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# m:iv seminar archive

past seminars

## Event details

### When

Nov 14, 2016
from 04:00 PM to 06:00 PM

MA119

### Contact Name

We give an introduction how the 3D projector in the VisLab can be used for 3D viewing of surfaces.

Slides

## Event details

### When

Nov 28, 2016
from 04:00 PM to 06:00 PM

MA119

### Contact Name

Abstract:

We will begin by surveying some topological obstructions for compact surfaces to be embedded minimally in different ambient three-manifolds. In the case of the Riemannian product S^2xS^1, we will show that a compact surface can be embedded minimally in S^2xS^1 if and only if it has odd Euler characteristic.To illustrate this result, we will construct compact embedded minimal surfaces in S^2xS^1 with a high number of symmetries, first by means of solutions to the Plateau problem with respect to suitable contours, and second by the so-called conjugate Plateau construction. Time permitting, we will explain how this conjugate technique can be extended to obtain constant mean curvature surfaces in H^2xR and S^2xR with prescribed symmetries. This is based on a joint work with Julia Plenhert and Francisco Torralbo.

We will go to lunch with Miguel at 12:30pm.

## 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.

## Event details

### When

Feb 02, 2017
from 11:00 AM to 12:00 PM

MA119

## Liam Collard : The Weierstrass representation for minimal surfaces

Abstract: The Weierstrass representation allows any minimal surface to be represented by a pair of a meromorphic function and a holomorphic 1-form, the so-called Weierstrass data. In particular, new families of minimal surfaces can be created by transforming the Weierstrass data. In this talk I will introduce the Weierstrass representation, show that minimal surfaces are isothermic surfaces and discuss possible transformations. Throughout the talk examples of minimal surfaces will be shown.

## Event details

### When

Feb 23, 2017
from 11:00 AM to 12:00 PM

MA119

## 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.

## Event details

### When

Mar 02, 2017
from 11:00 AM to 12:00 PM

MA119

## 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.

## Event details

### When

Mar 23, 2017
from 11:00 AM to 12:00 PM

MA119

## 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.

## Event details

### When

Jun 22, 2017 11:00 AM to
Jul 22, 2017 12:00 PM

MA119

## Josef F. Dorfmeister

Willmore surfaces in spheres and harmonic maps

## Event details

### When

Nov 10, 2017
from 02:00 PM to 03:00 PM

MA119

## Event details

### When

Nov 24, 2017
from 02:00 PM to 03:00 PM

MA119

## Keomkyo Seo (Sookmyung University, Korea) "Necessary conditions for submanifolds to be connected in a Riemannian manifold"

(Sookmyung University, Korea) "Necessary conditions for submanifolds to be connected in a Riemannian manifold"

## Event details

### When

Jan 16, 2018 02:00 PM to
Jan 19, 2018 03:00 PM

Abstract: It is well-known that any simple closed curve in ℝ3​​ bounds at least one minimal disk, which was independently proved by Douglas and Radó. However, for any given two disjoint simple closed curves, we cannot guarantee existence of a compact connected minimal surface spanning such boundary curves in general. From this point of view, it is interesting to give a quantitative description for necessary conditions on the boundary of compact connected minimal surfaces. We derive density estimates for submanifolds with variable mean curvature in a Riemannian manifold with sectional curvature bounded above by a constant. This leads to distance estimates for the boundaries of compact connected submanifolds. As applications, we give several necessary conditions and nonexistence results for compact connected minimal submanifolds, Bryant surfaces, and surfaces with small L2​ norm of the mean curvature vector in a Riemannian manifold.

## Prof. Fran Burstall (University of Bath): Linear Weingarten surfaces in Lie sphere geometry

Abstract: I shall give an elementary take on some joint work with Hertrich-Jeromin and Rossman which describes how linear Weingarten surfaces in 3-space are related to pairs of isothermic surfaces in the space of 2-spheres. Both smooth and discrete cases will be treated. No prior knowledge of the area will be assumed.

