July 30th, 1:00 P.M. BRT – Marco Vitturi (University College Cork)

Talk: The bilinear version of a result of Stein and Wainger

Abstract: In 2001 Stein and Wainger showed that the polynomial Carleson operators without linear term in the phase are all L^p bounded for any 1 < p < \infty (with a constant depending on the maximum polynomial degree allowed in the supremum). By replacing the linear singular integrals in the definition of such operators with the bilinear Hilbert transform we obtain a natural bilinear variant. We are then able to show that this bilinear variant is L^p x L^q -> L^r bounded in the same range of exponents for which the Bilinear Hilbert transform is known to be bounded, at least when the phase is restricted to be a multiple of a chosen polynomial - but the resulting constant only depends on the degree of the polynomial. Joint work with C. Benea, F. Bernicot, V. Lie.

Meeting link: https://meet.google.com/mvu-djoo-oes

July 21st, 1:00 P.M. BRT – Vjekoslav Kovač (University of Zagreb)

Talk: Density theorems for anisotropic point configuration

Abstract: Several results in the existing literature establish Euclidean density theorems of the strongest possible type. These results claim that every set of positive upper Banach density in the Euclidean space of an appropriate dimension contains isometric copies of all sufficiently large elements of a prescribed family of finite point configurations. So far, all results of this type discussed linear isotropic dilates of a fixed point configuration. In this note we initiate the study of analogous density theorems for families of point configurations generated by anisotropic dilations, i.e., families with power-type (e.g., polynomial) dependence on a single parameter (interpreted as their size). Another source of motivation for this talk is providing additional evidence for the versatility of the "largeness-smoothness approach" stemming from the work of Cook, Magyar, and Pramanik. Finally, yet another purpose of this talk is to single out anisotropic multilinear singular integral operators associated with the above combinatorial problems, as they might be interesting on their own.

Meeting link: https://meet.google.com/mvu-djoo-oes

July 14th, 1:00 P.M. BRT – Emanuel Carneiro (ICTP/IMPA)

Talk: Sunrise and the continuity of maximal operators

Abstract: We will explore how some insightful constructions related to the classical sunrise lemma in harmonic analysis can be used in connection to the endpoint continuity of certain maximal operators in Sobolev spaces. The statement of the main theorem of the lecture will look rather innocent and inviting, which will turn out to be somewhat deceiving. The proof will reveal the beautiful and subtle maze to be explored. This is based in a joint work with Jose Madrid and Cristian Gonzalez-Riquelme.

Meeting link: https://meet.google.com/mvu-djoo-oes

July 7th, 1:00 P.M. BRT – Danylo Radchenko (ETH Zürich)

Talk: Fourier interpolation from zeros of zeta and related problems

Abstract: I will talk about a recent result that shows that any sufficiently nice even analytic function can be recovered from its values at zeros of zeta(1/2+is) and the values of its Fourier transform at logarithms of integers. I will also discuss some related results and open problems. The talk is based on a joint work with Andriy Bondarenko and Kristian Seip.

Meeting link: https://meet.google.com/mvu-djoo-oes

July 2nd, 1:00 P.M. BRT – Carlos Pérez Moreno (University of the Basque Country/BCAM Bilbao)

Talk: BMO, old and new results: a tribute to B. Muckenhoupt and R. Wheeden

Abstract: It is well known the importance of the BMO space of functions with bounded mean oscillation especially due to the famous John-Nirenberg theorem of the early 60’s of the last century. This theorem was extended by B. Muckenhoupt and R. Wheeden in several directions including weights which turned out to be very useful in different situations. In this talk we will show that these weighted BMO results can be improved by an alternative proof that allows a better control of the key constants involved. If the time allows, we will discuss that the main idea above gives a way of defining the standard BMO using much weaker conditions than the usual L^1 oscillation. The first part is joint work with J. Canto and the second part with J. Canto and E. Rela.

Meeting link: https://meet.google.com/vmh-wrvi-efg

June 25th, 1:00 P.M. BRT – Dimitrije Cicmilovic (Universität Bonn)

Talk: Symplectic non-squeezing and Hamiltonian PDE

Abstract: In this talk we shall discuss infinite dimensional generalization of Gromov's sympelctic nonsqueezing result. As an application we will present mass subcritical and critical nonlinear Schrodinger equation. Nonsqueezing property of the said flows was already known, however the techniques used are based on finite dimensional Gromov's result, while ours presents a more natural way of looking at the infinite dimensional Hamiltonian structure of the equations. Additionally, we shall remark on future projects in terms of application of the non-squeezing property. Joint work with Herbert Koch.

Meeting link: https://meet.google.com/xdb-htwt-eam

June 18th, 1:00 P.M. BRT – Oscar Emilio Quesada Herrera (IMPA)

Talk: Generalized sign Fourier uncertainty

Abstract: The classical theme of Fourier uncertainty, roughly, is that one cannot have unrestricted control of a function and its Fourier transform, simultaneously. We will discuss a generalized (weighted) version of the uncertainty principle for signs.

In our setup, the signs of a function and its Fourier transform resonate with a generic given function P outside of a ball. One essentially wants to know if and how soon this resonance can happen, when facing a suitable competing weighted integral condition. The original version of the problem corresponds to the case P ≡ 1. Surprisingly, even in such a rough setup, we are able to identify sharp constants in some cases. This is joint work with Emanuel Carneiro.

