# Conferences 2020-2023

The Frankfurt University of Applied Sciences reports on its website about Forum Mathematics 2022 to the report

The download of the presentation documents is only possible after registration on the website.

## 27 - 28 September 2023, Bildungswerk Hessen Metall e.V., Bad Nauheim

**Hans Walser** (Frauenfeld, Switzerland)

The Semantics of Visual Language

The following topics will be discussed, respectively the image or the animation: Different types of curvature, difference between function graph and geometric curve, dangerous modelings of the beautiful appearance. In cartography, the disposition of parametrization, the relativity of scales, distortions, and straight line issues can be discussed and illustrated. Various representations in teaching and instructional materials are composed of partial images with different perspectives and focalizations. This creates conventional worldviews that can also be seen as flawed.

**Oliver Steinkamp** (Technical University of Middle Hesse)

The Consensus-based Global Optimization Method

The simplest optimization problem is to find a minimum or maximum of a differentiable real objective function, which is usually accomplished using the derivatives. In practice, however, one often encounters high-dimensional optimization problems with objective functions that are neither differentiable nor convex,

and of which the global optimum is sought rather than just a local minimum or maximum. The talk will give an overview of a relatively new method of global optimization: the consensus-based global optimization method consists of a system of coupled stochastic differential equations that models the interaction of particles moving through the set of unknown parameters in search of the global minimum of the objective function, exchanging information about their positions. The goal of the modeling is for the particles to reach consensus on a good approximation of the global minimum of the objective function.

**Jörg Schäfer **(Frankfurt University of Applied Sciences)

Information geometry - an informal introduction

The subject of the research area "information geometry" is the study of geometric structures of families of probability distributions and the application of such methods in statistics as well as in machine learning theory. The first contribution goes back to C. R. Rao (1945), who used the so-called Fisher-Rao metric to define geometric structures of parametric models. Information geometry uses concepts from differential geometry such as curvature, covariant derivatives, affine relations, and transport. With the help of these tools, statistical problems can then be treated in a new way. Already Rao had introduced notions such as geodesic distance to deal with classification problems and hypothesis testing in statistics. This talk attempts to give an informal introduction to some definitions, concepts, and theorems of information geometry, aimed at listeners who are familiar with elementary foundations of differential geometry and probability theory, but are not necessarily experts in these areas. An overview of possible application areas will also be given.

**Karlheinz Spindler** (RheinMain University of Applied Sciences)

On the usefulness of topological views

Should a rather dry and abstract subject like (set-theoretic) topology be part of application-oriented mathematics courses as well? This talk is a plea to answer this question with "yes", for several reasons. First, topology provides a language to adequately capture and express approximation phenomena, advantageously in great generality and using geometrically motivated conceptualizations that activate our spatial intuition in addressing analytic problems. Second, the study of topology promotes thinking in terms of structure and thus the practice of methods that are important both within and outside mathematics. Third, quite a few statements in calculus, algebra, or geometry follow most easily from explicit use of topological arguments, which will be demonstrated in the lecture with several examples. As these examples show, topology may not be as dry as one might think at first, but on the contrary rather beautiful, elegant and stimulating!

**Agnes Radl **(University of Applied Sciences Fulda)

Embeddability of real and positive operators

The embedding problem in probability theory deals with the question whether a Markov matrix can be embedded in a Markovian semigroup. The question dates back to Gustav Elfving (1937), but is still an active area of research with applications, for example, in biology or economics, see for example the recent review article "Notes on Markov embedding" by M. Baake and J. Sumner. Building on this, we now consider a similar problem: Given a (finite or infinite) matrix T, is it embeddable in a real or positive C0-semigroup, that is, is there a real or positive C0-semigroup T(t)t ³ 0 such that T(1)=T? We will give necessary and sufficient conditions for embeddability of real matrices in real semigroups and see that real embeddability is a typical property for real contractions in ℓ 2. In the case where T is positive, we show necessary conditions for embeddability.

**Martin Rehberg **(DB Systel GmbH).

NP-problems and modern cryptography

In currently used cryptographic methods, security guarantees take the form of number theoretic problems, such as the factorization problem or the discrete logarithm problem. Shor's quantum algorithm solves these in polynomial time, necessitating a shift to quantum-safe cryptographic methods. For such methods of post-quantum cryptography, a standardization process has been taking place for several years. In this talk, we will take a look at the security guarantees used in PQC in terms of NP-complete problems and provide the necessary foundations from complexity theory. In doing so, we will necessarily make the transition to quantum complexity theory and at least learn about the classes BQP, QCMA, and QMA as fundamental classes.

