Sergio Albeverio

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Sergio Albeverio

Sergio Albeverio (born January 17, 1939 in Lugano ) is a Swiss mathematician and mathematical physicist who is active in numerous areas of mathematics and its applications . He is known for his work on probability theory , analysis (including infinite-dimensional analysis , non-standard analysis and stochastic analysis ), mathematical physics and in the areas of algebra , geometry and number theory as well as in the application areas of mathematics and physics in natural , Social and economic science .

Career

Albeverio is the son of Olivetta Albeverio Brighenti (1910–1968, tailor and later housewife) and Luigi (Gino) Albeverio (1905–1968, plumber and later owner of a small heating and plumbing company). He grew up in Lugano (Switzerland). He has been married to Solvejg Albeverio-Manzoni (painter and writer) since 1970 and has a daughter with her, Mielikki Albeverio (graduate social scientist). He initiated (with Raphael Høegh-Krohn ) a systematic mathematical theory of Feynman path integrals and infinite-dimensional Dirichlet forms and the related stochastic processes (with applications in particular in the areas of quantum mechanics, statistical mechanics and quantum field theory). He also made significant contributions to the development of the fields of p -adic functional and stochastic analysis on the one hand and singular perturbation theory for differential operators on the other . He made other important contributions in the areas of constructive quantum field theory and the representation theory of infinite-dimensional groups . He also founded a new approach to studying the formations of galaxies and planets, inspired by stochastic mechanics .

Life and career

Research interests

Albeverio's main interests are in the areas of probability theory (stochastic processes, stochastic analysis, stochastic partial differential equations ), analysis (functional and infinite-dimensional analysis, non-standard analysis, p -adic analysis), mathematical physics ( classical and quantum physics , especially hydrodynamics , statistical physics) , Quantum field theory, quantum information and astrophysics ), geometry ( differential geometry , non-commutative geometry ), topology ( configuration spaces , knot theory ), operator algebras , spectral theory , fractals , number theory ( analytical and p -adic ), representation theory, algebra, information theory and statistics , mathematical applications in the field of mathematics Biology , geosciences , economics, engineering , physics, social sciences, in the field of models of urban systems, epistemology and more generally in the fields of philosophy he and cultural issues.

Memberships

S. Albeverio is or was a member of many bodies, committees and societies, including:

Honourings and prices

Selected publications

Over 900 publications in scientific journals or conference proceedings.

Monographs

  • with Raphael Høegh-Krohn : Mathematical theory of Feynman Path Integrals , Lecture Notes in Mathematics, Volume 523, Springer Verlag 1976, 2nd edition (with Raphael Høegh-Krohn and Sonia Mazzucchi) 2008
  • with Raphael Høegh-Krohn, Jens Erik Fenstad and Tom Lindstrøm: Nonstandard Methods in stochastic analysis and mathematical physics , Academic Press 1986, Dover 2009 Russian translation by AK Svonskin, MA Shubin, Moscow : Mir (1990)
  • with Fritz Gesztesy , Raphael Høegh-Krohn, Helge Holden : Solvable Models in Quantum Mechanics , Springer 1988, 2nd edition, American Mathematical Society Chelsea Publishing, 2005 Russian translation by Yu. A. Kuperin, KA Makarov, VA 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 Lecture Notes, 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 CIME Summer School held in Cetraro, 29 August – 3 September 2005. Lecture notes in mathematics, 1942. Berlin: Springer, Florence: Fondazione CIME 2008
  • with Yuri Kondratiev, Yuri Kozitsky, Michael Röckner: The statistical mechanics of quantum lattice systems. A path integral approach. EMS Tracts in Mathematics 8, Zurich: European Mathematical Society 2009
  • with R.-Z. Fan, FS 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, E. Nelson: Mathematical Physics at Saint-Flour , Berlin: Springer 2012. (Reprint of the Saint-Flour Lecture 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)

Published 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 AB 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 GF 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)

Web links

Individual evidence

  1. ↑ a b Gesztesy, Fritz; Holden, Helge; Jost, Jürgen; Paycha, Sylvie; Röckner, Michael; Scarlatti, Sergio (Ed.): Stochastic Processes, Physics and Geometry: New Interplays. I: A Volume in Honor of Sergio Albeverio . CMS / AMS, Providence, Rhode Island 2000, ISBN 978-0-8218-1959-3 , pp. Preface .
  2. ^ Sergio Albeverio - The Mathematics Genealogy Project. Retrieved June 23, 2017 .
  3. ↑ Gesztesy, Fritz; Holden, Helge; Jost, Jürgen; Paycha, Sylvie: Röckner, Michael; Scarlatti, Sergio (Ed.): Stochastic Processes, Physics and Geometry: New Interplays. II: A Volume in Honor of Sergio Albeverio . CMS / AMS, Providence, Rhode Island, ISBN 978-0-8218-1960-9 .
  4. ^ Sergio Albeverio: Publications. Retrieved August 2, 2017 .
personal data
SURNAME Albeverio, Sergio
BRIEF DESCRIPTION Swiss mathematical physicist and mathematician
DATE OF BIRTH January 17, 1939
PLACE OF BIRTH Lugano