Profile
Profile

Prof. Dr. Sergio Albeverio

E-mail: albeverio(at)uni-bonn.de
Phone: +49 228 73 3418
Fax: +49 228 73 6133
Homepage: http://wt.iam.uni-bonn.de/albeverio/home/
Room: 3.052
Location: Mathematics Center
Institute: Institute for Applied Mathematics
Research Areas: Research Area G
Former Research Area L
Research Area C (until 10/2012)
Research Area H (until 10/2012)
Birthdate: 17.Jan 1939
Mathscinet-Number: 24435

Academic Career

1966

Dr. rer. nat., ETH Zürich, Switzerland (supervisor: R. Jost)

1962 - 1971

Assistant Professor, Lecturer, Research Fellow: ETH Zürich (Switzerland), Imperial College London (England, UK), Princeton University (NJ, USA)

1972 - 1977

Professor (Marseille, Oslo and Naples)

1977 - 1979

Professor (H3), University of Bielefeld

1979 - 1997

Professor (H4), University of Bochum

1997 - 2008

Professor (H4/C4), University of Bonn

Since 2008

Professor Emeritus

Longer research and teaching positions at many universities (Europe, China, Japan, Mexico, Russia, USA)

Research Profile

Areas:
Probability theory (stochastic processes, SPDE), analysis (infinite dimensional-, non-standard-), mathematical physics (statistical mechanics, quantum mechanics, quantum fields, quantum computation), differential geometry, topology, noncommutative geometry, spectral theory, dynamical systems, number theory, representation theory, algebra, statistics. Applications in biology, economics, engineering, physics, and urbanism.

Main aim:
New interactions between different areas of mathematics and sciences.

Some highlights:
Creation of mathematical theories of Feynman path integrals and infinite dimensional Dirichlet forms, development of non-standard analytic methods, new methods of handling singular systems. Among the worldwide most cited mathematicians (Science Watch, 2002). Over 750 publications in scientific journals, 9 research monographs, 30 proceedings books.

Research Projects and Activities

11 exchange projects (DFG)

INTAS (EU; Leader)

EU Research Training Network

Bonn University Prize

Member of SFB 611

Currently: 4 A. v. Humboldt fellows

Scientific Board of various institutions (in CH, CZ, I, S, UK)

Contribution to Research Areas

Research Area C (until 10/2012)
Major developments include: construction of quantum fields and rigorous Feynman path integrals, study of spectral theory of multi particle systems (proof of Efimov effect), singular perturbations. Breakthroughs in quantum anharmonic crystals and in quantum wave guides shrinking to graphs. Contributions to p-adic analysis, noncommutative normed algebras and derivations.

New research plans include: Feynman path integrals in geometric contexts (manifolds, gauge fields, discrete geometric spaces; link invariants from the asymptotics of Chern-Simons functional integrals); spectral theory of quantum mechanical operators, quantum graphs theory, trace formulae and number theory; structure theory of operator algebras.
Research Area G
Major developments include: quantum statistical mechanics on lattices, phase transitions; nonequilibrium statistical mechanics; asymptotics of probabilistic path integrals with applications in neurobiology; probabilistic methods for 3D Navier-Stokes; blow up phenomena in hyperbolic systems; study of SPDE'S with non Lipschitz coefficients.

New research plans include: stochastic processes on singular structures (thin networks, fractals) random media; asymptotics of SPDEs with strongly growing coefficients (small noise, invariant measures...), with applications in neurobiology; infinite dimensional probabilistic integrals with degenerate phase functions and applications (physics, finance); stochastic analysis methods in representation theory of infinite dimensional groups; probabilistic construction of quantum fields; stochastic processes and pseudodifferential operators on discrete metric spaces.
Former Research Area L
Major developments include: characterization of entanglement of quantum states; study of stochastic dynamics and ergodic theory with applications to neurobiological networks; continuous state space stochastic cellular automatic in urban dynamics.

New research plans include: ergodic theory, structure theory of singular measures; quantum computation from topological quantum fields models; new relations between entanglement measures and theory of algebraic invariants; characterization of quantum algorithms; complexity theory, neural networks, statistical mechanics.
Research Area H (until 10/2012)
Major developments include: inclusion of economic features into models of urban development; incorporation of equity linked life insurance contracts in interacting assets model; Lévy processes in financial markets, empirical processes and large markets.

New research plans include: voltarget portfolio management; study of models with affine structure; study of models integrating macroeconomic features into microeconomic evolution.

