In the academic world, clear, concise, and well-written texts play an important role in convincing journal editors and conference organisers to accept a paper for review and publication, or to invite a researcher to present at a conference. This workshop provides PhD students with strategies to write short texts efficiently and effectively. It enables participants to organise ideas and structure texts effectively, to present their own and other researchers‘ findings and opinions appropriately, and to use correct terminology and vocabulary.

During the workshop, participants work with their own texts as well as with examples from their own disciplines that they bring along and consider to be particularly well written. They discuss features of good scientific papers and are equipped to use adequate language in different genres and for different audiences. In addition, they receive peer feedback on their own drafts. All exercises empower them to produce clearer, and more correct, concise, and reader-oriented papers.

The two-day workshop covers the following topics:
• taking inventory: participants‘ strengths and challenges in writing scientific papers in English
• a brief introduction to research and writing processes
• using text analysis to become a better writer
• reporting findings, ideas, and opinions professionally and adequately
• making yourself understood: principles of clear and concise writing
• structuring ideas, organising texts: transitions, connectives, & co.
• working effectively with co-authors and constructive text feedback
• useful online and offline resources

(After the workshop, participants have the opportunity to sign up for an individual writing coaching, or text feedback session. In this session, they can ask for individual feedback on an extract of their written work, or get deeper into issues from the workshop in a one-on-one setting.)

Models of non-Newtonian fluids play an important role in science and engineering and their mathematical analysis and numerical approximation have been active fields of research over the past decade. This lecture is concerned with the analysis of numerical methods for the approximate solution of a system of nonlinear partial differential equations that arise in models of chemically-reacting viscous incompressible non-Newtonian fluids, such as the synovial fluid found in the cavities of synovial joints. The synovial fluid consists of an ultra-filtrate of blood plasma that contains hyaluronic acid, whose function is to reduce friction during movement. The shear-stress appearing in the model involves a power-law type nonlinearity, where the power-law exponent depends on a spatially varying nonnegative concentration function, expressing the concentration of hyaluronic acid, which, in turn, solves a nonlinear convection-diffusion equation. In order to prove convergence of the sequence of numerical approximations to a solution of this coupled system of nonlinear partial differential equations one has to derive a uniform Hölder norm bound on the sequence of approximations to the concentration in a setting where the diffusion coefficient in the convection-diffusion equation satisfied by the concentration is merely a bounded function with no additional regularity. This necessitates the development of a discrete counterpart of the De Giorgi-Nash-Moser theory, which is then used, in conjunction with various compactness techniques, to prove the convergence of the sequence of numerical approximations to a weak solution of the coupled system of nonlinear partial differential equations under consideration.

Principal Component Analysis (PCA) is a standard tool to identify the important factors of variation of a dataset in an unsupervised manner. From a machine learning perspective, PCA can be interpreted as an encoder-decoder pair restricted to linear transformations. Normalizing flows (NF) are a natural non-linear generalization of encoder-decoder architectures, but lack the interpretability of PCA.

Entropy-ordered flows (EOFlows) overcome this limitation by using orthogonality regularization during NF training, such that the converged decoder induces an approximately orthogonal curvilinear coordinate system that is aligned with the data geometry. As a result, each latent dimension has a distinct semantic effect, and different dimensions can be sorted by importance according to their "explained entropy", analogous to "explained variance" in PCA. We show how EOFlows are trained, what factors they find on the portrait dataset CelebA, and how stable their outputs are under repeated training and in comparison to existing methods. Ideally, the colloquium would identify promising EOFlow applications in physics to pursue in the future.