Mathematical Theory of Feynman, Hyperfinite Dirichlet Forms an, Theory of P‑adic Distributi, The Statistical Mechanic, Mathematical Physics at Saint‑Flour
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Sergio Albeverio (born 17 January 1939) is a Swissmathematician and mathematical physicist working in numerous fields of mathematics and its applications. In particular he is known for his work in probability theory, analysis (including infinite dimensional, non-standard, and stochastic analysis), mathematical physics, and in the areas algebra, geometry, number theory, as well as in applications, from natural to social-economic sciences.
He initiated (with Raphael Høegh-Krohn) a systematic mathematical theory of Feynman path integrals and of infinite dimensional Dirichlet forms and associated stochastic processes (with applications particularly in quantum mechanics, statistical mechanics and quantum field theory). He also gave essential contributions to the development of areas such as p-adic functional and stochastic analysis as well as to the singular perturbation theory for differential operators. Other important contributions concern constructive quantum field theory and representation theory of infinite dimensional groups. He also initiated a new approach to the study of galaxy and planets formation inspired by stochastic mechanics.
Life and career
Albeverio is the son of Olivetta Albeverio Brighenti (1910–1968, tailor and then housewife) and Luigi (Gino) Albeverio (1905–1968, plumber and then owner of a small company of heating and plumbing). He grew up in Lugano, Switzerland. He is married to Solvejg Albeverio Manzoni (painter and writer) since 1970. They have a daughter, Mielikki Albeverio (dipl. socialsc.).
Study of mathematics and physics at the ETH Zürich with a Diploma Thesis (1962) under the direction of Markus Fierz and David Ruelle, and a Ph. D. Thesis (1966) under the direction of Res Jost and Markus Fierz.
Assistant at ETH Zürich (1962–67), visiting lecturer at Imperial College (1967–68, R. F. Streater). Invitation by Irving Segal as co-worker (MIT, 1968–69), replaced by a year stay as teacher at Liceo Cantonale, Lugano, due to family reasons.
Research Fellowship at Princeton University (1970–72, A. S. Wightman). Visiting Professorships at University of Oslo (1973–77, R. Høegh-Krohn), University of Naples (1973–74, G. F. Dell'Antonio), University of Aix-Marseille II (1976–77, D. Kastler, R. Stora).
2003: Prize for Interdisciplinary Project, University of Bonn
2015: Director (with A. B. Cruzeiro and D. Holm) of the Research Semester on Geometric Mechanics, Variational and Stochastic Methods at Centre Interfacultaire Bernoulli (CIB), EPFL
Over 250 invited lectures at international conferences in Mathematics, Physics and applications, including:
2000: Lectures at Saint-Flour on the occasion of the 30th anniversary of the Saint-Flour Lectures in Probability
2005: Plenary lecture for the conference on the occasion of K. Itô's 90th birthday, Oslo
Plenary lectures at symposia/conferences in honor of: G. Da Prato (1996), G. F. Dell'Antonio (2003 and 2013), L. Gross (2010), E. Balslev (2010), F. Guerra (2013), H. Holden (2016), D. Holm (2017)
Selected publications
Over 900 publications in scientific journals or volumes of proceedings.
