## Mathematisches Institutskolloquium

Das Mathematische Institutskolloquium richtet sich an ein breites mathematisches Publikum (mit Bachelor Abschluss in Mathematik). Es soll die Diskussionen über die mathematischen Spezialisierungen der verschiedenen Arbeitsgruppen am Institut fördern. Außerdem sollen auch Studierende (Master-Studierende und fortgeschrittene Bachelor-Studierende) durch das Kolloquium die Gelegenheit erhalten sich über aktuelle Themen der Mathematik zu informieren.

### Sommersemester 2024

**Institutskolloquium mit Herrn Univ.-Doz. Dr. Arne Winterhof **(RICAM - Johann Radon Institute for Computational and Applied Mathematics of the Austrain Academy of Science, Linz - Österreich, Project Leader Applied Discrete Mathematics and Cryptography)

**"Pseudorandom binary sequences: quality measures and number-theoretic constructions" *** ***Mittwoch, 10.07.2024, 15:15 Uhr, Ulmenstr. 69, Haus 3, SR 228 → **Auch interessierte Studierende sind herzlich eingeladen.

**Institutskolloquium mit Herrn Prof. Dr. Jens Schmidt (Universität Rostock, Institut für Informatik)**

**"Structures in Polyhedral Graphs****".***"We investigate long cycles and paths in polyhedral (i.e. planar and 3-connected) graphs and discuss long-standing conjectures for these. Our methods make use of Tutte paths, isolating cycles, discharging and Schnyder woods. In more detail, let a cycle C of a graph G be isolating if every component of G−V(C) consists of a single vertex. We show that isolating cycles in polyhedral graphs can be extended to larger ones: every isolating cycle C of length 6 <= |E(C)| < 2/3(|V(G)|+4) implies an isolating cycle of larger length that contains V(C). By “hopping” iteratively to such larger cycles, we obtain a powerful and very general inductive motor for proving long cycles and computing them (we will give an algorithm with quadratic running time). This is a first step towards the so far elusive quest of finding a universal induction that captures longest cycles of polyhedral graph classes.*

*"*

**Mittwoch, 15.05.2024, 15:15 Uhr, Ulmenstr. 69, Haus 3, HS 326/327 →**Auch interessierte Studierende sind herzlich eingeladen.

**Institutskolloquium mit Frau Prof. Melina Freitag (Universität Potsdam, Institut für Mathematik)**

**"Complexity reduction for data assimilation and inverse problems****".***"In this talk we will give an introduction to weak constraint four-dimensional variational data assimilation as an important method for incorporating data (typically observations) into a model. We will see that the resulting minimisation process takes place in very high dimensions. After an introduction we present two approaches for reducing the dimension and thereby the computational cost and storage of this method. The first approach formulates the linearised system as a saddle point problem. We present a low-rank approach which exploits the structure of the saddle point system using techniques and theory from solving large scale matrix equations and low-rank Krylov subspace methods. The second approach uses projection methods for reducing the system dimension. Numerical experiments with the linear advection-diffusion equation, and the nonlinear Lorenz-95 model demonstrate the effectiveness of both the low-rank Krylov subspace solver (compared to a standard Krylov solver) and applying projection methods within the minimisation process." ***Mittwoch, 10.04.2024, 15:15 Uhr, Ulmenstr. 69, Haus 3, HS 326 → **Auch interessierte Studierende sind herzlich eingeladen.

**Prof. Joachim Wagner**(Universität Rostock)**"Berechnung von zweiten Virialkoeffizienten konvexer Körper im D-dimensionalen Vektorraum mittels der Brunn-Minkowski-Theorie"**

Auch interessierte Studierende sind herzlich eingeladen.**Mittwoch, 06.12.2023, 15:00 Uhr, Ulmenstr. 69, Haus 3, HS 228**

**Dr. Sebastian Fuchs**(University of Salzburg, Austria)**"A model-free and dependence-based variable selection method for multi-outcome data"**

Auch interessierte Studierende sind herzlich eingeladen.**Mittwoch, 01.11.2023, 15:15 Uhr - ca. 17:00 Uhr, Ulmenstr. 69, Haus 3, HS 326/327**

**Prof. Jon Star**(Harvard - Graduate School of Education, Cambridge)**"Mathematical flexibility: A promising focus for research and practice".**

"Mathematical flexibility is increasingly recognized as an important construct of interest for both researchers and practitioners in mathematics education. Flexibility can be characterized as a learner's willingness to change strategies based on the particular problem-solving conditions or goals. In this talk, I first provide an introduction to flexibility. I then explore different ways that flexibility has been assessed, highlighting successes and challenges in the various forms of assessment. I then present recent empirical research results on flexibility, and I conclude by suggesting some promising areas for future research on flexibility."

