My research involves applying methods from topological data analysis to theoretical and computational particle physics.
I use high-performance computing paired with state-of-the-art data science methods to analyse Monte Carlo generated lattice gauge theory configurations.
In particular, I am interested in applying novel topological feature extraction methods to construct observables relevant for confinement in Yang-Mills theory. Topological excitations such as center vortices and Abelian magnetic monopoles can correlate with the deconfinement phase transition very precisely.
The hope is that these methods will allow us to delineate the phase structure of quantum chromodynamics, the theory underpinning the elementary strong interaction of quarks and gluons.
Topological complexity of Abelian monopole currents: a new order parameter for deconfinement in SU(3) Yang-Mills, Xavier Crean, Jeffrey Giansiracusa, Biagio Lucini (in preparation)
Topological Data Analysis of Abelian Magnetic Monopoles in Gauge Theories, Â Xavier Crean, Jeffrey Giansiracusa, Biagio Lucini, PoS LATTICE2024 (2025) 395; doi: 10.22323/1.466.0395
Topological data analysis of monopole current networks in U(1) lattice gauge theory, Xavier Crean, Jeffrey Giansiracusa, Biagio Lucini, SciPost Phys. 17, 100 (2024); doi: 10.21468/SciPostPhys.17.4.100