Computation and Combinatorics in Dynamics, Stochastics and Control

The Abel Symposia volume at hand contains a collection of high-quality articles written by the world's leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory.In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields.

The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.

Contenu
Facilitated Exclusion Process: Jinho Baik, Guillaume Barraquand, Ivan Corwin and Toufic Suidan.- Stochastic Functional Differential Equations and Sensitivity to their Initial Path: D. R. Baños, G. Di Nunno, H. H. Haferkorn, and F. Proske.- Grassmannian flows and applications to nonlinear partial differential equations: Margaret Beck, Anastasia Doikou, Simon J.A. Malham and Ioannis Stylianidis.- Gog and Magog triangles: Philippe Biane.- The Clebsch representation in optimal control and low rank integrable systems: Anthony M. Bloch, Francois Gay-Balmaz, Tudor S. Ratiu.- The geometry of characters of Hopf algebras: Geir Bogfjellmo and Alexander Schmeding.- Shape analysis on homogeneous spaces: a generalised SRVT framework: E. Celledoni, S. Eidnes, A. Schmeding.- Universality in numerical computation with random data. Case studies, analytical results and some speculations: Percy Deift and Thomas Trogdon.- BSDEs with default jump: Roxana Dumitrescu, Miryana Grigorova, Marie-Claire Quenez, Agnes Sulem.- The Faà di Bruno Hopf algebra for multivariable feedback recursions in the center problem for higher order Abel equations: Kurusch Ebrahimi-Fard, W. Steven Gray.- Continuous-time autoregressive moving-average processes in Hilbert space: Fred Espen Benth and André Süss.- Pre- and post-Lie algebras: The algebro-geometry view: Gunnar Fløystad and Hans Munthe-Kaas.- Extension of the product of a post-Lie algebra and application to the SISO feedback transformation group: Loïc Foissy.- Infinite dimensional rough dynamics: M. Gubinelli.- Heavy tailed random matrices: how they differ from the GOE, and open problems: Alice Guionnet.- An analyst's take on the BPHZ theorem: Martin Hairer.- Parabolic Anderson model with rough dependence in space: Yaozhong Hu, Jingyu Huang, Khoa Lê, David Nualart, Samy Tindel.- Perturbation of conservation laws and averaging on manifolds: Xue-Mei Li.- Free probability, random matrices, and representations of non-commutative rational functions: Tobias Mai and Roland Speicher.- A review on comodule-bialgebras: Dominique Manchon.- Renormalization: a quasi-shuffle approach: Frédéric Menous and Frédéric Patras.- Hopf algebra techniques to handle dynamical systems and numerical integrators: A. Murua and J.M. Sanz-Serna.- Quantitative limit theorems for local functionals of arithmetic random waves: Giovanni Peccati and Maurizia Rossi.- Combinatorics on words and the theory of Markoff: Christophe Reutenauer.- An algebraic approach to integration of geometric rough paths: Danyu Yang.