Wikipedia

Roberto Longo (mathematician)

Roberto Longo (born 9 May 1953) is an Italian mathematician, specializing in operator algebras and quantum field theory.[1]

Roberto Longo
Born(1953-05-09)9 May 1953
Rome, Italy
Alma materSapienza University of Rome
Awards
Scientific career
FieldsMathematics
Institutions
Thesis Tomita-Takesaki modular structure for AFD von Neumann algebras  (1975)
Academic advisors
Sergio Doplicher

Education and career

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Roberto Longo graduated in Mathematics[2] at the Sapienza University of Rome in 1975 under the supervision of the mathematical physicist Sergio Doplicher.[3] From 1975 to 1977 Longo was a predoctoral fellow of the Consiglio Nazionale delle Ricerche and later assistant professor at the Sapienza University of Rome, where he became an associate professor in 1980. In 1987, he was nominated full professor of functional analysis at the University of Rome Tor Vergata, and since 2010, he has been the director of the Center for Mathematics and Theoretical Physics in Rome.

Between 1978 and 1979, he was visiting scholar at the University of Pennsylvania and the University of California, Berkeley. He has been a visiting professor in numerous research centers, including the CNRS in Marseille, the Mathematical Sciences Research Institute in Berkeley, California, the Harvard University, MIT, and the University of Göttingen.[4]

Since 2024, Roberto Longo has been an Emeritus Professor at the University of Rome Tor Vergata.

Longo is an expert in the theory of operator algebras and its applications to quantum field theory. His work influenced the structural analysis of quantum field theory, especially of conformal field theory, and opened up to new developments in model-building methods of interest in local quantum physics.[5]

Roberto Longo is known in particular for his work with Sergio Doplicher on split inclusions of von Neumann algebras[6] and for having solved, independently with Sorin Popa, the Stone-Weierstrass conjecture for factorial states.[7] He also found the relationship between the statistical dimension[8] and the Jones index.[9] In a work with Yasuyuki Kawahigashi, Longo classified the discrete series of conformal chiral networks of von Neumann algebras.[10] Together with Vincenzo Morinelli and Karl-Henning Rehren, he also showed that particles with infinite spin cannot appear in a local theory.[11] His most recent works concern entropy and information for infinite quantum systems.[12]

Honours and awards

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In 1994 Longo was an invited speaker at the International Congress of Mathematicians in Zurich.[13] He was invited speaker at the International Congress on Mathematical Physics in 1981 in Berlin,[14] in 1988 in Swansea,[15] in 1994 in Paris,[16] and in 2003 in Lisbon.[17] In 2004 he was Andrejewski Lecturer in Göttingen.[18] He was a plenary speaker at the International Congress of Mathematicians in 2009 in Prague[19] and at Strings 2018 in Okinawa.[20]

In 2013 he was elected a Fellow of the American Mathematical Society[21] and in 2021 a member of the Academia Europaea.[22] He was awarded in 2016 the Humboldt Research Award[5][23] and in 2021 the XL medal from the Accademia Nazionale delle Scienze detta dei XL for his in-depth and innovative research in operator algebras and in conformal field theory.[24] In 2013 the conference Mathematics and Quantum Physics at the Lincei National Academy was dedicated to him on the occasion of his 60th birthday.[25] In 2008[26] and in 2015[27] he received two Advanced Grants from the European Research Council.[28] In 2018 he was member of the sectional panel Mathematical Physics of the International Congress of Mathematicians in Rio de Janeiro.[29]