**Ilka Agricola** (University of Marburg, President of DMV)

Calculating the Future: Developments in Mathematics in Higher Education and the Labor Market

Student numbers in mathematics have been declining in recent years, while the need for mathematicians in the labor market is growing. What does this mean for the development of university mathematics and the job prospects of its graduates? What changes are currently taking place in the mathematics labor market? These questions will be clarified, also with a special focus on the potential of HAWs for the future of mathematics.

**Karlheinz Spindler** (RheinMain University of Applied Sciences)

Parameter Estimation - Technical and Didactical Remarks

The best possible estimation of system parameters from measurements is a problem arising in many application situations, where different mathematical disciplines meet: optimization, theory of differential equations, stochastics. If the parameters to be estimated satisfy constraints, i.e. if they are elements of a nonlinear manifold, differential geometric aspects are added. In the lecture, mathematical theory and selected examples will be discussed, as well as didactic experiences gained in a course on the topic. Finally, a particularly nice application of parameter estimation methods will be presented, namely the determination of balancing ellipses by means of hyperbolic geometry

**Jan-Philipp Hoffmann** (Hochschule Darmstadt)

Alternative Determinants in Linear Algebra

An alternative but equivalent definition of determinant is more oriented towards the use of determinants in linear algebra than the classical Weierstrass definition as an alternating multilinear form is able to do. The focus is to emphasize the naturalness of determinants as group homomorphisms from the endomorphisms or linear groups into the basic body or ring, in order to facilitate access especially for students at HAW and those studying mathematics in engineering or in a natural science.

**Martin Rehberg** (Agency for Innovation in Cybersecurity Halle)

Fully Homomorphic Encryption

Fully Homomorphic Encryption (FHE) allows arbitrary computations to be performed on encrypted data without the need to decrypt it first. Starting from the original idea of securely offloading computations to non-trusted environments, formulated as early as 1978 by Rivest, Adleman and Dertouzos, the historical developments up to modern FHE methods are discussed. Formal requirements alternate with concrete procedures, and the different generations of FHE procedures are pointed out. The conclusion is an outlook on the underlying circuit model with the resulting requirements for programming and compiler construction.

**Andreas Görg** (Technische Hochschule Mittelhessen)

Parameter representations for slope surfaces

By so-called slope of a space point against a plane which does not contain the point, a slope cone or incision funnel is created. Slopes of space curves lead to slope surfaces, which can be understood as envelopes of slope cones. For differentiable space curves, parameter representations of associated slope surfaces can be obtained as solutions of a first order partial differential equation. One of the parameters corresponds to that of the space curve, the other can be chosen in such a way that contour lines of the slope surface become parameter lines.

**Thomas März** (Hochschule Darmstadt)

Model-Based Regularized Reconstruction Techniques for Magnetic Particle Imaging

Magnetic Particle Imaging (MPI) is an emerging imaging modality developed by Gleich and Weizenecker in 2005 and is today a very active field of research. In the multivariate MPI setup images are usually reconstructed using a system matrix which is obtained by a time consuming measurement procedure. We approach the reconstruction problem by employing a reconstruction formula which we derive from a mathematical model of the MPI signal encoding. Here, we present an enhanced reconstruction algorithm based on the decomposition of the imaging process provided by the model. Its variational formulation incorporates adequate regularization which yields promising reconstruction results.

**Volker Schulz** (University of Trier)**Mathematical optimization as a key technology **

Almost all industrial processes can be improved and thus optimized. This is a central goal of the description of technical processes with mathematical models. The triad Modeling, Simulation, Optimization (MSO) will be illustrated here with a focus on optimization. Furthermore, optimization also plays a central role in the current scientific branch of Data Science, especially in data modeling. This is the second focus of the talk, where new developments of optimization techniques in low rank tensors, cluster analysis and neural networks will be discussed.

The papers are 65 MB. Please contact Torsten-Karl Strempel if you are interested.

