Seminario di Dipartimento - 18/01/2024

giovedì 18 gennaio alle ore 11.30 in Sala di Consiglio


Giovedì 18 gennaio alle ore 11.30 in Sala di Consiglio si terrà il Seminario di Dipartimento del dott Valeriano Aiello, risultato vincitore di una procedura selettiva per una posizione da RTT nel SC 01/A3, SSD MAT05.

Speaker: Valeriano Aiello

Titolo: Some Results on Thompson Groups, Their Unitary Representations, a Knot Construction by Jones, and on some Cuntz Algebras

In 2014, Vaughan Jones introduced methods to construct unitary representations of Thomp- son groups F, T, V (from planar algebras or Cuntz algebras) and another to produce knots from their elements. These unitary representations have been instrumental in understanding the subgroup structure of F, while the knot construction allows for the initiation of a new theory analogous to that of braids and knots, but with the Thompson groups replacing the braid groups. On another topic, several C-algebras have been introduced by Cuntz and collaborators. The p-adic ring C-algebra is the universal C-algebra Qgenerated by an isometry sand a unitary u such that spu = upsand  ∑{i=0}{p-1} uis2s2u−i = 1. This algebra turns out to be simple and purely infinite. 
Inside Qp, the isometries T0 = sp, T1 = usp, . . . , T p − 1 = up−1sp generate a natural copy of the Cuntz algebra Op. I will report on some results regarding them.



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