Selected publications

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See also

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References

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  1. ↑ "Roberto Longo". Department of Mathematics, University of Rome Tor Vergata. Retrieved 19 February 2021.
  2. ↑ The academic degree is Laurea in Matematica and was the highest academic title at the epoch.
  3. ↑ The thesis is Longo, Roberto (1975). Tomita-Takesaki modular structure for AFD von Neumann algebras (Thesis). Rome. Roberto Longo at the Mathematics Genealogy Project
  4. ↑ "Roberto Longo, Curriculum Vitae" (PDF). University of Rome Tor Vergara. Retrieved 19 February 2021.
  5. 1 2 "Humboldt Foundation member page of Roberto Longo". humboldt-foundation.de. Retrieved 19 February 2021.
  6. ↑ Doplicher, S.; Longo, R. (1984). "Standard and split inclusions of von Neumann algebras". Inventiones Mathematicae. 75 (3): 493–536. Bibcode:1984InMat..75..493D. doi:10.1007/BF01388641. hdl:2108/53288. ISSN 0020-9910. S2CID 121819323.
  7. ↑ Longo, Roberto (1984). "Solution of the factorial Stone-Weierstrass conjecture. An application of the theory of standard split W*-inclusions". Inventiones Mathematicae. 76 (1): 145–155. Bibcode:1984InMat..76..145L. doi:10.1007/BF01388497. S2CID 122775835.
  8. ↑ Doplicher, Sergio; Haag, Rudolf; Roberts, John E. (1971). "Local observables and particle statistics. 1". Communications in Mathematical Physics. 23 (3): 199–230. Bibcode:1971CMaPh..23..199D. doi:10.1007/BF01877742. S2CID 189833852.
  9. ↑ Longo, Roberto; Roberts, John E. (1997). "A Theory of Dimension". K-Theory. 11 (2): 103–159. arXiv:funct-an/9604008. Bibcode:1996funct.an..4008L. doi:10.1023/A:1007714415067. S2CID 119581477.
  10. ↑ Kawahigashi, Yasuyuki; Longo, Roberto (2004). "Classification of local conformal nets: Case c < 1". Annals of Mathematics. 160 (2): 493–522. arXiv:math-ph/0201015. doi:10.4007/annals.2004.160.493. S2CID 7145642.
  11. ↑ Longo, Roberto; Morinelli, Vincenzo; Rehren, Karl-Henning (2016). "Where Infinite Spin Particles Are Localizable". Communications in Mathematical Physics. 345 (2): 587–614. arXiv:1505.01759. Bibcode:2016CMaPh.345..587L. doi:10.1007/s00220-015-2475-9. S2CID 119569712.
  12. ↑ Ciolli, Fabio; Longo, Roberto; Ruzzi, Giuseppe (2019). "The information in a wave". Communications in Mathematical Physics. 379 (3): 979–1000. arXiv:1906.01707. Bibcode:2019CMaPh.379..979C. doi:10.1007/s00220-019-03593-3. S2CID 174799030.
  13. ↑ "ICM Plenary and Invited Speakers". mathunion.org. Retrieved 19 February 2021. Longo, Roberto (1995). "Von Neumann algebras and quantum field theory". Proceedings of the International Congress of Mathematicians, 1994, Zürich. Vol. 2. pp. 1281–1291.
  14. ↑ Longo, Roberto (1981). "Modular Automorphisms of Local Algebras in Quantum Field Theory". 6th International Conference on Mathematical Physics - Congress of Association for Mathematical Physics. Berlin. pp. 372–373.{{cite book}}: CS1 maint: location missing publisher (link)
  15. ↑ Longo, Roberto (1988). "Inclusions of Von Neumann Algebrass and Quantum Field Theory". IX International Conference on Mathematical Physics (IAMP). Swansea. pp. 472–474.{{cite book}}: CS1 maint: location missing publisher (link)
  16. ↑ Longo, Roberto (1994). "Inclusions of von Neumann algebras and superselection structures". 11th International Conference on Mathematical Physics (ICMP-11). Paris. pp. 342–351.{{cite book}}: CS1 maint: location missing publisher (link)
  17. ↑ "ICMP 2003 schedule". XIV ICMP Lisbon. Retrieved 19 February 2021.
  18. ↑ "Mathematisches Institut - Andrejewski Vorlesung". uni-math.gwdg.de (in German). Archived from the original on 10 September 2022. Retrieved 23 February 2021.
  19. ↑ "Plenary Speakers". ICMP Prague. Archived from the original on 16 August 2022. Retrieved 19 February 2021.
  20. ↑ "Modular theory and Bekenstein's bound by Robert Longo, partly based on a joint work with Feng Xu" (PDF). Okinawa, OIST, Strings 2018. Retrieved 19 February 2021.
  21. ↑ "List of Fellows of the American Mathematical Society". American Mathematical Society. Retrieved 19 February 2021. Jackson, Allyn (2013). "Fellows of the AMS: Inaugural Class" (PDF). Notices of the AMS. 60 (5): 631–637.
  22. ↑ "Longo's member page of Academia Europæa". Academia Europæa. Retrieved 20 July 2021.
  23. ↑ "Humboldt-Preisträger". Uni Inform, Göttingen (in German): 5. April 2015.
  24. ↑ "A Roberto Longo la Medaglia dei XL per la Matematica 2021". uniroma2.it (in Italian). Retrieved 20 July 2021.
  25. ↑ "Mathematics and Quantum Physics Conference". cmtp.uniroma2.it. Retrieved 19 February 2021.
  26. ↑ "Scienze, Roma trionfa negli Advanced grants". Il Sole 24 Ore, Roma (in Italian) (40). 15 October 2008. "Advanced Grants: Operator Algebras and Conformal Field Theory". europa.eu. Retrieved 25 February 2021.
  27. ↑ "Advanced Grants: Quantum Algebraic Structures and Models". europa.eu. Retrieved 25 February 2021.
  28. ↑ "Un matematico di Tor Vergata vincitore dell'"Advanced Grants"". maddmaths.simai.eu (in Italian). Retrieved 23 February 2021.
  29. ↑ "Sectional Panels for ICM 2018" (PDF). mathunion.org/icm/past-icms. Retrieved 19 February 2021.
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