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Francesca Tripoli: On the topology of surfaces with the generalised simple lift property
Abstract: Motivated by the work of Colding and Minicozzi and Hoffman and White on minimal laminations obtained as limits of sequences of properly embedded minimal disks, Bernstein and Tinaglia introduce the concept of the simple lift property. Interest in these surfaces arises because leaves of a minimal lamination obtained as a limit of a sequence of properly embedded minimal disks satisfy the simple lift property. Bernstein and Tinaglia prove that an embedded minimal surface $\Sigma\subset\Omega$ with the simple lift property must have genus zero, if $\Omega$ is an orientable three-manifold satisfying certain geometric conditions. In particular, one key condition is that $\Omega$ cannot contain closed minimal surfaces. In my thesis, I generalise this result by taking an arbitrary orientable three-manifold $\Omega$ and introducing the concept of the generalised simple lift property, which extends the simple lift property. Indeed, it will be proved that leaves of a minimal lamination obtained as a limit of a sequence of properly embedded minimal disks satisfy the generalized simple lift property and one is then able to restrict the topology of an arbitrary surface $\Sigma\subset\Omega$ with the generalised simple lift property. Among other things, I prove that the only possible compact surfaces with the generalised simple lift property are the sphere and the torus in the orientable case, and the connected sum of up to four projective planes in the non-orientable case. In the particular case where $\Sigma\subset\Omega$ is a leaf of a minimal lamination obtained as a limit of a sequence of properly embedded minimal disks, we are able to sharpen the previous result, so that the only possible compact leaves are the torus and the Klein bottle.
Located in Projects / m:iv
Simon Cox: The mathematics of soap bubbles
Abstract: A soap film spanning a wire frame is a minimal surface, i.e. it is a surface of zero mean curvature. A soap film enclosing a certain volume of gas, i.e. a bubble, is a surface of constant mean curvature. Hence an aqueous foam at equilibrium is a collection of cmc surfaces subject to volume constraints. The way in which soap films meet, known as Plateau's laws, are a consequence of the fact that soap films minimize their surface area. I will introduce the basics of foam structure and describe the Kelvin problem, which is the search for the least area partition of space into bubbles of equal volume, and some of the, often surprising, consequences of area-minimization in driving foam dynamics in different applications.
Located in Projects / m:iv
TBA
Located in Projects / m:iv
Prof. Joeri Van Der Veken
University of Leuven Department of Mathematics
Located in Projects / m:iv
Fran Burstall: Introduction to discrete isothermic surfaces
Fran Burstall (University of Bath): Isothermic surfaces, of which minimal surfaces are an example, are perhaps the simplest geometric integrable system and have smooth, discrete and semi-discrete incarnations. In this talk, after a brief account of the smooth theory to set the scene, I shall discuss various approaches to the discrete theory including a gauge-theoretic approach that applies in all three settings.
Located in Projects / m:iv
m:iv Mini-Workshop 2018 Leicester
Located in Projects / m:iv
K Grosse-Brauckmann
Located in Projects / m:iv
Prof. Fran Burstall (University of Bath)
TBA
Located in Academic Departments / Mathematics
File mini-workshop slides Ferapontov
Located in Projects / m:iv
Dr Ross Ogilvie, Moduli of harmonic tori in S^3.
The primary focus of this talk is to discuss harmonic maps from a torus to the 3-sphere, which may be characterised by means of their 'spectral curves'. We will give a description of the moduli space of harmonic maps whose spectral curve is genus zero or one, and compare this to the similar case of constant mean curvature tori in S^3.
Located in Projects / m:iv

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