This volume and ""Stochastic Processes, Physics and Geometry: New Interplays II"" present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, 'Infinite Dimensional (Stochastic) Analysis and Quantum Physics', was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry.The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and non commutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers.
A brief curriculum vitae of Sergio Albeverio by F. Gesztesy, H. Holden, J. Jost, S. Paycha, M. Rockner, and S. Scarlatti Students and postdoctoral fellows supervised by Sergio Albeverio by F. Gesztesy, H. Holden, J. Jost, S. Paycha, M. Rockner, and S. Scarlatti Publications of Sergio Albeverio by F. Gesztesy, H. Holden, J. Jost, S. Paycha, M. Rockner, and S. Scarlatti On the occasion of Sergio Albeverio's 60th birthday by P. Blanchard Growth and saturation in random media by G. B. Arous and A. F. Ramirez Maximal inequalities and exponential estimates for stochastic convolutions in Banach spaces by Z. Brzezniak and S. Peszat On Markov evolution equations in quotient probability spaces by A. M. Chebotarev and V. P. Maslov Maximal dissipativity of the Dirichlet operator corresponding to the Burgers equation by G. Da Prato and A. Debussche The Schrodinger equation with moving point interactions in three dimensions by G. F. Dell'Antonio, R. Figari, and A. Teta The square of self intersection local time of Brownian motion by C. Drumond, M. de Faria, and L. Streit On the role of flux in scattering theory by D. Durr and S. Teufel Probability and nonlinear analysis by E. B. Dynkin Special Ito maps and an $L^2$ Hodge theory for one forms on path spaces by K. D. Elworthy and X.-M. Li The classical massive Thirring system revisited by V. Z. Enolskii, F. Gesztesy, and H. Holden On Ito's formulae for additive functionals of symmetric diffusion processes by M. Fukushima Spectral theory of sparse potentials by D. Hundertmark and W. Kirsch Invariant measures under Schrodinger evolution and quantum statistical mechanics by G. Jona-Lasinio Exponential mixing for classical continuous systems by Yu. G. Kondratiev, R. A. Minlos, M. Rockner, and G. V. Shchepan'uk Diffusions on ""simple"" configuration spaces by Z.-M. Ma and M. Rockner One- and two-particle branches of the spectrum of ""many component"" operators by R. A. Minlos Representation integrale de fonctionnelles analytiques positives by H. Ouerdiane and A. Rezgui Mean field models and propagation of chaos in feedforward neural networks by M. Piccioni and S. Scarlatti Path properties of a class of Gaussian processes with applications to spde's by M. Sanz-Sole and M. Sarra A Feynman-Kac formula for unbounded semigroups by B. Simon Hypercontractivity in non-commutative $\bfL_p$ spaces by B. Zegarlinski.
