I will give a short survey on classical inequalities for Laplace eigenvalues, tell about related history and questions. I will then discuss the so-called Korevaar method, and new results generalising to higher eigenvalues a number of classical inequalities known for the first Laplace eigenvalue only.
Oxford Mathematician Carla Groenland talks about her and Oxford colleagues' work on graph reconstruction.
A graph $G$ consists of a set of vertices $V(G)$ and a set of edges $E(G)$ which may connect two (distinct) vertices. (There are no self-loops or multiple edges.)
Oxford Mathematics is delighted to announce that Prof. Jon Keating FRS, the Henry Overton Wills Professor of Mathematics in Bristol, and Chair of the Heilbronn Institute for Mathematical Research, has been appointed to the Sedleian Professorship of Natural Philosophy in the University of Oxford.
I will talk about the implications of UV completion of quantum gravity on the low energy spectrums. I will introduce the constraints on low-energy effective theory due to unitarity and analyticity of scattering amplitudes, in particular an infinite set of new unitarity constraints on the forward-limit limit of four-point scattering amplitudes due to the work of Arkani-Hamed et al. In three dimensions, we find the constraints imply that light states with charge-to-mass ratio z greater than 1 can only be consistent if there exists other light states, preferably neutral. Applied to the 3D Standard Model like spectrum, where the low energy couplings are dominated by the electron with z \sim 10^22, this provides a novel understanding of the need for light neutrinos.
Given a stability condition defined over a category, every object in this category
is filtered by some distinguished objects called semistables. This
filtration, that is unique up-to-isomorphism, is know as the
Harder-Narasimhan filtration.
One less studied property of stability conditions, when defined over an
abelian category, is the fact that each of them induce a chain of torsion
classes that is naturally indexed.
In this talk we will study arbitrary indexed chain of torsion classes. Our
first result states that every indexed chain of torsion classes induce a
Harder-Narasimhan filtration. Following ideas from Bridgeland we
show that the set of all indexed chains of torsion classes satisfying a mild
technical condition forms a topological space. If time we
will characterise the neighbourhood or some distinguished points.
