NCG seminars at SISSA

[Emanuele Tuillier Illingworth]

====================================================

*"NON-COMMUTATIVE GEOMETRY" SEMINAR 
<https://www.math.sissa.it/content/non-commutative-geometry-seminars>*

Wednesday 2 December 11:00, SISSA room 136

John Barrett, Nottingham (UK)
"The non-commutative geometry of defects"

Abstract. A diagrammatic calculus for finite real spectral triples is
introduced. This calculus relates the axioms of non-commutative geometry
with geometric properties of the diagrams. The diagram calculus determines
a two-dimensional topological quantum field theory with defects.
Conversely, defects in a TQFT determine a generalised notion of
non-commutative geometry.

-----------------------------------------------

*"NON-COMMUTATIVE GEOMETRY" SEMINAR 
<https://www.math.sissa.it/content/non-commutative-geometry-seminars>*
Joint session with *"ANALYSIS, MATH-PHYS, AND QUANTUM" SEMINAR 
<http://people.sissa.it/%7Ealemiche/qm-seminar>*

Thursday 3 December 16:15, SISSA room 136

John Barrett, Nottingham (UK)
"Random non-commutative geometries"

Abstract. Real spectral triples with a finite-dimensional Hilbert space
are introduced. An example is the fuzzy sphere, which approximates the
Riemannian sphere in a certain way (arXiv:1502.05383). Random
non-commutative geometries are introduced by integrating over the space of
Dirac operators that form a spectral triple with a fixed algebra and
Hilbert space. Lisa Glaser and I have investigated the properties of
simple cases of this statistical system using Monte Carlo methods
(arXiv:1510.01377). Preliminary results indicate that some of the models
have a phase transition, with interesting behaviour near the transition.

====================================================