Roberto Longo | |
|---|---|
 | |
| Born | 9 May 1953 |
| Nationality | Italian |
| Alma mater | Sapienza University of Rome |
| Awards |
|
| Scientific career | |
| Fields | Mathematics |
| Institutions | |
| Thesis | Tomita-Takesaki modular structure for AFD von Neumann algebras (1975) |
| Academic advisors | Sergio Doplicher |
Roberto Longo (born 9 May 1953) is an Italian mathematician, specializing in operator algebras and quantum field theory. [1]
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]
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. [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]
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]
John Carlos Baez is an American mathematical physicist and a professor of mathematics at the University of California, Riverside (UCR) in Riverside, California. He has worked on spin foams in loop quantum gravity, applications of higher categories to physics, and applied category theory. Additionally, Baez is known on the World Wide Web as the author of the crackpot index.
In theoretical physics, twistor theory was proposed by Roger Penrose in 1967 as a possible path to quantum gravity and has evolved into a widely studied branch of theoretical and mathematical physics. Penrose's idea was that twistor space should be the basic arena for physics from which space-time itself should emerge. It has led to powerful mathematical tools that have applications to differential and integral geometry, nonlinear differential equations and representation theory, and in physics to general relativity, quantum field theory, and the theory of scattering amplitudes.
Algebraic quantum field theory (AQFT) is an application to local quantum physics of C*-algebra theory. Also referred to as the Haag–Kastler axiomatic framework for quantum field theory, because it was introduced by Rudolf Haag and Daniel Kastler. The axioms are stated in terms of an algebra given for every open set in Minkowski space, and mappings between those.
Rudolf Haag was a German theoretical physicist, who mainly dealt with fundamental questions of quantum field theory. He was one of the founders of the modern formulation of quantum field theory and he identified the formal structure in terms of the principle of locality and local observables. He also made important advances in the foundations of quantum statistical mechanics.
Arthur Michael Jaffe is an American mathematical physicist at Harvard University, where in 1985 he succeeded George Mackey as the Landon T. Clay Professor of Mathematics and Theoretical Science.
Jürg Martin Fröhlich is a Swiss mathematician and theoretical physicist. He is best known for introducing rigorous techniques for the analysis of statistical mechanics models, in particular continuous symmetry breaking, and for pioneering the study of topological phases of matter using low-energy effective field theories.
Huzihiro Araki was a Japanese mathematical physicist and mathematician who worked on the foundations of quantum field theory, on quantum statistical mechanics, and on the theory of operator algebras.
Matilde Marcolli is an Italian and American mathematical physicist. She has conducted research work in areas of mathematics and theoretical physics; obtained the Heinz Maier-Leibnitz-Preis of the Deutsche Forschungsgemeinschaft, and the Sofia Kovalevskaya Award of the Alexander von Humboldt Foundation. Marcolli has authored and edited numerous books in the field. She is currently the Robert F. Christy Professor of Mathematics and Computing and Mathematical Sciences at the California Institute of Technology.
In theoretical physics, the AGT correspondence is a relationship between Liouville field theory on a punctured Riemann surface and a certain four-dimensional SU(2) gauge theory obtained by compactifying the 6D (2,0) superconformal field theory on the surface. The relationship was discovered by Luis Alday, Davide Gaiotto, and Yuji Tachikawa in 2009. It was soon extended to a more general relationship between AN-1 Toda field theory and SU(N) gauge theories. The idea of the AGT correspondence has also been extended to describe relationships between three-dimensional theories.
In theoretical physics, the six-dimensional (2,0)-superconformal field theory is a quantum field theory whose existence is predicted by arguments in string theory. It is still poorly understood because there is no known description of the theory in terms of an action functional. Despite the inherent difficulty in studying this theory, it is considered to be an interesting object for a variety of reasons, both physical and mathematical.
Supersymmetric localization is a method to exactly compute correlation functions of supersymmetric operators in certain supersymmetric quantum field theories such as the partition function, supersymmetric Wilson loops, etc. The method can be seen as an extension of the Berline–Vergne– Atiyah– Bott formula for equivariant integration to path integrals of certain supersymmetric quantum field theories. Although the method cannot be applied to general local operators, it does provide the full nonperturbative answer for the restricted class of supersymmetric operators. It is a powerful tool which is currently extensively used in the study of supersymmetric quantum field theory. The method, built on the previous works by E.Witten, in its modern form involves subjecting the theory to a nontrivial supergravity background, such that the fermionic symmetry preserved by the latter can be used to perform the localization computation, as in.
Sergio Doplicher is an Italian mathematical physicist, who mainly dealt with the mathematical foundations of quantum field theory and quantum gravity.
In many-body physics, most commonly within condensed-matter physics, a gapped Hamiltonian is a Hamiltonian for an infinitely large many-body system where there is a finite energy gap separating the ground space from the first excited states. A Hamiltonian that is not gapped is called gapless.
Rinat Kedem is an American mathematician and mathematical physicist.
In mathematical physics, two-dimensional Yang–Mills theory is the special case of Yang–Mills theory in which the dimension of spacetime is taken to be two. This special case allows for a rigorously defined Yang–Mills measure, meaning that the (Euclidean) path integral can be interpreted as a measure on the set of connections modulo gauge transformations. This situation contrasts with the four-dimensional case, where a rigorous construction of the theory as a measure is currently unknown.
Klaus Fredenhagen is a German theoretical physicist who works on the mathematical foundations of quantum field theory.
Giovanni Felder is a Swiss mathematical physicist and mathematician, working at ETH Zurich. He specializes in algebraic and geometric properties of integrable models of statistical mechanics and quantum field theory.
Alberto Sergio Cattaneo is an Italian mathematician and mathematical physicist, specializing in geometry related to quantum field theory and string theory.
Yasuyuki Kawahigashi, formerly known as Yasuyuki Asano, is a Japanese mathematician and a professor at the Graduate School of Mathematical Sciences, the University of Tokyo. His primary area of expertise is operator algebra theory.
In condensed matter physics and quantum information theory, the quantum double model, proposed by Alexei Kitaev, is a lattice model that exhibits topological excitations. This model can be regarded as a lattice gauge theory, and it has applications in many fields, like topological quantum computation, topological order, topological quantum memory, quantum error-correcting code, etc. The name "quantum double" come from the Drinfeld double of a finite groups and Hopf algebras. The most well-known example is the toric code model, which is a special case of quantum double model by setting input group as cyclic group .
{{cite book}}: CS1 maint: location missing publisher (link){{cite book}}: CS1 maint: location missing publisher (link){{cite book}}: CS1 maint: location missing publisher (link)
| International | |
|---|---|
| National | |
| Academics | |
| Other | |
