I professori Gilles G. de Castro (UFSC, Brasile) e Piotr M. Hajac (IMPAN, Varsavia) visiteranno il nostro dipartimento dal 28 gennaio al 7 febbraio 2026. Terranno un seminario giovedì 5 febbraio in aula SP1L.

Seguono titoli e abstract. Tutti gli interessati sono invitati a partecipare.

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SPEAKER: Piotr M. Hajac (IMPAN, Warsaw, Poland)

TIME: 14:30 – 15:15

TITLE: Computing associated projective modules using the Milnor clutching

ABSTRACT

Principal bundles can be viewed as strongly monoidal functors from the finite-dimensional representation category of a structure group to the category of associated vector bundles. Much in the same way, principal comodule algebras can be characterized as comodule algebras inducing a strongly monodoidal functor from the finite-dimensional corepresentation category of a structure Hopf algebra to the category of associated bimodules. Principal comodule algebras enjoy fully fledged cyclic-homology Chern-Weil theory that can be used to compute idempotents of the associated finitely generated projective modules and classify their K-theory classes. The goal of this talk is to present a new method of computing such idempotents using the celebrated Milnor’s connecting homomorphism in K-theory. Although one can always try to compute these idempotents using strong connections, such calculations can be very complicated. I will show that, in the case of piecewise-cleft principal comodule algebras, we have an alternative way to compute the idempotents using the Milnor clutching construction. The new method will be demonstrated in the setting of the K-theory of quantum complex projective planes. (Based on joint work with F.

D’Andrea, T. Maszczyk and B. Zielinski.)

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SPEAKER: Gilles G. de Castro (UFSC, Florianopolis, Brazil)

TIME: 15:30 – 16:15

TITLE: Algebras of one-sided subshifts over arbitrary alphabets

ABSTRACT

Given an alphabet, which can be infinite, we consider subshifts defined by a set of forbidden words as a combinatorial object and define algebras associated with them. When the alphabet is finite, these include Carlsen’s C*-algebras associated with subshifts. In this talk, I will explain how one naturally obtains a partial action from a subshift and how to use it to define the subshift algebras. As with graphs, even though we start with a combinatorial object, certain topological spaces arise from these algebras, one of them being the Ott-Tomforde-Willis

(OTW) subshift. I will show how these C*-algebras are related to the conjugacy of Ott-Tomforde-Willis subshifts. At the end, I will briefly talk about the K-theory of the subshift C*-algebras. (Joint work with G.

Boava, D. Gonçalves and D. van Wyk.)