Roberto Longo (mathematician)

{{Infobox scientist

| name = Roberto Longo

| image = Roberto Longo Lago di Sabaudia 2019.jpg

| birth_date = {{birth date|1953|5|9|df=y}}

| birth_place = Rome, Italy

| nationality = Italian

| work_institution = {{Unbulleted list|University of Pennsylvania|University of California, Berkeley|University of Rome Tor Vergata}}

| alma_mater = Sapienza University of Rome

| academic_advisors = Sergio Doplicher

| thesis_title = Tomita-Takesaki modular structure for AFD von Neumann algebras

| thesis_year = 1975

| awards = {{Unbulleted list |Humboldt Prize {{smaller|(2016){{nbsp|2}}}} | Medaglia dei XL {{smaller|(2021){{nbsp|2}}}}}}

}}

Roberto Longo (born 9 May 1953) is an Italian mathematician, specializing in operator algebras and quantum field theory.{{cite web|title=Roberto Longo|website=Department of Mathematics, University of Rome Tor Vergata|url=http://www.mat.uniroma2.it/longo/|access-date=February 19, 2021}}

Education and career

Roberto Longo graduated in MathematicsThe academic degree is Laurea in Matematica and was the highest academic title at the epoch. at the Sapienza University of Rome in 1975 under the supervision of the mathematical physicist Sergio Doplicher.The thesis is {{cite thesis|last=Longo|first=Roberto|date=1975|title=Tomita-Takesaki modular structure for AFD von Neumann algebras|place=Rome}} {{MathGenealogy|id=100244}} 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.{{cite web|title=Roberto Longo, Curriculum Vitae|website=University of Rome Tor Vergara|url=http://www.mat.uniroma2.it/longo/Home_files/CV-2010.pdf|access-date=February 19, 2021}}

From 2024 Roberto Longo is 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.{{cite web|url=https://www.humboldt-foundation.de/en/connect/explore-the-humboldt-network/singleview?tx_rsmavhsolr_solrview%5BpPersonId%5D=1154986&cHash=13869c9b9202d59fc4928bef1b780146|title=Humboldt Foundation member page of Roberto Longo|website=humboldt-foundation.de|access-date=February 19, 2021}}

Roberto Longo is known in particular for his work with Sergio Doplicher on split inclusions of von Neumann algebras{{cite journal|last1=Doplicher|first1=S.|last2=Longo|first2=R.|title=Standard and split inclusions of von Neumann algebras|journal=Inventiones Mathematicae|volume=75|issue=3|year=1984|pages=493–536|issn=0020-9910|doi=10.1007/BF01388641|url=https://eudml.org/doc/143108|bibcode=1984InMat..75..493D|s2cid=121819323|url-access=subscription}} and for having solved, independently with Sorin Popa, the Stone-Weierstrass conjecture for factorial states.{{cite journal|last=Longo|first=Roberto|title=Solution of the factorial Stone-Weierstrass conjecture. An application of the theory of standard split W*-inclusions|journal=Inventiones Mathematicae|volume=76|number=1|year=1984|pages=145–155|doi=10.1007/BF01388497|bibcode=1984InMat..76..145L|s2cid=122775835}} He also found the relationship between the statistical dimension{{Cite journal|last1=Doplicher|first1=Sergio|last2=Haag|first2=Rudolf|last3=Roberts|first3=John E.|title=Local observables and particle statistics. 1|journal=Communications in Mathematical Physics|volume=23|pages=199–230|year=1971|issue=3|doi=10.1007/BF01877742|bibcode=1971CMaPh..23..199D|s2cid=189833852|url=http://projecteuclid.org/euclid.cmp/1103857630 }} and the Jones index.{{cite journal|arxiv=funct-an/9604008|last1=Longo|first1=Roberto|last2=Roberts|first2=John E.|title=A Theory of Dimension|journal=K-Theory|year=1997|volume=11|issue=2|pages=103–159|doi=10.1023/A:1007714415067|bibcode = 1996funct.an..4008L|s2cid=119581477}} In a work with Yasuyuki Kawahigashi, Longo classified the discrete series of conformal chiral networks of von Neumann algebras.{{cite journal|title=Classification of local conformal nets: Case c < 1|journal=Annals of Mathematics|volume=160|pages=493–522|year=2004|last1=Kawahigashi|first1=Yasuyuki|last2=Longo|first2=Roberto|issue=2|doi=10.4007/annals.2004.160.493|arxiv=math-ph/0201015|s2cid=7145642}} Together with Vincenzo Morinelli and Karl-Henning Rehren, he also showed that particles with infinite spin cannot appear in a local theory.{{cite journal|last1=Longo|first1=Roberto|last2=Morinelli|first2=Vincenzo|last3=Rehren|first3=Karl-Henning|title=Where Infinite Spin Particles Are Localizable|journal=Communications in Mathematical Physics|volume=345|year=2016|issue=2|pages=587–614|doi=10.1007/s00220-015-2475-9|arxiv=1505.01759|bibcode=2016CMaPh.345..587L|s2cid=119569712}} His most recent works concern entropy and information for infinite quantum systems.{{cite journal|last1=Ciolli|first1=Fabio|last2=Longo|first2=Roberto|last3=Ruzzi|first3=Giuseppe|title=The information in a wave|journal=Communications in Mathematical Physics|volume=379|year=2019|issue=3|pages=979–1000|doi=10.1007/s00220-019-03593-3|arxiv=1906.01707|bibcode=2019CMaPh.379..979C|s2cid=174799030}}

