2018, Schlein, Benjamin, Sohinger, Vedran

In this mini-workshop we brought together leading experts working on the application of Gibbs measures to the study of nonlinear PDEs. This framework is a powerful tool in the probabilistic study of solutions to nonlinear dispersive PDEs, in many ways alternative or complementary to deterministic methods. Among the special topics discussed were the construction of the measures, applications to dynamics, as well as the microscopic derivation of Gibbs measures from many-body quantum mechanics.

2016, Demba, Susanne, Sabrina, Sabrina, Ammon, Christian, Rose-Meierhöfer, Sandra

Prevention of damage to the teat and mastitis requires determination of the teat load caused by a collapsing liner. The aim of this study was to test a pressure-indicating film designed to measure the pressure between a collapsing liner and artificial teats. The Ultra Super Low and the Extreme Low pressure-indicating films were tested on two types of artificial teat. The experiments were performed with a conventional milking cluster equipped with round silicone liners. For each teat and film type, 30 repetitions were performed. Each repetition was performed with a new piece of film. Kruskal-Wallis tests were performed to detect differences between the pressure values for the different teats. The area of regions where pressure-indication color developed was calculated to determine the most suitable film type. Both film types measured the pressure applied to both artificial teats by the teat cup liner. Thus, the pressure-indicating films can be used to measure the pressure between a collapsing liner and an artificial teat. Based on the results of the present investigation, a pressure-indicating film with the measurement ranges of both film types combined would be an optimal tool to measure the overall pressure between an artificial teat and a collapsing liner.

2018, Baghdasaryan, Tigran, Geernaert, Thomas, Chah, Karima, Caucheteur, Christophe, Schuster, Kay, Kobelke, Jens, Thienpont, Hugo, Berghmans, Francis

It is common belief that photonic crystals behave similarly to isotropic and transparent media only when their feature sizes are much smaller than the wavelength of light. Here, we counter that belief and we report on photonic crystals that are transparent for anomalously high normalized frequencies up to 0.9, where the crystal’s feature sizes are comparable with the free space wavelength. Using traditional photonic band theory, we demonstrate that the isofrequency curves can be circular in the region above the first stop band for triangular lattice photonic crystals. In addition, by simulating how efficiently a tightly focused Gaussian beam propagates through the photonic crystal slab, we judge on the photonic crystal’s transparency rather than on isotropy only. Using this approach, we identified a wide range of photonic crystal parameters that provide anomalous transparency. Our findings indicate the possibility to scale up the features of photonic crystals and to extend their operational wavelength range for applications including optical cloaking and graded index guiding. We applied our result in the domain of femtosecond laser micromachining, by demonstrating what we believe to be the first point-by-point grating inscribed in a multi-ring photonic crystal fiber.

2019, Gubler, Walter, Schneider, Peter, Werner, Annette

The workshop focused on recent developments in non-Archimedean analytic geometry with various applications to other fields. The topics of the talks included applications to complex geometry, mirror symmetry, p-adic Hodge theory, tropical geometry, resolution of singularities, p-adic dynamical systems and diophantine geometry.

2016, Linkhorst, John, Beckmann, Torsten, Go, Dennis, Kuehne, Alexander J. C., Wessling, Matthias

Filtration of natural and colloidal matter is an essential process in today’s water treatment processes. The colloidal matter is retained with the help of micro- and nanoporous synthetic membranes. Colloids are retained in a “cake layer” – often coined fouling layer. Membrane fouling is the most substantial problem in membrane filtration: colloidal and natural matter build-up leads to an increasing resistance and thus decreasing water transport rate through the membrane. Theoretical models exist to describe macroscopically the hydrodynamic resistance of such transport and rejection phenomena; however, visualization of the various phenomena occurring during colloid retention is extremely demanding. Here we present a microfluidics based methodology to follow filter cake build up as well as transport phenomena occuring inside of the fouling layer. The microfluidic colloidal filtration methodology enables the study of complex colloidal jamming, crystallization and melting processes as well as translocation at the single particle level.

2015, Mitra, C., Kurths, J., Donner, R.V.

2014, Guta, Madalin, Nussbaum, Michael

The classical metric theory of statistical models (experiments) has recently been extended towards an asymptotic equivalence paradigm, allowing to classify and relate problems which are essentially infinite dimensional and ill-posed. Modern statistical concepts like these are also being integrated into the emerging field of quantum statistics, which is developing on the background of technological breakthroughs in quantum engineering. The workshop brought together leading experts in these areas, with the goal of establishing a common language, and fostering collaborations between mathematical statisticians, theoretical physicists and experimentalists.

2019, Kostenko, Aleksey, Pankrashkin, Konstantin

The main focus of the workshop is on the analysis of boundary value problems for differential and difference operators in some non-classical geometric settings, such as fractal graphs, sub-Riemannian manifolds or non-elliptic transmission problems. Taking into account their importance in modern mathematical analysis, we aim at developing suitable tools in the operator theory to deal with the new problem settings.

2018, Hotz, Thomas, Huckemann, Stephan, Miller, Ezra

Statistics for data with geometric structure is an active and diverse topic of research. Applications include manifold spaces in directional data or symmetric positive definite matrices and some shape representations. But in some cases, more involved metric spaces like stratified spaces play a crucial role in different ways. On the one hand, phylogenetic trees are represented as points in a stratified data space, whereas branching trees, for example of veins, are data objects, whose stratified structure is of essential importance. For the latter case, one important tool is persistent homology, which is currently a very active area of research. As data sets become not only larger but also more complex, the need for theoretical and methodological progress in dealing with data on non-Euclidean spaces or data objects with nontrivial geometric structure is growing. A number of fundamental results have been achieved recently and the development of new methods for refined, more informative data representation is ongoing. Two complimentary approaches are pursued: on the one hand developing sophisticated new parameters to describe the data, like persistent homology, and on the other hand achieving simpler representations in terms of given parameters, like dimension reduction. Some foundational works in stochastic process theory on manifolds open the doors to this field and stochastic analysis on manifolds, thus enabling a well-founded treatment of non-Euclidean dynamic data. The results presented in the workshop by leading experts in the field are great accomplishments of collaboration between mathematicians from statistics, geometry and topology and the open problems which were discussed show the need for an expansion of this interdisciplinary effort, which could also tie in more closely with computer science.

2018, Langer, Ulrich, Monk, Peter, Pauly, Dirk

In this mini-workshop 17 leading mathematicians from Europe and United States met at the MFO to discuss and present new developments in the mathematical and numerical analysis of Maxwell’s equations and related systems of partial differential equations. The report at hand offers the extended abstracts of their talks.