Project description DEENESFRITPL Research could offer clues to key questions on smooth ergodic theory and dynamical systems The EU-funded Resonances project plans to develop new, original methods to address a number of fundamental questions regarding smooth ergodic theory and dynamical systems. The newly proposed methods should find applications in different areas of mathematics, in particular geometry, number theory and topology. The questions under study are specifically related to resonances, which characterise statistical properties of dynamical systems through the correlation function and the zeta function. The project aims to develop a new theory of resonances and correlation functions for a broader class of systems that are currently not being addressed by any existing theories. Show the project objective Hide the project objective Objective The objective of this research project is to develop new and original methods to address a number of fundamental questions in the development of smooth ergodic theory and dynamical systems. Furthermore, this theory will have important and diverse applications to many different areas of mathematics (in particular geometry, but also number theory and topology).The questions we are interested in are specifically related to the study of resonances, which characterise statistical properties of dynamical systems via the correlation function and the zeta function.The generality of the approach draws heavily on the PI's experience with the ergodic theory of hyperbolic systems, an area of research in which the PI has played a leading role for many years, but the risk and ambition stems from the novelty and risk inherent in trying to apply new ideas.There are three major strands to this work although they are bound together by interactions both at the level of the conclusions and the methodology.(a) The first is the development of new methods for determining numerically basic characteristic values, which are theoretically poorly understood, for classical (``chaotic'') hyperbolic systems. The important new development is a completely rigorous estimate on the approximation.(b) The second main theme will be the establishment of a radically new theory of resonances and correlation functions for a broader classes of systems, for which there is presently no existing theory. Typically these examples arise in geometry, and will help advancing our understanding of problems in that area.(c) The third main topic will be applications to specific major problems, particularly in hyperbolic geometry, and number theory. A key ingredient in our approach is the blending of classical ideas from classical thermodynamic formalism with more progressive functional analytic techniques that continue to emerge. Fields of science natural sciencesmathematicspure mathematicstopologynatural sciencesmathematicsapplied mathematicsdynamical systemsnatural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicspure mathematicsgeometry Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-2018-ADG - ERC Advanced Grant Call for proposal ERC-2018-ADG See other projects for this call Funding Scheme ERC-ADG - Advanced Grant Coordinator THE UNIVERSITY OF WARWICK Net EU contribution € 1 904 305,00 Address Kirby corner road - university house CV4 8UW Coventry United Kingdom See on map Region West Midlands (England) West Midlands Coventry Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00 Beneficiaries (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all THE UNIVERSITY OF WARWICK United Kingdom Net EU contribution € 1 904 305,00 Address Kirby corner road - university house CV4 8UW Coventry See on map Region West Midlands (England) West Midlands Coventry Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00
