The Centre for Mathematical Sciences research seminars and events are listed below.
The four main seminar series are in applied mathematics, pure mathematics, statistics and theoretical physics. Visit the centre's webpages for the latest seminar updates and information.
6 December (16:00-17:00): Gauge-invariant observables in perturbative quantum gravity
- Speaker: Markus Fröb (York)
It is well known that the diffeomorphism invariance of gravitational theories makes it impossible to define local and gauge-invariant observables in perturbative (quantum) gravity, except at linear order. While in flat space one can study the S-Matrix, which is a gauge-invariant global observable, no analogue exists in a general curved space. Relational observables (i.e., the value of one field at the point where a second field has a prescribed value) are natural candidates for observables in (quantum) gravity, but they are not local when constructed around flat space or around a cosmological (FLRW) background spacetime due to the high symmetry of the latter.
We present two different approaches to this problem: a) correlation functions at fixed geodesic distance, and b) a construction of invariant coordinates, for which explicit and fully renormalised results for one-graviton-loop corrections to two-point functions and coupling constants have been obtained.
13 December (15:00-16:00): The birational geometry of moduli spaces via Bridgeland stability
- Speaker: Barbara Bolognese (Sheffield)
In 2006, Tom Bridgeland introduced the notion of stability conditions for objects in an arbitrary triangulated category. The original motivation came from Mirror Symmetry, as this was the generalization of the notion of stability for D-branes fathered by Michael Douglas. Soon afterwards, a whole stream of results flourished around Bridgeland’s original idea, and Bridgeland stability conditions had been seen to find applications in geometric representation theory and in binational geometry. In our talk, we will see how wall-crossing phenomena arising from the structure of the set of stability conditions on an algebraic surface give a new powerful machinery to study and, in some cases, to completely describe the binational geometry of certain moduli spaces of sheaves on the given algebraic surface. In a joint work with Huizenga, Lin, Riedl, Schmidt, Woolf and Zhao, we will apply this machinery to a very special moduli space of sheaves, called Hilbert scheme of points, to progress towards a description of its binational geometry via its Nef cone.
17 January (14:00-15:00): Acoustic-gravity waves, theory and applications
- Speaker: Usama Kadri (Cardiff)
Acoustic–gravity waves (AGWs) are compression-type waves generated as a response to a sudden change in the water pressure, e.g. due to nonlinear interaction of surface waves, submarine earthquakes, landslides, falling meteorites and objects impacting the sea surface. AGWs can travel at near the speed of sound in water (ca. 1500 m/s), but can also penetrate through the sea-floor surface amplifying their speed, which turns them into excellent precursors. “Acoustic–gravity waves” is an emerging field that is rapidly gaining popularity among the scientific community, as it finds broad utility in physical oceanography, marine biology, geophysics, water engineering, and quantum analogues. This talk is an overview on AGWs, with emphasis on recent developments, current challenges, and future directions.