Luca Giorgetti

Assistant professor, non-tenure (Ricercatore RTDA)


University of Rome Tor Vergata, Department of Mathematics

Via della Ricerca Scientifica 1, I-00133 Roma, Italy

email: giorgett (at) mat.uniroma2.it

phone: +39 06 7259 4621 - office: 0212 corridoio B0

My scientific interests focus on the mathematical description of Quantum Field Theory using Operator Algebras, on the mathematical objects arising from this description and on their interplay. I do research in Analysis (C*/von Neumann algebras, Subfactors), Mathematical Physics (Conformal Field Theory in low dimensions, Algebraic Quantum Field Theory, Quantum Information) and Category Theory (tensor categories, 2-categories).

About me: I studied Maths in Bologna and Rome La Sapienza and I graduated in Physics at Georg-August-Universität Göttingen under the supervision of Karl-Henning Rehren (here is my CV). I led as PI the project "Beyond Rationality in Algebraic CFT: mathematical structures and models" as Marie Skłodowska–Curie Individual Fellow (MSCA IF-GF), funded by the EU Horizon 2020 research and innovation programme under Grant Agreement 795151, acronym "beyondRCFT". Coordinator: University of Rome Tor Vergata. Partner institution: Vanderbilt University.

Research

  • S. Carpi, T. Gaudio, L. Giorgetti, R. Hillier. Haploid algebras in C*-tensor categories and the Schellekens list. arXiv:2211.12790, 2022.

  • M. Bischoff, S. Del Vecchio, L. Giorgetti. Quantum operations on conformal nets. Rev. Math. Phys., 2022. (arXiv:2204.14105, DOI: 10.1142/S0129055X23500071)

  • L. Giorgetti, A. J. Parzygnat, A. Ranallo, B. P. Russo. Bayesian inversion and the Tomita-Takesaki modular group. arXiv:2112.03129, 2021.

  • L. Giorgetti. A planar algebraic description of conditional expectations. Internat. J. Math., 33:2250037-1–23, 2022. (arXiv:2111.04488, DOI: 10.1142/S0129167X22500379)

  • M. Benini, L. Giorgetti, A. Schenkel. A skeletal model for 2d conformal AQFTs. Comm. Math. Phys., 395:269–298, 2022. (arXiv:2111.01837, DOI: 10.1007/s00220-022-04428-4)

  • M. Bischoff, S. Del Vecchio, L. Giorgetti. Galois correspondence and Fourier analysis on local discrete subfactors. Ann. Henri Poincaré, 23:2979–3020, 2022. (arXiv:2107.09345, DOI: 10.1007/s00023-022-01154-4)

  • M. Bischoff, I. Charlesworth, S. Evington, L. Giorgetti, D. Penneys. Distortion for multifactor bimodules and representations of multifusion categories. arXiv:2010.01067, 2020.

  • L. Giorgetti, W. Yuan. Realization of rigid C*-bicategories as bimodules over type II1 von Neumann algebras. arXiv:2010.01072, 2020.

  • M. Bischoff, S. Del Vecchio, L. Giorgetti. Compact hypergroups from discrete subfactors. J. Funct. Anal., 281:109004-1–78, 2021. (arXiv:2007.12384, DOI: 10.1016/j.jfa.2021.109004)

  • L. Giorgetti. Compact hypergroups from discrete subfactors. In Subfactors and Applications. Oberwolfach Rep., 16:3087–3092, 2019. (DOI: 10.4171/OWR/2019/49)

  • S. Del Vecchio, F. Fidaleo, L. Giorgetti, S. Rossi. Ergodic properties of the Anzai skew-product for the noncommutative torus. Ergodic Theory Dynam. Systems, 41:1064–1085, 2021. (arXiv:1910.11839, DOI: 10.1017/etds.2019.116)

  • L. Giorgetti. Minimal index and dimension for inclusions of von Neumann algebras with finite-dimensional centers. OT27 Proceedings (Timișoara, 2018), Theta Ser. Adv. Math., AMS, 183–191, 2020. (arXiv:1908.09121, ISBN: 978-606-8443-12-6)

  • L. Giorgetti, R. Longo. Minimal index and dimension for 2-C*-categories with finite-dimensional centers. Comm. Math. Phys., 370:719–757, 2019. (arXiv:1805.09234, DOI: 10.1007/s00220-018-3266-x)

  • L. Giorgetti, W. Yuan. Realization of rigid C*-tensor categories via Tomita bimodules. J. Operator Theory, 81:433–479, 2019. (arXiv:1712.09311, DOI: 10.7900/jot.2018mar08.2219)

  • S. Del Vecchio, L. Giorgetti. Infinite index extensions of local nets and defects. Rev. Math. Phys., 30:1850002-1–58, 2018. (arXiv:1703.03605, DOI: 10.1142/S0129055X18500022)

  • L. Giorgetti, K.-H. Rehren. Bantay’s trace in unitary modular tensor categories. Adv. Math., 319:211–223, 2017. (arXiv:1606.04378, DOI: 10.1016/j.aim.2017.08.018)

  • L. Giorgetti, K.-H. Rehren. Braided categories of endomorphisms as invariants for local quantum field theories. Comm. Math. Phys., 357:3–41, 2018. (arXiv:1512.01995, DOI: 10.1007/s00220-017-2937-3)

  • L. Giorgetti. Braided actions of DHR categories and reconstruction of chiral conformal field theories. PhD thesis, Georg-August-Universität Göttingen, 2016. (available at: http://ediss.uni-goettingen.de/handle/11858/00-1735-0000-002B-7C2E-0, DOI: 10.53846/goediss-5913)

Reviewing

Reviewer for: Zentralblatt Math (zbMATH), Mathematical Reviews (AMS).

Referee for: Higher Structures, American Journal of Mathematics, Advances in Mathematics, Communications in Mathematical Physics, Annals of Functional Analysis, Analysis and Mathematical Physics.