2025 CMS Winter Meeting
Toronto, Dec 5 - 8, 2025
Analytic–Geometric Synergies: Harmonic Analysis and Convexity
Org: Almaz Butaev (University of the Fraser Valley), Galia Dafni (Concordia University) and Serhii Myroshnychenko (University of the Fraser Valley)
[PDF]
Org: Almaz Butaev (University of the Fraser Valley), Galia Dafni (Concordia University) and Serhii Myroshnychenko (University of the Fraser Valley)
[PDF]
- ALMUT BURCHARD, University of Toronto
- BLAIR DAVEY, Montana State University
Self-similar sets and Lipschitz curves [PDF]
- BLAIR DAVEY, Montana State University
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If E is a purely unrectifiable 1-set in the plane, then the intersection of E with any Lipschitz graph has zero 1-dimensional Hausdorff measure. This leads to a natural question: Given a purely unrectifiable 1-set, can we find a Lipschitz curve for which the intersection with E is non-trivial in some dimension less than 1? Going further, how close to 1 can we get? We discuss the answer to this question for self-similar sets. This talk covers joint work with Silvia Ghinassi and Bobby Wilson.
- DMITRY FAIFMAN, Université de Montréal
- FERENC FODOR, University of Szeged, Hungary
Central diagonal sections of Gaussian cubes [PDF]
- FERENC FODOR, University of Szeged, Hungary
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We consider Gaussian-type probability measures in the standard $n$-dimensional cube and study the induced measure of hyperplane sections through the origin and orthogonal to a main diagonal. Using a formula proved by K\"onig and Koldobsky (2013), we investigate the asymptotic behaviour of the measure of sections as $n$ tends to infinity. Joint work with Bernardo Gonzalez Merino (University of Murcia, Spain).
- RYAN GIBARA, Cape Breton University
- PAUL HAGELSTEIN, Baylor University
Current developments in the theory of differentiation of integrals [PDF]
- PAUL HAGELSTEIN, Baylor University
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We will provide an overview of current developments in the theory of differentiation of integrals. Particular emphasis will be placed on a recent result, extending prior work of Bateman and Katz, that provides a condition on directional maximal operators on $\mathbb{R}^2$ sufficient to ensure that they are unbounded on $L^p(\mathbb{R}^2)$ for $1 \leq p < \infty$. This recent work is joint with Blanca Radillo-Murguia and Alex Stokolos.
- ALEX IOSEVICH, University of Rochester
The Fourier ratio, probabilistic method and signal recovery [PDF]
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We are going to discuss the ratio of the L1 to L2 norms of the Fourier transform in a variety of different contexts as a proxy for the complexity of a signal. We are going to see that if the Fourier ratio is small, the signal can be well-approximated by a trigonometric polynomial of a low degree. Applications to signal recovery and connections with restriction theory of the Fourier transform will be discussed.
- DMITRY JACOBSON, McGill
Extremal metrics on graphs [PDF]
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We review several old and new results about extremal metrics for various graph functionals.
- PAVLOS KALANTZOPOULOS, Waterloo University
- LIANGBING LUO, York University
- MARCU-ANTONE ORSONI, Université Laval
- ANDRIY PRYMAK, University of Manitoba
On asymptotic Lebesgue's universal covering problem [PDF]
- LIANGBING LUO, York University
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A classical theorem of Jung states that any set of diameter 1 in an $n$-dimensional Euclidean space is contained in a ball $J_n$ of radius $\sqrt{\tfrac{n}{2n+2}}$; in other words, $J_n$ is a universal cover in $\mathbb{E}^n$.
Lebesgue’s universal covering problem, posed in 1914, asks for the convex set of smallest area that serves as a universal cover in the plane ($n=2$). We show that in high dimensions, Jung’s ball $J_n$ is asymptotically optimal with respect to volume: for any universal cover $U \subset \mathbb{E}^n$, $$ {\rm Vol}(U) \ge (1-o(1))^n{\rm Vol}(J_n). $$
Joint work with A. Arman, A. Bondarenko and D. Radchenko.
- SCOTT RODNEY, Cape Breton University
- YANA TEPLITSKAYA, Paris-Saclay University
About maximal distance minimizers. Regularity and explicit examples [PDF]
- YANA TEPLITSKAYA, Paris-Saclay University
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Consider a compact set $M \subset \mathbb{R}^d$ and $l>0$. A maximal distance minimizer problem is to find a connected compact set $\Sigma$ of the length (that is, one-dimensional Hausdorff measure $\mathcal{H}^1$) at most $l$ that minimizes
\[
\max_{y \in M} \text{dist}(y, \Sigma),
\]
where $dist$ stands for the Euclidean distance.
In this talk, I will survey known results on maximal distance minimizers, including explicit examples (such as a circle, a rectangle, and a minimizer with an infinite number of corner points), as well as the regularity of their local structure (a finite number of branching points in the plane and at most three tangent rays at any point of a minimizer in any dimension). I will also discuss several open problems in this area.
- DENIS VINOKUROV, Université de Montréal
- ELISABETH WERNER, Case Western Reserve University
- ELISABETH WERNER, Case Western Reserve University