Talks

Outline of Topics:

Minimal Surfaces in Diblock Copolymers: the P,G, and D triply periodic minimal surfaces.
Smectic Liquid Crystals: the simplest crystals and they are built from surfaces.
Using minimal surfaces to knit: geometric scaffolds in materials science.

Introduction: In the last decades, advances in bone tissue engineering mainly based on osteoinduction and on stem cell research. Only recently, new efforts focused on the micro- and nanoarchitecture of bone substitutes to improve and accelerate bone regeneration. By the use of additive manufacturing, diverse microarchitectures were tested to identify the ideal pore size [1], the ideal filament distance and diameter [2], or light-weight microarchitecture [3], for osteoconduction to minimize the chance for the development of non-unions. Overall, the optimal microarchitecture doubled the efficiency of scaffold-based bone regeneration without the need for growth factors or cells. Another focus is on bone augmentation, a procedure mainly used in the dental field.

Methods: For the production of scaffolds, we applied the CeraFab 7500 from Lithoz, a lithographybased additive manufacturing machine. Hydroxyapatite-based and tri-calcium-phosphate-based scaffolds were produced with Lithoz TCP 3...

I will first consider the geometry of the complex hyperbolic plane and immersed surfaces therein, in particular the cases of Lagrangian and complex surfaces. The complex surfaces are all minimal, but there are many others as well. As it is a symmetric space, the more general case of harmonic maps from a Riemann surface into the complex hyperbolic plane naturally generates holomorphic data of a Higgs bundle. We impose a compactness condition to relate our study of minimal surfaces to Higgs bundles. Let S be a closed Riemann surface of genus at least 2. Consider then harmonic immersions of the universal cover of S into the complex hyperbolic plane which are equivariant with respect to some representation of the fundamental group of S into the group P U(2, 1) of holomorphic isometries of the complex hyperbolic plane. In this case, the nonlinear Hodge correspondence applies and thus there is a (poly-)stable Higgs bundle over S. In the standard case of the group GL(n, C), this consists of a...

Outline of Topics:

Minimal Surfaces in Diblock Copolymers: the P,G, and D triply periodic minimal surfaces.
Smectic Liquid Crystals: the simplest crystals and they are built from surfaces.
Using minimal surfaces to knit: geometric scaffolds in materials science.

I will describe recent work which defines a class of multi-party measures of entanglement which are characterized by tensorial contractions of copies of a density matrix with respect to an arbitrary finite group symmetry.

For AdS3/CFT2 they can be determined by both boundary replica trick calculations of twist operators and by bulk quotients of Euclidean AdS3 by Kleinian groups. The technology developed allows for the determination of all such measures which can preserve bulk replica symmetry.

I will provide several explicit examples including a complete classification of measures with genus zero and one replica surfaces.

First Talk (90 minutes) I would like to give a brief introduction of spacelike hypersurfaces and maximal hypersurfaces in Minkowski space. Then I would like to introduce maximal surfaces with singularities in Minkowsiki 3-space and give examples.