# Workshop on Harmonic analysis, Singular Integrals and PDEs

**Dates:** January 31 - February 4, 2022**Venue:** HIM lecture hall, Poppelsdorfer Allee 45, Bonn

Due to COVID-19, participation must be coupled with proof that each participant is either fully COVID-19 vaccinated or cured from COVID-19 (so-called "2G"). This procedure corresponds to the current hygienic regulations. Participation can therefore only be allowed to registered participants, who will be informed about the corresponding on-site procedure in due time.

The workshop will be held as a hybrid event. The lectures given during the workshop will be recorded by default.

Organizers: Marianna Csörnyei (Chicago), Tuomas Orponen (Jyväskylä), Xavier Tolsa (Barcelona), Tatiana Toro (Washington), Alexander Volberg (Michigan)

Click here for the schedule.

Click here for the abstracts.

# Video Recordings:

# Day 1

Joseph Feneuil: Carleson estimates on solutions in domains with uniformly rectifiable boundaries

Bruno Poggi: Some eigenvalue counting problems for the magnetic Schrödinger operator and their solutions via the Filoche Mayboroda landscape function

Mihalis Mourgoglou: The regularity problem for the Laplace equation in rough domains

Ben Jaye: Two Extremal Classes of Measures Associated to Singular Integral Operators

Giacomo Del Nin: Endpoint Fourier restriction and unrectifiability

# Day 2

Kaj Nyström: Parabolic operators: fractional powers, weights and Kato

Mingming Cao: Absolute continuity of elliptic measure in 1-sided NTA domains satisfying CDC

Chanden Biswas: On extremizers for Fourier restriction onto the moment curve

Martí Prats: The two-phase problem for harmonic measure in VMO via jump formulas for the Riesz transform

Carmelo Puliatti: L^2 -boundedness of gradients of single layer potentials for elliptic operators with coffiecients of Dini mean oscillation-type

Max Engelstein: Harmonic analysis techniques for (Almost-)Minimizers

# Day 3

Steve Hofmann: Quantitative rectifiability in the parabolic setting: a survey of recent progress

Paolo Bonicatto: Moving Currents: on the Lie transport equation and a Rademacher type theorem

Tomasz Adamowicz: Geometry of level sets of harmonic functions and p-harmonic mappings: convexity, curvature, isoperimetric inequalities for PDE and three-spheres theorems

Alan Chang: Analytic capacity and projections

Damian Dabrowski: Vitushkin's conjecture and sets with plenty of big projections

# Day 4

Keith Rogers: Improved bounds for the Kakeya conjecture using semialgebraic geometry

Hong Wang: Distance sets spanned by sets of dimension d/2

# Day 5

José María Martell: Layer potentials, Extrapolation, and Boundary Value Problems in unbounded domains

Michele Villa: Quantitative affine approximation on uniformly rectifiable sets

Max Goering: Regularity and a degenerate class of PDEs stemming from anisotropic minimal surfaces

Dmitriy Bilyk: Discrete minimizers of energy intervals

Stefano Decio: Bounds on the Hausdorff measure of zero sets of Steklov eigenfunctions

Mariana Smit Vega-Garcia: Almost minimizers for obstacle problems