Anàlisi

On Tangential and Projectively Adjacent Approach Regions
Fausto Di Biase (Università "G. D'Annunzio" di Chieti-Pescara)
Dia: 29/01/2026
Hora: 15:00
Lloc: CRM

Resum: In 1906 Fatou proved that bounded holomorphic functions on the unit disc converge a.e. on the boundary along nontangential approach regions. In 1927 Littlewood proved a “negative” result, i.e., that a.e. convergence fails for certain approach regions: More precisely, it fails for the rotationally invariant families of tangential approach regions that end curvilinearly at the boundary. The fact that tangential approach regions which end sequentially at the boundary may instead be very well conducive to a.e. convergence was understood more recently by W. Rudin (in 1979) and A. Nagel and E.M. Stein (in 1984), in contributions that provided additional and much needed insight, and that prompted the question of giving an a priori description of those families of tangential approach regions which end sequentially at the boundary and for which a.e. convergence fails. Our main result is the first one of this kind. Indeed, we prove the failure of a.e. convergence for a class of approach regions, introduced in this work, which we call projectively adjacent, that contains curvilinear approach regions as well as sequential ones. Our result recaptures the aforementioned theorem of Littlewood as well as some of the other theorems of that type, but its novelty lies in the fact that, while all previous “negative” results for tangential approach (Littlewood, 1927; Lohwater and Piranian, 1957; Aikawa, 1990-1991, and others) dealt with approach regions that either are curves or share with curves a certain topological property that excludes the possibility that they could end sequentially at the boundary, our “negative” result deals with a class of approach regions that contains both the curvilinear and the sequential ones. Hence we present a significant extension of the class of those families of approach regions for which a.e. convergence fails.

Based on work in collaboration with Olof Svensson and Haguma Gratien.

Geometria

Projective background of (2+1)-spacetimes of constant curvature
Roman Prosanov (UAB)
Dia: 30/01/2026
Hora: 12:00
Lloc: Dpt Matematiques, Seminari C3B (C3B/158)

Web: Departament de Matemàtiques de la UAB

Resum:
William Thurston in his Geometrization Program suggested a new approach to locally homogeneous Riemannian structures and highlighted their significance for 3-dimensional topology. It was soon recognized that Thurston's approach is also very fruitful in non-Riemannian settings, particularly in Lorentzian, as it was demonstrated by the pioneering work of Geoffrey Mess on (2+1)-spacetimes of constant curvature. Geometries of constant curvature, whether Riemannian or Lorentzian, can be considered as subgeometries of projective geometry, which in particular allows to perform interesting geometric transitions between different geometries. In my talk I will describe how this viewpoint allows to deduce rigidity results on anti-de Sitter (2+1)-spacetimes using the resolution of analogous problems in the setting of Minkowski spacetimes. The talk is partially based on joint works with François Fillastre and Jean-Marc Schlenker.

Teoria d'Anells

The multiplicative group of a finite skew left brace of nilpotent type
Ferran Cedó (UAB)
Dia: 14/01/2026
Hora: 12:00
Lloc: Dpt Matematiques, Seminari C3B (C3B/158)

Web: Laboratori d'Interaccions entre Geometria, Àlgebra i Topologia

Resum: It is known that the multiplicative group of a finite skew left brace of nilpotent type is solvable. We conjecture that every finite solvable group is isomorphic to the multiplicative group of some skew left brace of nilpotent type. In this talk, we shall show some results that support this conjecture.