Ring Theory SeminarSpeaker: Lucas Hataishi (University of Oxford)
Title: Inclusions of operator algebras from tensor categories
Date: 17/12/2025
Time: 10:00
Web: http://mat.uab.cat/web/ligat/
Abstract: The works of V. Jones and A. Ocneanu suggested the interpretation of subfactors as quantum symmetries. There is indeed a group-like object one can extract from a given subfactor, called the standard invariant, nowadays described as a W*-tensor category. In this talk, I will summarize this story, and report on my joint work with R. Hernández Palomares, where we study C*-algebraic inclusions through the subfactor philosophy, motivated by a topological quantum field theoretic construction called factorization homology.
Geometry SeminarSpeaker: Fabio Gironella (Université de Nantes - CNRS)
Title: On rigidity of Poisson homeomorphisms
Date: 18/12/2025
Time: 14:30
Web: http://mat.uab.cat/
Abstract: Symplectic topology/geometry is well known for being a huge source of interesting interactions between flexible, i.e. topological, and rigid, i.e. geometric, phenomena. Diffeomorphisms preserving symplectic structures, also called symplectomorphisms, are in particular an interesting class of diffeomorphisms as they exist in abundance, containing for instance all the time-1 Hamiltonian flows, but they are also more rigid than volume preserving diffeomorphisms, due e.g. to Gromov's non-squeezing theorem. Recently there has been a rising interest in the study of symplectic homeomorphisms, i.e. of homeomorphisms that are uniform C^0-limits of symplectomorphisms: indeed, they are in certain aspects more flexible than their smooth counterparts, while preserving some of their rigid features. In this talk I will report on a joint work in progress with Robert Cardona, where we study analogous C^0 questions in the more general context of Poisson geometry. Namely, I will discuss to what extent known results about symplectic homeomorphisms generalize to Poisson homeomorphisms, i.e. homeomorphisms that are uniform C^0-limits of Poisson diffeomorphisms.
Geometry SeminarSpeaker: Matthieu Madera (UAB)
Title: Holomorphic geometric structures on Hopf manifolds.
Date: 18/12/2025
Time: 15:30
Web: http://mat.uab.cat/
Abstract: Complex Hopf manifolds were the first known examples of compact non-Kähler complex manifolds. Their study is closely related to a classical result in holomorphic dynamics: the Poincaré–Dulac theorem. This theorem provides geometric information on Hopf manifolds, in particular the existence of holomorphic geometric structures. The aim of this talk is to present a kind of converse. I will explain how to construct holomorphic geometric structures on Hopf manifolds, such as G-structures or Cartan connections, without using the Poincaré–Dulac theorem. I will also show how the existence of these structures yields a new proof of the latter. These results extend recent work of Ornea and Verbitsky, obtained in the non-resonant case.