Monographs
with Raphael Høegh-Krohn: Mathematical theory of Feynman Path Integrals, Lecture Notes in Mathematics, Band 523, Springer Verlag 1976, 2nd ed. (with Raphael Høegh-Krohn and Sonia Mazzucchi) 2008
with Raphael Høegh-Krohn, Jens Erik Fenstad, Tom Lindstrøm: Nonstandard Methods in stochastic analysis and mathematical physics, Academic Press 1986, Dover 2009 Russian translation by A. K. Svonskin, M. A. Shubin, Moscow: Mir (1990)
with Fritz Gesztesy, Raphael Høegh-Krohn, Helge Holden: Solvable Models in Quantum Mechanics, Springer 1988, 2nd ed., American Mathematical Society Chelsea Publishing, 2005 Russian translation by Yu. A. Kuperin, K. A. Makarov, V. A. Geilerk, Moscow: Mir (1990)
with Raphael Høegh-Krohn, J. Marion, D. Testard, B. Torresani: Noncommutative distributions: unitary representations of gauge groups and algebras, Marcel Dekker 1993
with Jürgen Jost, Sylvie Paycha, Sergio Scarlatti: A mathematical introduction to String Theory. Variational Problems, Geometric and Probabilistic Methods, Cambridge University Press 1997
with Pavel Kurasov: Singular perturbations of differential operators. Solvable Schrödinger type operators, London Mathematical Society Lecturenotes, Cambridge University Press 2000
with Franco Flandoli, Yakov G. Sinai, edited by Giuseppe Da Prato and Michael Röckner: SPDEs in hydrodynamics: recent progress and prospects. Lectures given at the C.I.M.E. Summer School held in Cetraro, 29 August –3 September 2005. Lecture notes in mathematics, 1942. Berlin: Springer, Florence: Fondazione C.I.M.E. 2008
with Yuri Kondratiev, Yuri Kozitsky, Michael Röckner: The statistical mechanics of quantum lattice systems. A path integral approach. EMS Tracts in Mathematics 8, Zürich: European Mathematical Society 2009
with R.-Z. Fan, F. S. Herzberg: Hyperfinite Dirichlet forms and stochastic processes, Berlin: Springer 2010
with A. Khrennikov, V. Shelkovich: Theory of p-adic distributions: linear and nonlinear models, Cambridge University Press 2010
with L. Gross and E. Nelson: Mathematical Physics at Saint-Flour, Berlin: Springer 2012. (Reprint of Saint-Flour Lecture in 2000, first published in S. Albeverio, W. Schachermayer, M. Talagrand: Lectures in Probability and Statistics. Lectures from the 30th Summer School in Probability Theory held in Saint-Flour, 2000. Berlin: Springer 2003)
Edited Books (Selection)
with M. Demuth, E. Schrohe, B.-W. Schulze: Parabolicity, Volterra calculus, and conical singularities. A volume of advances in partial differential equations. Operator Theory: Advances and Applications 138, Basel: Birkhäuser (2002)
with M. Demuth, E. Schrohe, B.-W. Schulze: Nonlinear hyperbolic equations, spectral theory, and wavelet transformations. Operator Theory: Advances and Applications 145, Basel: Birkäuser (2003)
with Z.-M. Ma, M. Röckner: Recent Developments in Stochastic Analysis and Related Topics. Proceedings of the first Sino-German conference on stochastic analysis, Beijing, China, 29 August–3 September 2002, World Scientific (2004)
with A. B. de Monvel, H. Ouerdiane: Proceedings of the International Conference on Stochastic Analysis and Applications. Hammamet, October 22–27, 2001. Dordrecht: Kluwer Academ. Publ. (2004)
with F. De Martini and G. F. Dell'Antonio: Entanglement and decoherence: mathematics and physics of quantum information and computation. Oberwolfach Rep. 2 (1), pp. 185–255 (2005) (EMS Publ.)
with V. Jentsch, H. Kantz: Extreme events in nature and society. Berlin: Springer (2006)
with F. Minazzi: Foundations of Mathematics today. Note di Matematica, Storia, Cultura, PRISTEMStoria 14/15 (2006)
with A. Vancheri, P. Giordano, D. Andrey: The Dynamics of the Complex Urban Systems: An interdisciplinary approach. Heidelberg: Springer (2007)
with M. Marcolli, S. Paycha, J. Plazas: Traces in Geometry, Number Theory, and Quantum Fields. Wiesbaden: Vieweg (2008)
with S.-M. Fei, A. Cabello, N.-H. Jing, D. Goswami: Quantum Information and Entanglement. Advances in Mathematical Physics 2010 (2010)
with Ph. Blanchard: Direction of Time. Berlin: Springer (2016)