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Roberto Longo (mathematician)

Summary

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
NationalityItalian
Alma materSapienza University of Rome
Awards
Scientific career
FieldsMathematics
Institutions
Thesis Tomita-Takesaki modular structure for AFD von Neumann algebras  (1975)
Academic advisorsSergio Doplicher

Education and career edit

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 is 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]

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]

Honors and awards edit

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 edit

  • Hislop, Peter D.; Longo, Roberto (1982). "Modular structure of the local algebras associated with the free massless scalar field theory". Communications in Mathematical Physics. 84 (1): 71–85. Bibcode:1982CMaPh..84...71H. doi:10.1007/BF01208372. S2CID 119856852.
  • 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. ISSN 0020-9910. S2CID 121819323.
  • 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.
  • Longo, Roberto (1989). "Index of subfactors and statistics of quantum fields. I". Communications in Mathematical Physics. 126 (2): 217–247. Bibcode:1989CMaPh.126..217L. doi:10.1007/BF02125124. S2CID 122420613.
  • Longo, Roberto (1994). "A duality for Hopf algebras and for subfactors. I". Communications in Mathematical Physics. 159 (1): 133–150. Bibcode:1994CMaPh.159..133L. doi:10.1007/BF02100488. ISSN 0010-3616. S2CID 123347247.
  • Guido, Daniele; Longo, Roberto (1996). "The conformal spin and statistics theorem". Communications in Mathematical Physics. 181 (1): 11–35. arXiv:hep-th/9505059. Bibcode:1996CMaPh.181...11G. doi:10.1007/BF02101672. S2CID 17663903.
  • 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.
  • Kawahigashi, Yasuyuki; Longo, Roberto; Müger, Michael (2001). "Multi-Interval Subfactors and Modularity of Representations in Conformal Field Theory". Communications in Mathematical Physics. 219 (3): 631–669. arXiv:math/9903104. Bibcode:2001CMaPh.219..631K. doi:10.1007/PL00005565. S2CID 15568392.
  • 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.
  • Kac, Victor G.; Longo, Roberto; Xu, Feng (2004). "Solitons in affine and permutation orbifolds". Communications in Mathematical Physics. 253 (3): 723–764. arXiv:math/0312512. doi:10.1007/s00220-004-1160-1. S2CID 14298134.
  • Longo, Roberto; Witten, Edward (2011). "An Algebraic Construction of Boundary Quantum Field Theory". Communications in Mathematical Physics. 303 (1): 213–232. arXiv:1004.0616. Bibcode:2011CMaPh.303..213L. doi:10.1007/s00220-010-1133-5. S2CID 115174261.
  • 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.
  • Carpi, Sebastiano; Kawahigashi, Yasuyuki; Longo, Roberto; Weiner, Mihály (2018). "From vertex operator algebras to conformal nets and back". Memoirs of the American Mathematical Society. 254 (1213). arXiv:1503.01260. doi:10.1090/memo/1213. S2CID 119618626.
  • 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.

See also edit

References edit

  1. ^ "Roberto Longo". Department of Mathematics, University of Rome Tor Vergata. Retrieved February 19, 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 February 19, 2021.
  5. ^ a b "Humboldt Foundation member page of Roberto Longo". humboldt-foundation.de. Retrieved February 19, 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. 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 February 19, 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 February 19, 2021.
  18. ^ "Mathematisches Institut - Andrejewski Vorlesung". uni-math.gwdg.de (in German). Retrieved February 23, 2021.
  19. ^ "Plenary Speakers". ICMP Prague. Retrieved February 19, 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 February 19, 2021.
  21. ^ "List of Fellows of the American Mathematical Society". American Mathematical Society. Retrieved February 19, 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 July 20, 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 July 20, 2021.
  25. ^ "Mathematics and Quantum Physics Conference". cmtp.uniroma2.it. Retrieved February 19, 2021.
  26. ^ "Scienze, Roma trionfa negli Advanced grants". Il Sole 24 Ore, Roma (in Italian) (40). October 15, 2008. "Advanced Grants: Operator Algebras and Conformal Field Theory". europa.eu. Retrieved February 25, 2021.
  27. ^ "Advanced Grants: Quantum Algebraic Structures and Models". europa.eu. Retrieved February 25, 2021.
  28. ^ "Un matematico di Tor Vergata vincitore dell'"Advanced Grants"". maddmaths.simai.eu (in Italian). Retrieved February 23, 2021.
  29. ^ "Sectional Panels for ICM 2018" (PDF). mathunion.org/icm/past-icms. Retrieved February 19, 2021.

External links edit

 
Wikimedia Commons has media related to Roberto Longo.
  • Roberto Longo at the Mathematics Genealogy Project.
  • Roberto Longo at zbMATH.
  • "Center for Mathematics and Theoretical Physics webpage". Center for Mathematics and Theoretical Physics. Retrieved February 21, 2021.
  • "Longo's personal webpage". uniroma2.it. Retrieved February 21, 2021.
  • "Longo's seminar in the conference about the 50 years of algebraic quantum field theory". gwdg.de. July 30, 2009. Retrieved February 19, 2021.
  • Longo, Roberto (July 6, 2016). "KMS states in Conformal Field Theory". YouTube. Hausdorff Center for Mathematics. Retrieved February 19, 2021.
  • Longo, Roberto (2017). "Noncommutative Geometry: State of the Art and Future Prospects, Alain Connes 70th Birthday". mat.uniroma2.it. Shanghai. Retrieved February 21, 2021.
  • Longo, Roberto (June 12, 2017). "Discussion about the Landauer principle (and bound)". Isaac Newton Institute for Mathematical Sciences. Retrieved February 21, 2021.
  • Longo, Roberto (May 5, 2020). "The Information in a Wave". YouTube. Retrieved February 21, 2021.

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