Honors and awards

In 1994 Longo was an invited speaker at the International Congress of Mathematicians in Zurich.{{cite web|title=ICM Plenary and Invited Speakers|website=mathunion.org|url=https://www.mathunion.org/icm-plenary-and-invited-speakers?combine=longo|access-date=February 19, 2021}} {{cite book|author=Longo, Roberto|chapter=Von Neumann algebras and quantum field theory|title=Proceedings of the International Congress of Mathematicians, 1994, Zürich|volume=2|pages=1281–1291|year=1995}} He was invited speaker at the International Congress on Mathematical Physics in 1981 in Berlin,{{cite book|author=Longo, Roberto|chapter=Modular Automorphisms of Local Algebras in Quantum Field Theory|title=6th International Conference on Mathematical Physics - Congress of Association for Mathematical Physics|pages=372–373|year=1981|place=Berlin}} in 1988 in Swansea,{{cite book|author=Longo, Roberto|chapter=Inclusions of Von Neumann Algebrass and Quantum Field Theory|title=IX International Conference on Mathematical Physics (IAMP)|pages=472–474|year=1988|place=Swansea}} in 1994 in Paris,{{cite book|author=Longo, Roberto|chapter=Inclusions of von Neumann algebras and superselection structures|title=11th International Conference on Mathematical Physics (ICMP-11)|place=Paris|pages=342–351|year=1994}} and in 2003 in Lisbon.{{cite web|title=ICMP 2003 schedule|website=XIV ICMP Lisbon|url=http://icmp2003.net/schedule/|access-date=February 19, 2021}} In 2004 he was Andrejewski Lecturer in Göttingen.{{cite web|title=Mathematisches Institut - Andrejewski Vorlesung|website=uni-math.gwdg.de|url=https://www.uni-math.gwdg.de/andrej/longo.html|access-date=February 23, 2021|language=de}} He was a plenary speaker at the International Congress of Mathematicians in 2009 in Prague{{cite web|title=Plenary Speakers|website=ICMP Prague|url=http://icmp.ujf.cas.cz/confirmed-plenary-speakers.htm|access-date=February 19, 2021}} and at Strings 2018 in Okinawa.{{cite web|title=Modular theory and Bekenstein's bound by Robert Longo, partly based on a joint work with Feng Xu|website=Okinawa, OIST, Strings 2018|url=https://indico.oist.jp/indico/event/5/picture/116.pdf|access-date=February 19, 2021}}

In 2013 he was elected a Fellow of the American Mathematical Society{{cite web|url=https://www.ams.org/cgi-bin/fellows/fellows.cgi#d|title=List of Fellows of the American Mathematical Society|website=American Mathematical Society|access-date=February 19, 2021}} {{cite journal|last=Jackson|first=Allyn|title=Fellows of the AMS: Inaugural Class|journal=Notices of the AMS|volume=60|number=5|year=2013|pages=631–637|url=https://www.ams.org/profession/ams-fellows/rnoti-p631.pdf}} and in 2021 a member of the Academia Europaea.{{cite web|url=https://www.ae-info.org/ae/Member/Longo_Roberto|title=Longo's member page of Academia Europæa|website=Academia Europæa|access-date=July 20, 2021}} He was awarded in 2016 the Humboldt Research Award{{Cite journal|title=Humboldt-Preisträger|journal=Uni Inform, Göttingen|date=April 2015|page=5|language=de}}

