Oxford Mathematicians Stephen Haben and Peter Grindrod and colleagues have won an outstanding certificate as part of the new IIF Tao Hong Award for papers in energy forecasting published in the International Journal of Forecasting.
As part of our series of research articles deliberately focusing on the rigour and intricacies of mathematics, we look at Oxford Mathematician Minyhong Kim's research in to the relationship between number theory and topology. Minhyong Kim is Professor of Number Theory here in Oxford and Fellow of Merton College.
It is probably well-known that number theory is the source of some of the oldest and most accessible questions in mathematics:
The study of networks offers a fruitful approach to understanding human behaviour. Sanjeev Goyal is one of its pioneers. In this lecture Sanjeev presents a puzzle:
A nonparametric significance test for sampled networks
Elliott, A
Leicht, E
Whitmore, A
Reinert, G
Reed-Tsochas, F
Bioinformatics
volume 34
issue 1
64-71
(01 Jul 2017)
Congratulations to the Oxford Mathematicians who have just been awarded LMS prizes.
Conditional risk measures in a bipartite market structure
Kley, O
Klueppelberg, C
Reinert, G
Scandinavian Actuarial Journal
volume 2018
issue 4
328-355
(13 Jul 2017)
Mon, 27 Nov 2017
16:00 -
17:00
L4
Homogenization of the eigenvalues of the Neumann-Poincaré operator
Charles Dapogny
(Universite Grenoble-Alpes)
Abstract
In this presentation, we investigate the spectrum of the Neumann-Poincaré operator associated to a periodic distribution of small inclusions with size ε, and its asymptotic behavior as the parameter ε vanishes. Combining techniques pertaining to the fields of homogenization and potential theory, we prove that the limit spectrum is composed of the `trivial' eigenvalues 0 and 1, and of a subset which stays bounded away from 0 and 1 uniformly with respect to ε. This non trivial part is the reunion of the Bloch spectrum, accounting for the collective resonances between collections of inclusions, and of the boundary layer spectrum, associated to eigenfunctions which spend a not too small part of their energies near the boundary of the macroscopic device. These results shed new light about the homogenization of the voltage potential uε caused by a given source in a medium composed of a periodic distribution of small inclusions with an arbitrary (possibly negative) conductivity a surrounded by a dielectric medium, with unit conductivity.
