Everyday life tells us that curved objects may have two stable states: a contact lens (or the spherical cap obtained by cutting a tennis ball, see picture) can be turned ‘inside out’. Heuristically, this is because the act of turning the object inside out keeps the central line of the object the same length (the centreline does not stretch significantly). Such deformations are called ‘isometries’ and the ‘turning inside out’ (or everted) isometry of a thin shell is often referred to as mirror buckling.

Cycling science is a lucrative and competitive industry in which small advantages are often the difference between winning and losing. For example, the 2017 Tour de France was won by a margin of less than one minute for a total race time of more than 86 hours. Such incremental improvements in performance come from a wide range of specialists, including sports scientists, engineers, and dieticians. How can mathematics assist us?

Spatio-Temporal Dynamics and Turnover of Lipopolysaccharide in the Bacterial Outer Membrane
Lenton, S Leaman, R Spears, R Fascione, M Pushkin, D Coles, M Baumann, C Biophysical Journal volume 114 issue 3 550a (Feb 2018)
Thu, 10 May 2018

16:00 - 17:00
C5

Morse subsets of hierarchically hyperbolic spaces

Davide Spriano
(ETH Zurich)
Abstract

When dealing with geometric structures one natural question that arise is "when does a subset inherit the geometry of the ambient space"? In the case of hyperbolic space, the concept of quasi-convexity provides answer to this question. However, for a general metric space, being quasi-convex is not a quasi-isometric invariant. This motivates the notion of Morse subsets. In this talk we will motivate the definition and introduce some examples. Then we will introduce the class of hierarchically hyperbolic groups (HHG), and furnish a complete characterization of Morse subgroups of HHG. If time allows, we will discuss the relationship between Morse subgroups and hyperbolically-embedded subgroups. This is a joint work with Hung C. Tran and Jacob Russell.

Electrostatic potential variations on stellarator magnetic surfaces in low collisionality regimes
Calvo, I Velasco, J Parra Diaz, F Alonso, J García-Regaña, J Journal of Plasma Physics volume 84 issue 4 905840407 (02 Aug 2018)

The generation of electricity from elevated water sources has been the subject of much scientific research over the last century. Typically, in order to produce cost-effective energy, hydropower stations require large flow rates of water across large pressure drops. Although there are many low head sites around the UK, including numerous river weirs and potential tidal sites, the pursuit of low head hydropower is often avoided because it is uneconomic.

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