Time Zone Notice.
All talk times listed below are in US Central Time (America/Chicago).
To view a talk in your local time zone, click the “view in your time zone” link under that talk.
Note: The final hour on March 8 (11:00 AM–12:00 PM, US Central) is reserved as a buffer / discussion period.
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Talk 01 — Parasar Mohanty (IIT Kanpur, India) — [computing…]Local time: click here to view in your time zoneTitle: Endpoint estimate of rough maximal singular integral operator
Abstract
Singular integral operators, introduced by Calder\'on and Zygmund in the 1950s, remain fundamental in Fourier analysis. While the classical theory covers smooth kernels, rough singular integrals require deeper methods. Endpoint boundedness questions were settled through work of Seeger and, more recently, Xudong Lai, improving earlier results of Bhojak and Mohanty. This talk surveys these developments and ends with new endpoint weighted estimates for the associated maximal operator.
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Talk 02 — Palle Jorgensen (University of Iowa, USA) [CANCELLED]Status: This talk was cancelled.Title: Hilbert space valued Gaussian processes, their kernels, factorizations, and covariance structure
Abstract
We introduce a general and new framework for operator valued positive definite kernels. We give applications both to operator theory, dynamics, and to stochastic processes. The first one yields several dilation constructions in operator theory, and the second to general classes of stochastic processes. For the latter, we apply our operator valued kernel-results in order to build new Hilbert space-valued Gaussian processes, and to analyze their structures of covariance configurations.
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Talk 03 — Sui Tang (UCSB, USA) — [computing…]Local time: click here to view in your time zoneTitle: Operator estimation in dynamical sampling
Abstract
Dynamical sampling explores the recovery of dynamical systems using limited space-time samples. This presentation will focus on recent theoretical and algorithmic advancements in reconstructing evolution operators from these sparse space-time samples.
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Talk 04 — Nathan A. Wagner (George Mason University, USA) — [computing…]Local time: click here to view in your time zoneTitle: Optimal Sparse Bounds and Commutator Characterizations Without Doubling
Abstract
We examine dyadic paraproducts and commutators in the non-homogeneous setting, where the underlying Borel measure $\mu$ is not assumed doubling. We first establish a pointwise sparse domination for dyadic paraproducts and related operators with symbols $b \in \mathrm{BMO}(\mu)$, improving upon a result of Lacey, where $b$ satisfied a stronger Carleson-type condition coinciding with $\mathrm{BMO}$ only in the doubling case. As an application, we derive sharpened weighted inequalities for the commutator of a dyadic Hilbert transform $H$ previously studied by Borges, Conde Alonso, Pipher, and Wagner. We also characterize the symbols for which $[H,b]$ is bounded on $L^p$ for $1<p<\infty$, and provide examples showing that this symbol class lies strictly between those satisfying the $p$-Carleson packing condition and those belonging to martingale $\mathrm{BMO}$. This talk is based on joint work with Francesco D’Emilio, Yongxi Lin, and Brett D. Wick.
This talk is based on joint work with Francesco D’Emilio, Yongxi Lin, and Brett D. Wick. -
Talk 05 — Alexia Yavicoli (The University of British Columbia, Canada) — [computing…]Local time: click here to view in your time zoneTitle: The Erdős similarity problem for non-small Cantor sets
Abstract
The Erdős similarity conjecture posits that any infinite set of real numbers cannot be affinely embedded into every measurable set of positive Lebesgue measure. I will show that Cantor sets of "positive logarithmic dimension" satify the Erdős similarity conjecture. This talk is based on a work with Pablo Shmerkin.
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Talk 06 — Izabella Laba (The University of British Columbia, Canada) — [computing…]Local time: click here to view in your time zoneTitle: On the minimal period of integer tilings
Abstract
A finite set A ⊂ Z is said to tile the integers by translations if there exists a set T ⊂ Z such that each integer x ∈ Z has a unique representation x = a + t with a ∈ A and t ∈ T. It is well known that each such tiling must be periodic, so that T = B+ MZ for some M ∈ N and a finite set B ⊂ Z. An interesting question that is still open is to estimate the minimal period of such tilings. We will review what is currently known on the subject, with both upper and lower bounds on minimal tiling periods. The talk will be based in part on my joint work with Dmitrii Zakharov.
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Talk 07 — Phuc Cong Nguyen (Louisiana State University, USA) — [computing…]Local time: click here to view in your time zoneTitle: Some new capacitary inequalities and related function spaces
Abstract
Motivated by a conjecture of D. R. Adams, we present some new capacitary strong type inequalities that generalize the classical capacitary strong type inequality of V. G. Maz'ya. As a consequence, we characterize related function spaces as K\"othe duals to a class of Sobolev multiplier type spaces. Related results on the boundedness of the Hardy-Littlewood and spherical maximal functions on Choquet spaces will also be discussed. This talk is based on joint work with Keng H. Ooi.
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Talk 08 — Dorin Dutkay (University of Central Florida, USA) — [computing…]Local time: click here to view in your time zoneTitle: Fuglede’s conjecture and unitary groups of translations
Abstract
The Fuglede Conjecture relates the existence of orthonormal Fourier series on a measurable subset $\Omega$ of $\mathbb R^d$, also called the spectral properties of $\Omega$, to the geometric/tiling properties of this set. The conjecture originates in a question of Irving Segal about the existence of commuting self-adjoint extensions of the partial differential operators in $L^2(\Omega)$. Such extensions give rise to a unitary group $\{U(t)\}_{t\in\mathbb R^d}$, and the converse is also true due to Stone's Theorem. We will present the connection between the spectral properties of $\Omega$, the existence of such extensions of the partial differential operators, and the properties of the associated unitary group.