## Event details

### When

Feb 19, 2018
from 04:00 PM to 05:00 PM

TBA

## Event details

### When

Feb 20, 2018
from 02:00 PM to 03:00 PM

## Prof. Joeri Van Der Veken

University of Leuven Department of Mathematics

## Event details

### When

Mar 13, 2018
from 02:00 PM to 03:00 PM

### Where

MA119

Title: Lagrangian submanifolds of S3 x S3

## Event details

### When

Jul 17, 2018
from 10:00 AM to 05:00 PM

MA119

## Speakers:

Joseph Cho (Kobe)

Title: Discrete omega surfaces - a rough introduction

Abstract: Omega-surfaces were discovered by Demoulin, and one of the motivations of studying Omega-surfaces arise from the fact that well-known classes of surfaces such as constant mean curvature surfaces, constant Gaussian curvature surfaces, and linear Weingarten surfaces are all examples of Omega-surfaces. Demoulin showed that Omega-surfaces are the class of surfaces that envelop a pair of isothermic sphere congruences, allowing one to apply the rich theory of isothermic surfaces to examine the properties of Omega-surfaces. Recent interest in integrable systems has led to renewed interest in Omega-surfaces, exemplified in works by Burstall, Cecil, Ferapontov, Hertrich-Jeromin, Musso, Nicolodi, etc..
In this talk, we look at discrete Omega-surfaces. First, we give different characterizations of discrete Omega-surfaces: via Konigs dual lifts, via Moutard lifts, and via gauge-theoretic description. Then, using the transformation theory developed for discrete isothermic surfaces, we discuss Darboux transformations of discrete Omega-surfaces. This talk is based on the joint work with Fran Burstall (University of Bath), Udo Hertrich-Jeromin (Technische Universität Wien), Mason Pember (Technische Universität Wien), and Wayne Rossman (Kobe University).

Joshua Cork (Leeds)

Title: Symmetric calorons and the rotation map.

Abstract: For quite some time, there has been much interest in Yang-Mills instantons. These are manifested as finite-action anti-self-dual connections over some four manifold. They possess a very rich geometry, providing examples of hyperkahler metrics, and various applications to physics. A great deal of the progress in understanding the most basic examples of these objects has been through studying fixed points under isometries. In this talk, I will discuss calorons, which are instantons on S^1\times R^3. In particular, I shall present a classification result of cyclically symmetric calorons, where the cyclic groups considered are coupled to a non-spatial isometry known as the rotation map.

Jenya Ferapontov (Loughborough)

Title: DISPERSIONLESS INTEGRABLE SYSTEMS IN 3D AND EINSTEIN-WEYL GEOMETRY
(based on joint work with Boris Kruglikov)

Abstract

For several classes of second-order dispersionless PDEs, we show that their characteristic varieties define conformal structures which must be Einstein-Weyl in 3D (or self-dual in 4D) if and only if the PDE is integrable by the method of hydrodynamic reductions. This demonstrates that the integrability of dispersionless PDEs can be seen from the geometry of their characteristic varieties.

Title: Conformal volume, eigenvalue problems, and related topics

Abstract: I will give a short survey about the classical inequalities for the first Laplace eigenvalue on Riemannian manifolds, such as the Reilly inequality, the Li-Yau inequality, and tell about related history and questions. I will then discuss results concerning their versions for the higher Laplace eigenvalues and concerning estimates for the number of negative eigenvalues of Schrodinger operators.

Yuta Ogata (Okinawa)

Title: Constant mean curvature surfaces and positon-like solutions

Abstract:The classical Bianchi-Baecklund transformation for constant mean curvature surfaces in Euclidean 3-space has been studied by many researchers. In this talk, we introduce the method to construct positon-like solution of elliptic sinh-Gordon equation via successive Bianchi-Baecklund transformations with a single spectral parameter. We also show the recipe of the corresponding constant mean curvature surfaces of positon-like solutions.

Gudrun Szewieczek (Wien)

Title: Combescure transformations – a helpful tool for the study of Guichard nets

Abstract : Two surfaces are Combescure transformations of each other if they have parallel tangent planes along corresponding curvature lines. The existence of particular Combescure transformations can be used to characterize various classes of integrable surfaces, e.g. the Christoﬀel transformation for isothermic surfaces. In this talk we investigate this concept for triply orthogonal systems and discuss the subclass of Guichard nets, which arise as special coordinate systems of 3-dimensional conformally ﬂat hypersurfaces.