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.{{cite web|url=https://web.uniroma2.it/module/name/Content/newlang/italiano/navpath/HOM/action/showpage/content_id/94622|title=A Roberto Longo la Medaglia dei XL per la Matematica 2021|website=uniroma2.it|language=it|access-date=July 20, 2021}} In 2013 the conference Mathematics and Quantum Physics at the Lincei National Academy was dedicated to him on the occasion of his 60th birthday.{{cite web|url=http://cmtp.uniroma2.it/13MQP/|title=Mathematics and Quantum Physics Conference|website=cmtp.uniroma2.it|access-date=February 19, 2021}} In 2008{{Cite journal|title = Scienze, Roma trionfa negli Advanced grants|journal = Il Sole 24 Ore, Roma|number = 40|date = October 15, 2008|language=it}} {{cite web|title=Advanced Grants: Operator Algebras and Conformal Field Theory|website=europa.eu|url=https://cordis.europa.eu/project/id/227458|access-date=February 25, 2021}} and in 2015{{cite web|title=Advanced Grants: Quantum Algebraic Structures and Models|website=europa.eu|url=https://cordis.europa.eu/project/id/669240|access-date=February 25, 2021}} he received two Advanced Grants from the European Research Council.{{cite web|title=Un matematico di Tor Vergata vincitore dell'"Advanced Grants"|website=maddmaths.simai.eu|url=http://maddmaths.simai.eu/news-2/roberto-longo-si-aggiudica-il-suo-secondo-erc-con-un-progetto-su-matematica-e-fisica-quantistica/|access-date=February 23, 2021|language=it}} In 2018 he was member of the sectional panel Mathematical Physics of the International Congress of Mathematicians in Rio de Janeiro.{{cite web|url=https://www.mathunion.org/fileadmin/IMU/ICM2018/Panelists_2018.pdf|title=Sectional Panels for ICM 2018|website=mathunion.org/icm/past-icms|access-date=February 19, 2021}}

Selected publications

{{cite journal|doi=10.1007/BF01208372|title=Modular structure of the local algebras associated with the free massless scalar field theory|journal=Communications in Mathematical Physics|volume=84|issue=1|pages=71–85|year=1982|last1=Hislop|first1=Peter D.|last2=Longo|first2=Roberto|bibcode=1982CMaPh..84...71H|s2cid=119856852|url=http://projecteuclid.org/euclid.cmp/1103921046 }}
{{cite journal|last1=Doplicher|first1=S.|last2=Longo|first2=R.|title=Standard and split inclusions of von Neumann algebras|journal=Inventiones Mathematicae|volume=75|issue=3|year=1984|pages=493–536|issn=0020-9910|doi=10.1007/BF01388641|url=https://eudml.org/doc/143108|bibcode=1984InMat..75..493D|s2cid=121819323|url-access=subscription}}
{{cite journal|last=Longo|first=Roberto|title=Solution of the factorial Stone-Weierstrass conjecture. An application of the theory of standard split W*-inclusions|journal=Inventiones Mathematicae|volume=76|number=1|year=1984|pages=145–155|doi=10.1007/BF01388497|bibcode=1984InMat..76..145L|s2cid=122775835}}
{{cite journal|doi=10.1007/BF02125124|title=Index of subfactors and statistics of quantum fields. I|journal=Communications in Mathematical Physics|volume=126|issue=2|pages=217–247|year=1989|last1=Longo|first1=Roberto|bibcode=1989CMaPh.126..217L|s2cid=122420613|url=http://projecteuclid.org/euclid.cmp/1104179850 }}
{{cite journal|last=Longo|first=Roberto|title=A duality for Hopf algebras and for subfactors. I|journal=Communications in Mathematical Physics|volume=159|issue=1|year=1994|pages=133–150|issn=0010-3616|doi=10.1007/BF02100488|url=https://projecteuclid.org/euclid.cmp/1104254494|bibcode=1994CMaPh.159..133L|s2cid=123347247|hdl=2108/54271|hdl-access=free}}
{{cite journal|doi=10.1007/BF02101672|title=The conformal spin and statistics theorem|journal=Communications in Mathematical Physics|volume=181|issue=1|pages=11–35|year=1996|last1=Guido|first1=Daniele|last2=Longo|first2=Roberto|bibcode=1996CMaPh.181...11G|arxiv=hep-th/9505059|s2cid=17663903}}
{{cite journal|arxiv=funct-an/9604008|last1=Longo|first1=Roberto|last2=Roberts|first2=John E.|title=A Theory of Dimension|journal=K-Theory|year=1997|volume=11|issue=2|pages=103–159|doi=10.1023/A:1007714415067|bibcode = 1996funct.an..4008L|s2cid=119581477}}
{{cite journal|doi=10.1007/PL00005565|title=Multi-Interval Subfactors and Modularity of Representations in Conformal Field Theory|journal=Communications in Mathematical Physics|volume=219|issue=3|pages=631–669|year=2001|last1=Kawahigashi|first1=Yasuyuki|last2=Longo|first2=Roberto|last3=Müger|first3=Michael|bibcode=2001CMaPh.219..631K|arxiv=math/9903104|s2cid=15568392}}
{{cite journal|title=Classification of local conformal nets: Case c < 1|journal=Annals of Mathematics|volume=160|pages=493–522|year=2004|last1=Kawahigashi|first1=Yasuyuki|last2=Longo|first2=Roberto|issue=2|doi=10.4007/annals.2004.160.493|arxiv=math-ph/0201015|s2cid=7145642}}
{{cite journal|last1=Kac|first1=Victor G.|last2=Longo|first2=Roberto|last3=Xu|first3=Feng|title=Solitons in affine and permutation orbifolds|journal=Communications in Mathematical Physics|volume=253|year=2004|issue=3|pages=723–764|doi=10.1007/s00220-004-1160-1|arxiv=math/0312512|s2cid=14298134}}
{{cite journal|last1=Longo|first1=Roberto|last2=Witten|first2=Edward|title=An Algebraic Construction of Boundary Quantum Field Theory|journal=Communications in Mathematical Physics|volume=303|year=2011|issue=1|pages=213–232|doi=10.1007/s00220-010-1133-5|arxiv=1004.0616|bibcode=2011CMaPh.303..213L|s2cid=115174261}}
{{cite journal|last1=Longo|first1=Roberto|last2=Morinelli|first2=Vincenzo|last3=Rehren|first3=Karl-Henning|title=Where Infinite Spin Particles Are Localizable|journal=Communications in Mathematical Physics|volume=345|year=2016|issue=2|pages=587–614|doi=10.1007/s00220-015-2475-9|arxiv=1505.01759|bibcode=2016CMaPh.345..587L|s2cid=119569712}}
{{cite journal|last1=Carpi|first1=Sebastiano|last2=Kawahigashi|first2=Yasuyuki|last3=Longo|first3=Roberto|last4=Weiner|first4=Mihály|title=From vertex operator algebras to conformal nets and back|journal=Memoirs of the American Mathematical Society|volume=254|number=1213|year=2018|doi=10.1090/memo/1213|arxiv=1503.01260|s2cid=119618626}}
{{cite journal|last1=Ciolli|first1=Fabio|last2=Longo|first2=Roberto|last3=Ruzzi|first3=Giuseppe|title=The information in a wave|journal=Communications in Mathematical Physics|volume=379|year=2019|issue=3|pages=979–1000|doi=10.1007/s00220-019-03593-3|arxiv=1906.01707|bibcode=2019CMaPh.379..979C|s2cid=174799030}}