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Talk 09 — Naga Manasa Vempati (Louisiana State University, USA) — [computing…]Local time: click here to view in your time zoneTitle: Boundedness and Compactness of Bloom Sparse operators
Abstract
We will discuss several boundedness and compactness characterizations for sparse operators and singular integrals, briefly discussing the the tools used in obtaining these characterizations.
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Talk 10 — Razvan Teodorescu (University of South Florida, USA) — [computing…]Local time: click here to view in your time zoneTitle: Connectivity bounds in quantization on 2D domains
Abstract
Two-dimensional quantum systems have been studied for a long time as a rich source of exact models in quantum field theory, especially with a focus on classical conformal symmetry and its quantum deformations. We consider the role of domain connectivity in constructing such a quantum field theory, specifically topological constraints induced by connectivity on the deformation quantization procedure. We prove that the domain connectivity cannot exceed n=2, and explore the implications of this constraint on the physical phenomena described by the theory.
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Talk 11 — Pu-Ting Yu (University of Oregon, USA) — [computing…]Local time: click here to view in your time zoneTitle: Density of Unconditional Gabor Schauder frames
Abstract
A famous density theorem by Christensen, Deng and Heil states that the Beurling density of the time-frequency shifts associated with a Gabor frame must be somewhere between 1 and infinity. This result provides a monumental criterion characterizing certain Gabor systems that admits a reconstruction formula in the L2 space. The final missing piece in this direction is the density associated with unconditional Gabor Schauder frames. In this talk, we complete this missing piece by showing the Beurling density associated with an unconditional Gabor Schauder frame must be somewhere between 1 and infinity as well (could be equal to infinite). We then apply this result to show that if a closed subspace of L2 is closed under modulation and contains a nonzero function in the Feichtinger algebra, then it does not admit any unconditional Schauder frame of translates.
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Talk 12 — Cody Stockdale (Clemson University, USA) — [computing…]Local time: click here to view in your time zoneTitle: Sharp weighted weak-type bounds for operators
Abstract
The area of weighted norm inequalities has been at the forefront of harmonic analysis since the seminal work of Muckenhoupt et al. in the 1970s. More recently, researchers have sought sharp bounds with respect to A_p weight characteristics. We discuss new quantitative weak-type bounds for operators in harmonic and complex analysis.
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Talk 13 — Qiyu Sun (University of Central Florida, USA) — [computing…]Local time: click here to view in your time zoneTitle: Linearization of Nonlinear Dynamical Systems
Abstract
Taylor expansion and Fourier expansion have been widely used to represent functions. A natural question is whether there is some analog for nonlinear dynamic systems. In this talk, we consider Carlemen linearization and Carleman-Fourier linearization of nonlinear dynamical systems and show that the primary block of the finite-section approach has exponential convergence to the solution of the original dynamical system.
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Talk 14 — Dmitry Ryabogin (Kent State University, USA) — [computing…]Local time: click here to view in your time zoneTitle: On floating bodies and related topics
Abstract
We will discuss how some classical methods of Harmonic Analysis are applied to several problems on sections and projections of convex bodies.
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Talk 15 — Lars Niedorf (UW Madison, USA) — [computing…]Local time: click here to view in your time zoneTitle: Bochner-Riesz means on Heisenberg groups
Abstract
We discuss recent sharp Bochner-Riesz estimates for sub-Laplacians on Heisenberg groups. Since favorable restriction estimates fail in this setting, we developed an approach that relies on square function bounds for the wave equation associated with the sub-Laplacian. This is joint work with Detlef Müller, Andreas Seeger, and Betsy Stovall.
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Talk 16 — Chenxing Qian (University of Pittsburgh, USA) — [computing…]Local time: click here to view in your time zoneTitle: Constrained Quantization for Compactly Supported Measures: Dimension and Asymptotic Analysis from a GMT Perspective
Abstract
This talk explores the high-rate constrained quantization of a probability measure $P$ on $\mathbb{R}^D$, focusing on the interplay between measure-theoretic properties and the geometry of constraints. Given a closed constraint set $S$, we analyze how the metric projection $\pi_S$ acts as a fundamental operator that transforms the support $K$ and governs the quantization error asymptotics. From a Harmonic Analysis and GMT perspective, we characterize the error decay through the lens of dimensional analysis and scaling properties. By establishing a "projection pull-back inequality," we link the upper bounds to the covering geometry of $\pi_S(K)$. For the lower bounds, we utilize a weighted distance perturbation argument, applicable whenever the projected image is nowhere dense—a condition naturally satisfied in many non-overlapping cases. The proof combines covering/packing geometry, dimension comparison, and projection-based pull-back estimates in a GMT/HA framework. Our main result identifies that for measures whose push-forwards $(\pi_S)_\# P$ exhibit Ahlfors $d$-regularity, the quantization error scales as $n^{-1/d}$. This provides a definitive dimension comparison formula that bridges the gap between discrete approximation and the fractal dimensions arising in Dynamics (e.g., self-similar measures). These findings extend classical unconstrained theory to general closed constraints, highlighting the profound role of projection geometry in optimal transport and data compression.