Auch interessierte Studierende sind herzlich eingeladen.**Freitag, 06.10.2023, 15:00 - 17:00 Uhr, Ulmenstr. 69, Haus 3, SR 228**

**Fr. Dr. Alethea B. T. Barbaro**(Associate Professor, Delft University of Technology, Institute of Applied Mathematics, NL)**"A model for territorial development: from particles to continuum****"**

Many species demonstrate territoriality, with individuals or groups marking their territories either chemically or visually. In this talk, we will present an agent-based lattice model for territorial development. In this model, there are several groups, and agents from each group put down that group’s territorial markings as they move on the lattice. Agents move away from areas with territorial markings which do not belong to their own group. We will show that this model undergoes a phase transition between well-mixed collective dynamics and distinct territories as parameters are varied. We will then discuss the derivation of a system of coupled convection-diffusion equations from this model. This system exhibits cross-diffusion due to the avoidance of other groups’ markings. We will pinpoint the critical value for the phase transition using linear stability analysis and discuss further analytical and numerical work stemming from this model.**05.07.2023, 15:15 Uhr, Ulmenstraße 69, Haus 3, HS 326/327**

**Fr. Prof. Ursula Müller-Harknett**(Universität Rostock, Institut für Mathematik)**"Estimating the error distribution in semiparametic models"**

I will give an overview of my research on estimating the error distribution in semiparametic models, with emphasis on regression models with independent errors and covariates. My work in this area started with a 2004 paper on efficient estimation of the error variance and other expectations of the error distribution in nonparametric regression. Several papers followed on estimating the error distribution in various semiparametic regression models. In most models a simple uniform expansion of the residual-based empirical distribution function can be derived, if suitable estimators of the regression function are used to form the residuals. The expansion also characterizes efficient estimators of the error distribution function and provides the basis for constructing goodness-of-fit tests, for example distribution free martingale-transform tests about the form of the error distribution.**21.06.2023, 15:15 Uhr, Ulmenstraße 69, Haus 3, HS 326/327**

**Léo Perrin**(INRIA Paris Centre, France)**" How can we ensure that (symmetric) cryptographic primitives are trustworthy?"**

There cannot be any data security without cryptography. Among cryptographic algorithms, "primitives" are those at the core of all protocols, and aim to provide crucial mathematical properties. For instance, a block "block cipher" (such as the AES) with a secret key should emulate a permutation picked uniformly at random. Should it not be the case, data security would be threatened.In practice, how do we ensure that the symmetric primitives we use every day deserve our trust? From standardization process to Kolmogorov complexity, we will look at various problems that were raised in recent years, in particular pertaining to the S-box of the latest symmetric standards from Russia.**07.06.2023, 15:15 Uhr, Ulmenstraße 69, Haus 3, HS 326/327**

**Herr Prof. Henning Stichtenoth**(Sabanci University - FENS, Istanbul, Turkey)**"Rational points on curves over finite fields”**

"We consider rational points on a curve*C*over a finite field F*q*, i.e. points P ∈*C*, all of whose coordinates are in F*q*. The question "How many rational points can*C*have?" is interesting for many reasons:

• as a 'pure mathematical' problem in number theory/algebraic geometry,

• because of numerous applications, for instance in information transmission and cryptography.

In this talk I will discuss some aspects of the question above. Of special interest are upper bounds for the number of rational points on*C*."**03.05.2023, 15:15 Uhr, Ulmenstraße 69, Haus 3, HS 326/327**

**Herr Prof. Gary Froyland**(School of Mathematics and Statistics, University of New South Wales)**"Transfer operator analysis of the ocean and climate”**

"I will illustrate how operator-theoretic methods can help us learn about our oceans and climate by discussing two examples: estimating basins of attraction on the global surface ocean and constructing improved characterisations of the El Nino Southern Oscillation. I will draw on data sourced from fleets of ocean drifters, and satellite-derived sea-surface temperature observations."**05.04.2023 (fällt leider aus!)**

**Herr Dr. Stefan Tappe**(Institut für Mathematik, Universität Rostock)**"****Stochastic partial differential equations and invariant manifolds in embedded Hilbert spaces”**

In this presentation we investigate stochastic partial differential equations (SPDEs) in continuously embedded Hilbert spaces with non-smooth coefficients. More precisely, we are interested in the question when a finite dimensional submanifold is locally invariant for such an equation. We start with reviewing some classical results for ordinary differential equations (ODEs) and stochastic differential equations (SDEs). Afterwards, we move on to general SPDEs and establish an invariance result where the coefficients of the SPDE are merely assumed to be continuous. As a concrete example we consider SPDEs with values in the space of tempered distributions; in this situation the continuously embedded Hilbert spaces are given by Hermite-Sobolev spaces and the coefficients are differential operators of first and second order. At this juncture there is an interplay between finite dimensional SDEs and particular types of SPDEs. This presentation is based on joint work with Rajeev Bhaskaran (Indian Statistical Institute, Bangalore Centre). Das Kolloquium findet diesmal*ausschließlich als Zoom-Meeting online*statt.**11.01.2023, 15:15 Uhr**

