp have been defined and studied recently and some characterizations for those vanishing subspaces have been developed. Another active line of research involves studying the regularity of (fractional) maximal functions of various types of functions. In the talk I will present some recent results about JNp functions, the vanishing subspaces of JNp, and the (fractional) maximal functions of BMO, VMO and JNp functions.
Friday, October 31, 2pm, hybrid seminar at UdeM, Pavillon André-Aisenstadt, room 5183
Denis Vinokurov (Université de Montréal)
Maximizing Laplace eigenvalues with density in higher dimensions
We will discuss the problem of maximizing the k-th Laplace eigenvalue with density on a closed Riemannian manifold of dimension m ≥ 2. The Euler–Lagrange equation identifies critical densities with the energy densities of harmonic maps into spheres, linking spectral optimization to harmonic-map theory. Unlike the case m = 2, where a priori multiplicity bounds yield existence and regularity, higher dimensions allow unbounded multiplicities.
In the talk, we will present topological tensor products techniques that handle this setting and prove the existence of maximizing densities for all m ≥ 3. For regularity, optimizers are smooth away from a singular set; when m ≥ 7, this set can have any prescribed integer dimension up to m − 7, as we will illustrate with examples on the m-sphere. These techniques have potential for other eigenvalue-optimization problems in higher dimensions where unbounded multiplicities arise.
References:
D. Vinokurov, Maximizing higher eigenvalues in dimensions three and above, preprint, arXiv:2506.09328 [math.SP] (2025).
Friday, November 14, 2:30pm *note later time*, hybrid seminar at ULaval, VCH-2880
Eugenio Dellepiane (Université Laval)
Boundedness, compactness and Schatten class for Rhaly matrices
Thursday, November 27, 3pm *note different day and time*, joint with Geometric Analysis Seminar, McGill, Burnside Hall room 1205
Joshua Flynn (MIT)
Anisotropic Varifolds
A varifold is a measure theoretic generalization of a surface. In this talk I will introduce a varifold theory suitable for certain geometric settings which are locally "anisotropic."
Friday, November 28, 1:30pm *the first of two talks*, hybrid seminar at CRM, room 5183
Jan Kotrbaty (Charles University)
A Generalization of Godbersen's Conjecture
The long-standing Godbersen's conjecture asserts that the Rogers-Shephard inequality for the volume of the difference body is refined by an inequality for the mixed volume of a convex body and its reflection about the origin. The conjecture is known in several special cases, notably for anti-blocking convex bodies. In this talk, we will propose a generalization of Godbersen's conjecture that refines Schneider's generalization of the Rogers-Shephard inequality to higher-order difference bodies and we will show it is true for anti-blocking convex bodies. We will also discuss the connection of the conjectured inequality to the Alesker product of smooth valuations and the intersection product of polytopes introduced recently by Wannerer.
Friday, November 28, 2:30pm *the second of two talks*, hybrid seminar at CRM, room 5183
Yair Shenfeld (Brown)
Sectional curvature, matrix displacement convexity, and intrinsic dimensional functional inequalities
The behavior of entropy along optimal transport flows captures the geometry of the underlying space and gives rise to important functional inequalities. In particular, the Ricci curvature and the dimension turn out to be the fundamental building blocks of this theory. I will survey these classical results and then show how an analogous theory can be developed for sectional curvature and intrinsic dimensional functional inequalities.
Friday, December 12, 2:15pm, hybrid seminar at UdeM, Pavillon André-Aisenstadt, room 5183
David Sher (DePaul University)
The Dirichlet heat trace for domains with curved corners
Consider the heat problem with Dirichlet boundary conditions on a curvilinear polygon in the plane. We examine the short-time asymptotic expansion of the associated heat trace, focusing on the interaction between the curvature of the boundary and the corners of the domain. The coefficients of this expansion are well-understood in the case where the curvilinear polygon has ``straight corners", that is, where each corner is locally isometric to the tip of a Euclidean sector. In the setting where the curvature is nontrivial all the way down to a corner, much less is known. In this talk, I will explain why the interaction of the curvature and corner does contribute to the heat trace expansion, characterize the form of this contribution, and compute it explicitly in a special case. This is joint work with Sam Looi (Caltech).
Galia Dafni (Concordia)
Dmitry Faifman (Université de Montréal)
Dmitry Jakobson (McGill)
Maria Ntekoume (Concordia)
Marcu-Antone Orsoni (ULaval)