Meeting Link: https://meet.google.com/vmo-uhhb-jmr

June 9th, 1:00 P.M. BRT – Olli Saari (Universität Bonn)

Talk: Energy contractivity and gradient flows

Abstract: Several interesting time-dependent PDEs arise as gradient flows of energy quantities related to Sobolev spaces: the heat equation, the p-parabolic equation and the total variation flow. They represent evolutions along which the energy decreases (Lyapunov principle). In this talk, I discuss a maximal version of the Lyapunov principle for the p-parabolic equation. This is based on a joint work with Simon Bortz and Moritz Egert.

Meeting link: https://meet.google.com/hho-moss-jie

June 2nd, 1:00 P.M. BRT – Federico Glaudo (ETH Zürich)

Talk: On Cabré's ABP method

Abstract: In 2000, Cabré found a beautiful proof of the classical isoperimetric inequality exploiting an idea originally used by Alexandrov-Bakelman-Pucci to show an important result in partial differential equations (the ABP estimate).

A large part of this talk will be devoted to present the proof by Cabré, then I will describe two recent applications of his idea: the proof, by Brendle, of the isoperimetric inequality for minimal surfaces and the proof of the quantitative stability for a class of isoperimetric inequalities with weights.

Part of this talk is about a joint work with E. Cinti, A. Pratelli, X. Ros-Oton, J. Serra.

Meeting link: https://meet.google.com/wmr-yghv-vcg

May 28th, 1:00 P.M. BRT – Kristian Seip (NTNU Trondheim)

Talk: Fourier interpolation from zeros of zeta and L-functions

Abstract: The main result of this talk is a new construction of Fourier interpolation bases giving in particular a basis associated with the nontrivial zeros of the Riemann zeta function. On our way to this result, we establish a general duality principle for Fourier interpolation bases in terms of certain kernels of general Dirichlet series with variable coefficients. Such kernels admit meromorphic continuation, with poles at a sequence dual to the sequence of frequencies of the Dirichlet series, and they satisfy a functional equation. Our construction of concrete bases relies on a strengthening of Knopp's abundance principle for Dirichlet series with functional equations and a careful analysis of the associated Dirichlet series kernel, with coefficients arising from certain modular integrals for the theta group. The talk is based on joint work with Andriy Bondarenko and Danylo Radchenko.

Meeting link: https://meet.google.com/deo-vkiu-ppu

May 26th, 1:00 P.M. BRT – Cristian González Riquelme (IMPA)

Talk: Sharp p-bounds for maximal operators on finite graphs.

Abstract: Maximal operators are a central theme in harmonic analysis. Historically, the main interest have been the properties of the L^p-norm (or L^{1,weak}-norm) of these operators. In other words, one is interested in how big can be the L^p-norm (or L^{1,weak}-norm) of a maximal function. Along the last century, many researchers have been working on estimates for these norms for different classes of operators and in several contexts. More recently, questions about the p-variation of these operators have caught attention. In short, one is interested in how big can be the p-variation of a maximal function.

In this talk, we will introduce these two kinds of questions in the context of finite graphs and we will present recent progress concerning sharp results for both kinds of problems in this setting. This is joint work with José Madrid.

Meeting link: https://meet.google.com/wdd-ygzo-wdb

May 21st, 1:00 P.M. BRT – Luccas Campos (UFMG)

Talk: Threshold solutions to the NLS equation

Abstract: It is known from the works of Kenig-Merle (in the energy-critical regime), Duyckaerts-Holmer-Roudenko and Fang-Xie-Cazenave (in the mass-supercritical and energy-subcritical regime) that the ground state for the NLS equations establishes a mass-energy threshold, below which there is a dichotomy between scattering and blow-up.

In this talk, we aim to describe the behavior of solutions to the NLS equation that lie exactly at the threshold. We will show the existence of special solutions, that are close to the standing wave in one time direction and either scatter or blow up in the oposite direction, and then we will completely classifiy the possible behaviors at the threshold.

Meeting link: https://meet.google.com/cri-aivn-ufw

May 14th, 1:00 P.M. BRT – Felipe Gonçalves (Universität Bonn)

Talk: Sign Uncertainty

Abstract: We will talk about recent developments of the sign uncertainty principle. These are in turn connected with packing bounds, spherical designs and measures of complexity for Boolean functions. This is joint work with J. P. Ramos and D. Oliveira e Silva.

Meeting link: https://meet.google.com/fhs-oudi-dra

May 7th, 10:30 A.M. BRT – João Pedro Ramos (IMPA)

Talk: Recent Progress on Fourier Uncertainty

Abstract: The classical Heisenberg Uncertainty Principle shows that a function and its Fourier transform cannot be too concentrated around a point simultaneously. In other words, if we force a function and its Fourier transform to vanish outside a small neighborhood of a point, then the function is zero. This classical principle has been generalized to many levels in the past, including results of Hardy, Beurling and many others. In this talk, we will recall old and new results about Fourier ncertainty, focusing more on the most recent developments on the field and its relationship to various topics, such as the sphere packing problem, interpolation formulae and many others.

Meeting link: https://meet.google.com/zjz-yqpc-hhf