Joint ICTP/SISSA Condensed Matter Seminar, 17 January at 11:30am, Ginestra Bianconi

[CMSP Seminars Secretariat]

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  Joint ICTP/SISSA Condensed Matter Seminar
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** * * Tuesday**, 17 January 2023, 11:30**am ***(CET)** * **
In person: *Luigi Stasi Seminar Room **(Leonardo Building, second floor)***
**
/Zoom: 
/https://zoom.us/meeting/register/tJIsfuuhqjsrE9EZY2loNxNobg8Lf39NUVHJ
<https://zoom.us/meeting/register/tJIsfuuhqjsrE9EZY2loNxNobg8Lf39NUVHJ>

Speaker: *Ginestra Bianconi *(Queen Mary University of London)

Title: *The Dirac operator and the dynamics of topological sign

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Abstract:
Topological signals associated not only to nodes but also to links and 
to the higher dimensional simplices of simplicial complexes are 
attracting increasing interest in machine learning and network science. 
However, little is known about the collective dynamical phenomena 
involving topological signals. In this talk, I will introduce the Hodge 
Laplacian  and the topological Dirac operator that can be used to 
process simultaneously topological signals of different dimensions.  I 
will discuss the main spectral properties of the Dirac operator defined 
on networks and simplicial complexes. I will present the topological 
Dirac equation in which the spinor has a geometrical interpretation and 
is defined on both nodes and links of the network and the potential 
implications of this model.   I will show that topological signals 
treated with the Hodge Laplacians or with the Dirac operator can undergo 
collective synchronization phenomena displaying different types of 
critical phenomena. The coherent state of these processes are localized 
on the higher-dimensional cavities of the simplicial complex opening new 
perspectives to characterize the interplay between topology and dynamics.

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CMSP, Condensed Matter & Statistical Physics Section
http://www.ictp.it/research/cmsp.aspx

The Abdus Salam International Centre for Theoretical Physics
https://www.ictp.it/

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