**Karlheinz Spindler** (RheinMain University of Applied Sciences)**Mathematics as a Key Technology - A Historical View**

Mathematics is considered a key technology, and mathematical methods and concepts play an important role in questions of digitization and algorithmization, data analysis and data security, and the development of planning strategies for climate protection, energy transition, and mobility. However, the widespread consensus about the growing importance of mathematics is often based on naive ideas about its reasons and about the relationship between "pure" and "applied" mathematics. The lecture will use historical examples to examine the relationship between mathematical insights and their practical/technological implementation. The talk may be followed by a discussion of the implications of the observed patterns for research and higher education policy and, in particular, for mathematics teaching.

**Thomas Skill** (Bochum University of Applied Sciences)**Higher education didactic activities in the DMV**

A mini-symposium on "Teaching and Testing Scientific Mathematics" was held at the 2018 DMV Annual Meeting. This was the kick-off of the working group "Teaching and Learning University Mathematics", which was recognized as a specialist group in the DMV in 2021. The goal of this specialist group is to be a platform where teachers of mathematics exchange ideas about their teaching and student learning. In the introduction of the group, the work done so far will be presented and an outline and overview of initiatives in higher education didactics will be given. We will then discuss content, ideas, and activities.

**Martin Bokler** (Technische Hochschule Mittelhessen)**Common requirements for STEM studies?**

In this impulse lecture, possible measures will be addressed in order to get a better grasp on the well-known mathematics problems of many first-year students than has been the case so far.

**Horst Zisgen** (Darmstadt University of Applied Sciences)**Does Layerwise Relevance Propagation Explain CNNs? - A critical review of an Explainable AI approach.**

Convolutional Neural Networks (CNNs) have recently established themselves as one of the most widely used machine learning methods. Along with this, more and more methods are being published that attempt to explain the decision making of CNNs, such as layerwise relevance propagation (LRP). In this talk, we present an analysis of the explanatory power of the relevance values that LRP uses to try to explain CNN decision making. The results suggest that relevance values do not provide a suitable basis for interpreting CNN decision making.

**Jochen Rau** (RheinMain University of Applied Sciences)**What is special about quantum theory?**

Quantum theory is associated with numerous unusual properties and effects: Interference, non-compatibility of measurements, uncertainty principle, change of state after measurement, entanglement, and many more. However, many of these effects can also be mimicked with classical stochastic models. So which effects are "real" quantum effects?

**Bettina Just** (Technische Hochschule Mittelhessen)**How do quantum computers work, and why are they so fast?**

Quantum computers are all over the press, and everyone is talking about their disruptive potential. But why are quantum computers so fast? In the talk, the two models for quantum computers will be presented: The (universal) circuit model, and the (more specialized, adiabatic) Quantum Simulated Annealing. The point is to understand the basic ideas for their speed without having to know the technical details.

**Torsten-Karl Strempel** (Darmstadt University of Applied Sciences)**W? (Do you need to know the Lambertian W-function)?**

How do you solve the equation x^x=b? The equation a^x=b is solved with the logarithm function. Is there such a thing as an extended logarithm function? Yes, the so-called Lambertian W-function. After its "discovery" during the treatment of the equation x=x^m+q in the year 1758 it played at first no larger role in mathematics. Then, in 1993, a closed description for the double delta potential was given using the Lambert W-function. The Lambert W-function awoke from its slumber and thereafter other explicit solutions were found for applications in various fields. In addition to these application-oriented examples, you can now find lots of videos on the Internet for solving seemingly unsolvable equations, some of which also use the Lambert W function. Is this just a gimmick or another "useful" application? In the lecture, an overview of everything will be given and everyone can ask himself the question at the end: Do I really need to know the Lambert W-function?

- Prof. Dr. Stephan Weyers, Dortmund University of Applied Sciences: Activating Teaching Methods in Mathematics, Part 1+2
- Martin Rehberg, Hessen3C: Hessen CyberCompetenceCenter
- Prof. Dr. Karlheinz Spindler, RheinMain University of Applied Sciences: Research-based learning in mathematics
- Prof. Dr. Jan-Philipp Hoffmann, Darmstadt University of Applied Sciences: Topological Data Analysis
- Prof. Dr. Andreas Görg, Technical University of Central Hesse: Geometric continuity
- Prof. Dr. Hagen Knaf, RheinMain University of Applied Sciences: Resolution of singularities of algebraic varieties - on the problem and its history

## CONTACT

For questions regarding access to the documents and the website, please contact:

**Prof. Dr. Torsten-Karl Strempel**

Hochschule Darmstadt

FB Mathematik und Naturwissenschaften

Torsten-Karl Strempel