Selected Publications

[1] Sergio Albeverio, Zdzisław Brzeźniak, Jiang-Lun Wu
Existence of global solutions and invariant measures for stochastic differential equations driven by Poisson type noise with non-Lipschitz coefficients
J. Math. Anal. Appl. , 371: (1): 309--322
2010
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2010.05.039
[2] S. Albeverio, A. Yu. Khrennikov, V. M. Shelkovich
Theory of p-adic distributions: linear and nonlinear models
of London Mathematical Society Lecture Note Series : xvi+351
Publisher: Cambridge University Press, Cambridge
2010
ISBN: 978-0-521-14856-6
DOI: 10.1017/CBO9781139107167
[3] S. Albeverio, Sh. A. Ayupov, R. Z. Abdullaev
Arens spaces associated with von Neumann algebras and normal states
Positivity , 14: (1): 105--121
2010
ISSN: 1385-1292
DOI: 10.1007/s11117-009-0008-5
[4] Sergio Albeverio, Sonia Mazzucchi
Infinite dimensional oscillatory integrals with polynomial phase function and the trace formula for the heat semigroup
Astérisque (327): 17--45 (2010)
2009
ISBN: 978-2-85629-288-4
ISSN: 0303-1179
[5] S. Albeverio, V. Steblovskaya, K. Wallbaum
Valuation of equity-linked life insurance contracts using a model with interacting assets
Stoch. Anal. Appl.
, 27: (5): 1077--1095
2009
ISSN: 0736-2994
DOI: 10.1080/07362990902844462
[6] Sergio Albeverio, Alexander K. Motovilov, Andrei A. Shkalikov
Bounds on variation of spectral subspaces under J-self-adjoint perturbations
Integral Equations Operator Theory , 64: (4): 455--486
2009
ISSN: 0378-620X
DOI: 10.1007/s00020-009-1702-1
[7] Sergio Albeverio, Yuri Kondratiev, Yuri Kozitsky, Michael Röckner
The statistical mechanics of quantum lattice systems
A path integral approach
of EMS Tracts in Mathematics : xiv+379
Publisher: European Mathematical Society (EMS), Zürich
2009
ISBN: 978-3-03719-070-8
DOI: 10.4171/070
[8] Sergio Albeverio, Oleksandr Baranovskyi, Mykola Pratsiovytyi, Grygoriy Torbin
The Ostrogradsky series and related Cantor-like sets
Acta Arith. , 130: (3): 215--230
2007
ISSN: 0065-1036
DOI: 10.4064/aa130-3-2
[9] Sergio Albeverio, Claudio Cacciapuoti, Domenico Finco
Coupling in the singular limit of thin quantum waveguides
J. Math. Phys. , 48: (3): 032103, 21
2007
ISSN: 0022-2488
DOI: 10.1063/1.2710197
[10] Sergio Albeverio, Christof Cebulla
Müntz formula and zero free regions for the Riemann zeta function
Bull. Sci. Math. , 131: (1): 12--38
2007
ISSN: 0007-4497
DOI: 10.1016/j.bulsci.2006.03.002

Publication List

Editorships

16 journals/book series, a.a.:
• Akademie Verlag
• Expositiones Mathematicae
• IDAQP
• Reviews of Mathematical Physics
• Rep. Math. Phys.
• P-Adic Numbers, Ultrametric Analysis, and Applications
• Math. Physics, Analysis and Geometry
• Adv. Math. Phys.
• Encyclopedia of Mathematics (Springer)
• Encyclopedia of Mathematical Physics (Elsevier) Scholarpedia
• Cognitive Processing

Awards

1993

Max Planck Research Award

2002

Doctor honoris causa, Oslo University, Norway (Bicentennial of N.H. Abel)

Selected Invited Lectures

Plenary lecturer at over 230 international meetings, including:

1977

International Congress on Mathematical Physics, Rome, Italy

1983

International Congress on Mathematical Physics, Boulder, CO, USA

1986

International Congress on Mathematical Physics, Marseille, France

1988

International Congress on Mathematical Physics, Swansea, Wales, UK

2000

St. Flour, France

2003

International Congress on Mathematical Physics, Organization of Session, Lisbon, Portugal

2005

Abel Symp., Oslo, Norway

2010

L. Gross Symp., Cornell, NY, USA

2010

E. Balslev Symp., Aarhus, Denmark

Offers

1988

Chair of Mathematics, per chiara fama, Roma University II, Italy

Habilitations

Over 20 Habilitations

Selected PhD students

Werner Kirsch (1981): “Über Spektren stochastischer Schrödingeroperatoren”,
now Professor, Fernuniversität Hagen (University of Hagen)

Michael Röckner (1984): “A Dirichlet Problem for Distributions and the Construction of Specifications for Gaussian Generalized Random Fields”,
now Professor, University of Bielefeld

Sylvie Paycha (1988): “Probability measures in infinite dimensional manifolds and Polyakov strings”,
now Professor, University of Potsdam

Koichiro Iwata (1990): “On Linear Maps Preserving Markov Properties and Applications to Multicomponent Generalized Random Fields”,
now Professor, Hiroshima University, Japan

Hanno Gottschalk (1999): “Green's Functions for Scattering in Local, Relativistic Quantum Field Theory”,
now Professor, University of Wuppertal

Eva Lütkebohmert (2004): “Finite dimensional realizations for Heath, Jarrow and Morton type forward rate models with jumps and an asymptotic expansion for the Black-Scholes model with generalized volatility”,
now Professor, University of Freiburg

Frederik Herzberg (2005): “Path-Dependent Utility Functions and Nonstandard Analysis”,
now Junior Professor, University of Bielefeld

Supervised Theses

  • Diplom theses: 110
  • PhD theses: 42
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