References

External links

{{MathGenealogy|id=100244|title=Roberto Longo}}.
{{zbMATH|id=longo.roberto}}.
{{cite web|title=Center for Mathematics and Theoretical Physics webpage|website=Center for Mathematics and Theoretical Physics|url=http://cmtp.uniroma2.it/|access-date=February 21, 2021}}
{{cite web|title=Longo's personal webpage|website=uniroma2.it|url=https://www.mat.uniroma2.it/longo/|access-date=February 21, 2021}}
{{cite web|title=Longo's seminar in the conference about the 50 years of algebraic quantum field theory|website=gwdg.de|url=https://www.uni-math.gwdg.de/aufzeichnungen/AQFT50/Longo/|date=July 30, 2009|access-date=February 19, 2021}}
{{cite web|first=Roberto|last=Longo|title=KMS states in Conformal Field Theory|date=July 6, 2016|publisher=Hausdorff Center for Mathematics|website=YouTube|url=https://www.youtube.com/watch?v=DuzdXw_Yldg|access-date=February 19, 2021}}
{{cite web|first=Roberto|last=Longo|title=Noncommutative Geometry: State of the Art and Future Prospects, Alain Connes 70th Birthday|date=2017|place=Shanghai|website=mat.uniroma2.it|url=https://www.mat.uniroma2.it/longo/Videos_files/Shanga17-video.mp4|access-date=February 21, 2021}}
{{cite web|first=Roberto|last=Longo|title=Discussion about the Landauer principle (and bound)|date=June 12, 2017|website=Isaac Newton Institute for Mathematical Sciences|url=https://www.newton.ac.uk/seminar/20170612143015301|access-date=February 21, 2021}}
{{cite web|first=Roberto|last=Longo|title=The Information in a Wave|date=May 5, 2020|website=YouTube|url=https://www.youtube.com/watch?v=n7svXoev7H0|access-date=February 21, 2021}}