# Hi. I'm Gabriele Tornetta.

I'm a Postgraduate Student at the School of Mathematics and Statistics of the University of Glasgow.

I'm part of the Analysis research group within the School and my research is focused on Operator Algebras. I work under the supervision of Dr. Joachim Zacharias.

## The Bivariant Cuntz Semigroup

A novel invariant for the classification of C*-algebras.

According to the Elliott's Conjecture, a rather vast class of C*-algebras can be classified by means of K-theoretic data. A counterexample due to Andrew Toms shows that the Cuntz Semigroup should be included in the set of Elliott's invariants. KK-theory is another tool that can be employed for the purpouses of the classification of C*-algebras (cf. Kirchberg-Phillips).

The Bivariant Cuntz Semigroup is an attempt towards the definition of a new invariant, based on the idea of comparison of positive elements, as in the Cuntz semigroup, but with a bifunctor flavour, much like KK-theory. As completely positive maps of order zero induce maps between Cuntz semigroups, one can postulate that the right definition of such a new theory should be based on the introduction of an equivalence relation between such maps.

Under some simplifying assumption, one can carry out some standard simplification in the formulation of KK-theory. The open projection picture of the Cuntz Semigroup might offer a similar simplification for this new bivariant theory, so we have further explored its implications. From this analysis it emerged that the Scale of the Cuntz semigroup can be identified with the set of Cuntz-equivalence classes of positive elements from the positive cone of the C*-algebra.

### Resources

Towards the Bivariant Cuntz Semigroup, Mathematisches Institut, Fachbereich Mathematik und Informatik der Westfälische Wilhelms-Universität Münster (January 14, 2013), Münster, Germany (slides).

## List of publications

• Open projections and hereditary subalgebras with applications to the Cuntz semigroup, Joan Bosa, Gabriele Tornetta, Joachim Zacharias, in preparation.
• A scale-covariant quantum spacetime, Claudio Perini, Gabriele N. Tornetta, Rev. Math. Phys., Vol 27, No 4 (May 2014), DOI: 10.1142/S0129055X14500068, arXiv:1211.7050
• ## Duties

Work that I have done during the years. You can find my full CV here.

### University of Glasgow

School of Mathematics and Statistics
• Committee member of the University of Glasgow Snooker Club with the role of Ordinary Member, 2014/15.
• Member of the Postgraduate Staff and Student Committee, 2012 - present.
• Tutor for the 1S course, 2013/14
• Tutor for the 2D course Topics in Linear Algebra and Calculus, 2013/14
• Tutor for the 1R course, 2013/14
• Tutor for the 2A course Multivariable Calculus, 2013/14
• Tutor for the 2E course Introduction to Real Analysis, 2012/13
• Tutor for the 2T course Discrete Mathematics, 2012/13
• Tutor for the 2C course Topics in Applied Mathematics, 2012/13
• Tutor for the 2M course Financial Modelling, 2012/13
• Invigilator for the Maths Skills Test, 2012 - 2014
• ## Extra

The other me, outside of the research world...in some randomly scattered and unorganised thoughts.

I'm very passionate about Sport. I used to practice team sports, like Football and Volleyball. I enjoyed my youth playing as a goalkeeper and a setter. I practices some martial arts too, specifically Ju Jutsu and Anti-Terror-Kampf.

At the University of Glasgow I managed to get into the Man's Volleyball Club of which I've been member for two years already.

I've always enjoyed watching Snooker on TV when I was a teenager, and in Glasgow I had the chance to join the Snooker Club of the University and play this game. I managed to get into the second team to represent the University of Glasgow in the 2014 edition of the BUCS Snooker Championship in Leeds.

I started studying Chinese while still in Rome, and I could immerse myself more into this language thanks to the Confucius Institute of Glasgow. As a personal interest I'm also studying German on my own. My Spanish-speaker friends at the University of Glasgow are offering me an extremely good chance to improve my Spanish as well.

One of my hobbies remains Application Development. After a lot of experience with languages like C, C++, x86 assembly and python, to name a few, I started developing an interest for Android applications, which I intend to combine with my passion for Snooker. My favourite operating system has been Ubuntu since the auld times of Breezy Badger.

g (dot) tornetta (dot) 1 (at) research (dot) gla (dot) ac (dot) uk
Room 309
School of Mathematics and Statistics, University of Glasgow
15 University Gardens
G12 8QW
Glasgow
Scotland