Réunion d'hiver SMC 2025
Toronto, 5 - 8 decembre 2025
Analyse harmonique et EDP
Org: Galia Dafni (Concordia University), Ryan Gibara (Cape Breton University) et Scott Rodney (Cape Breton University)
[PDF]
Org: Galia Dafni (Concordia University), Ryan Gibara (Cape Breton University) et Scott Rodney (Cape Breton University)
[PDF]
- RYAN ALVARADO, Amherst College
- ALMAZ BUTAEV, University of the Fraser Valley
- ANA ČOLOVIĆ, University of Missouri
- APARAJITA DASGUPTA, Indian Institute of Technology Delhi
- JOSHUA FLYNN, Massachusetts Institute of Technology
- JESSE HULSE, University of Manitoba
- RITVA HURRI-SYRJÄNEN, University of Helsinki
- NGUYEN LAM, Memorial University of Newfoundland
Sharp Stability of the Second-order Heisenberg Uncertainty Principle [PDF]
- ALMAZ BUTAEV, University of the Fraser Valley
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In this talk, we present sharp stability estimates for the second-order Heisenberg Uncertainty Principle. We derive explicit lower and upper bounds for the associated sharp stability constants and determine their exact asymptotic limits as the dimension N tends to infinity. This is joint work with Anh Do, Guozhen Lu, and Lingxiao Zhang.
- JUYOUNG LEE, Universitiy of British Columbia
Variational inequalities for two-parameter averages over tori [PDF]
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Variational inequalities have been extensively studied in various branches of mathematics. In particular, variational inequalities for averaging operators provide valuable insights into the pointwise convergence properties of averages. While maximal averaging operators offer similar results, variational inequalities yield more refined and powerful information regarding the behavior of averages. In this talk, we focus on a variational inequality for a two-parameter averaging operator. Indeed, a well-defined formulation of variational inequalities for two-parameter averages has not yet been established. We introduce a precise definition for two-parameter averages over tori and present a sharp boundedness result.
- SULLIVAN MACDONALD, University of Toronto
Progress toward the Krzyz conjecture [PDF]
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The Krzyz conjecture is a long-standing open problem in complex analysis. Despite initially appearing simpler than related problems which have since been solved, such as the Bieberbach conjecture (now de Branges' Theorem), it remains open. If \(D\) is the unit disc and \(\mathcal{B}^*=\{f\in\textrm{Hol}(D)\;|\;0<|f|\leq 1\textrm{ in }D\}\), it states that (1) \(\sup_{f\in\mathcal B^*}|f^{(n)}(0)|/n!=2/e\) for any \(n\in\mathbb N\), and (2) the supremum is attained only by functions of the form \(e^{i\theta}f_0(e^{i\eta}z)\), where \(\theta,\eta\in\mathbb R\) and \(f_0(z)=\exp((z^n-1)/(z^n+1))\).\newline
In this talk we present recent work on the conjecture. Using techniques from classical harmonic analysis, we find new constraints on the singular inner functions which attain the supremum. It has long been known that extremal functions in \(\mathcal B^*\) for the \(n\)th coefficient exist and are of the form \[ f(z)=\exp\bigg(\sum_{j=1}^N\lambda_j\frac{e^{i\theta_j}z-1}{e^{i\theta_j}z+1}\bigg) \] for $N\leq n$, positive \(\lambda_1,\dots,\lambda_N\), and distinct \(\theta_1,\dots,\theta_N\in[0,2\pi)\). Using oscillatory integral methods, we show that \(N\geq c\,n\) for a universal constant \(c>0\). This marks modest progress toward proving the expected \(N=n\). Various other new properties of extremal functions and their consequences will also be discussed.\newline
Furthermore, we will report on progress related to other aspects of the conjecture.
- ÁNGEL DAVID MARTÍNEZ MARTÍNEZ, CUNEF Universidad
- YUVESHEN MOOROOGEN, University of British Columbia
- TIAGO PICON, Universidade de São Paulo
- CRISTIAN RIOS, University of Calgary
- YURIJ SALMANIW, Cape Breton University
- ERIC SAWYER, McMaster University
- SHAHABODDIN SHAABANI, University of Toronto
A view from above on $\text{JN}_p(\mathbb(R)^n$ [PDF]
- YUVESHEN MOOROOGEN, University of British Columbia
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In this talk, we discuss the John--Nirenberg space $\text{JN}_p(\mathbb{R}^n)$ from the tent-space point of view. We show how the ``tent perspective'' on this space leads to a natural extension of the Riesz--Markov--Kakutani representation theorem to the upper half-space $\mathbb{R}^{n+1}_+$. We also demonstrate that this extension connects such representation theorems to well-known combinatorial geometric problems concerning intersection graphs of shapes and their chromatic numbers. If time permits, we will discuss an application related to the construction of functions in $\text{JN}_p(\mathbb{R}^n)$.
- IGNACIO URIARTE-TUERO, University of Toronto
- DIMITER VASSILEV, University of New Mexico
- KATJA VASSILEV, University of Chicago
- CHENJIAN WANG, University of British Columbia
- JULIAN WEIGT, Abdus Salam International Centre for Theoretical Physics
- ALEXIA YAVICOLI, The University of British Columbia
The Erdős similarity problem for non-small Cantor sets [PDF]
- DIMITER VASSILEV, University of New Mexico
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I will introduce the Erdős similarity problem, providing background and an overview of known partial results. I will then discuss a recent joint work with P. Shmerkin, in which we show that Cantor sets with positive logarithmic dimension satisfy the conjecture.