Luca Giorgetti
Researcher in Mathematics, RTT
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, operator theory, subfactors, abstract harmonic analysis), Mathematical Physics (Conformal Field Theory, Algebraic QFT, 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 Global Fellow (MSCA IF-GF), funded by the EU Horizon 2020 research and innovation programme. Coordinator: University of Rome Tor Vergata. Partner institution: Vanderbilt University. I obtained the National Scientific Qualification (ASN) as Associate Professor in Mathematical Analysis, Probability and Mathematical Statistics (01/A3).
Research
R. Correa da Silva, L. Giorgetti, G. Lechner. Crossing symmetry and the crossing map. arXiv:2402.15763, 2024.
L. Giorgetti, W. Yuan, X. R. Zhao. Separable algebras in multitensor C*-categories are unitarizable. AIMS Mathematics, 9:11320–11334, 2024. Special Issue “Operator Theory: Advances and Applications”. (arXiv:2312.12019, DOI: 10.3934/math.2024555)
L. Giorgetti. Quantum Operations in Algebraic QFT. Functional Analysis, Approximation Theory and Numerical Analysis, FAATNA20>22, Matera, Italy, 2022, conference proceedings. Note Mat., 43:41–56, 2023. (arXiv:2303.15171, DOI: 10.1285/i15900932v43n1p41)
M. S. Adamo, L. Giorgetti, Y. Tanimoto. Wightman fields for two-dimensional conformal field theories with pointed representation category. Comm. Math. Phys., 404:1231–1273, 2023. (arxiv:2301.12310, DOI: 10.1007/s00220-023-04835-1)
S. Carpi, T. Gaudio, L. Giorgetti, R. Hillier. Haploid algebras in C*-tensor categories and the Schellekens list. Comm. Math. Phys., 402:169–212, 2023. (arXiv:2211.12790, DOI: 10.1007/s00220-023-04722-9)
M. Bischoff, S. Del Vecchio, L. Giorgetti. Quantum operations on conformal nets. Rev. Math. Phys., 35:2350007-1–30, 2023. (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. Quart. J. Math., 74:975–1014, 2023. (arXiv:2112.03129, DOI: 10.1093/qmath/haad014, available here)
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. Adv. Math., 415:108886-1–27, 2023. (arXiv:2010.01072, DOI: 10.1016/j.aim.2023.108886)
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. Operator Theory 27, OT27, Timișoara, Romania, 2018, conference proceedings. In 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, Quantum Topology, Annales Henri Poincaré, Forum of Mathematics Pi, Journal of Noncommutative Geometry.
Other online ID's
My Google Scholar, ResearchGate, LQP2, INSPIREhep, MathSciNet and here is my CV.