**Herr Dr. Matthias Schymura**(Institut für Mathematik, Universität Rostock)**"****A geometric view on the Lonely Runner Problem: Coverings by Zonotopes”**

The Lonely Runner Conjecture concerns k runners on a circular track of length 1 who start running from a common starting position with pairwise distinct constant velocities. The claim is that for each runner there is a certain point in time at which she is at distance at least 1/k from all the other runners on the track. This is a picturesque formulation of a conjecture by Jörg Wills (1967) in the theory of Diophantine Approximation. The problem is strongly linked to Dirichlet's classical approximation theorem and has found various reinterpretations, for instance, in terms of view-obstructions and billiard ball motions. Many efforts on the conjecture have been taken over the last five decades, yielding important partial results by attacking the problem from many different angles. However, a complete solution to the Lonely Runner Conjecture is only known for up to 7 runners to date.The talk aims to give an overview over the history of the problem, its various interpretations, and the state of the art. In particular, we introduce yet another interpretation in terms of the existence of integer points in certain zonotopes (projections of the cube). We report how this geometric approach leads to new insights on the Lonely Runner Problem, and how it motivates the investigation of covering properties of zonotopes in general.**14.12.2022, 15:15 Uhr, Ulmenstr. 69, Haus 3, HS 326/327**

**Herr Prof. Dr. Viktor Avrutin**(Institut für Systemtheorie und Regelungstechnik, Universität Stuttgart)**"A hidden bridge between continuous and discontinuous worlds (and how period two implies chaos)"**

Many problems in engineering and applied science lead us to consider piecewise smooth maps. Examples of such systems include applications in electronics (switching circuits), mechanics (systems with dry friction or impacts), economics and social sciences (systems involving decision making processes), as well as other systems with thresholds and constraints. From the mathematical point of view, piecewise smooth maps are extremely challenging and can be subdivided in two classes, namely, continuous and discontinuous maps. Possibly dynamics and bifurcation phenomena in both classes differ significantly, and at present, they are understood much better for the former class than for the latter one. Recently, a novel approach for investigation of discontinuous maps has been suggested which surprisingly combines several aspects of the dynamics commonly observed in both classes of maps. The idea of this approach is to extend the definition of a discontinuous map in such a way that at the points of discontinuities, the function is considered to be set-valued. This unifies the bifurcation analysis for continuous and discontinuous maps; makes several theorems proven for continuous maps applicable to discontinuous ones; and helps us to understand the dynamics of maps with steep branches which are hard to deal with otherwise.**16.11.2022, 15:15 Uhr, Ulmenstr.****69, Haus 3, HS****326/327**

**Dr. Dirk Hartmann**(Siemens Digital Industry Software)**"Scalable Digital Twins - Combining Machine Learning and Physics-based Simulations"**

Abstract: Digital Twins, tightly connecting the real and the digital world, are a key enablers to support industrial decision making for complex systems. They allow informing operational as well as strategic decisions upfront through accepted virtual predictions and optimizations of their real-world counter parts. Sufficiently accurate and fast digital models are required to do so, which today involves significant manual expert efforts limiting industrial scalability.

Integrating machine learning and physics-based methods offers opportunities to overcome these limitations. In this context, we will review selected use cases covering 3D and lumped system simulation and demonstrate limitations and potential of hybrid methods along these. Finally, we will indicate fields requiring more research from an industrial point of view in the field of computational science & engineering and machine learning.**19.10.2022, 14:00 Uhr, Ulmenstr. 69, Haus 3, SR 322**(Hybrid-Veranstaltung)

**Prof. Dr. Thomas Mikosch**(University of Copenhagen, Denmark)**"Richard von Mises and the development of modern extreme value theory"**

Abstract: This talk has the following goals:

(1) To present Richard von Mises’s achievements in extreme value theory in their historical context.

(2) To provide a short history of extreme value theory and statistics since the 1920s.

(3) To discuss some of the challenges in modern extreme value theory.**22.06.2022, 15:15 Uhr, Ulmenstr. 69, Haus 3, HS 326/327**(Hybrid-Veranstaltung)

**Dr. rer. nat. Isabelle Schneider**(University of Rostock)**"Pattern-Selective Feedback Stabilization of Ginzburg-Landau Spiral Waves"**

Abstract: The complex Ginzburg-Landau equation serves as a paradigm of pattern formation and the existence and stability properties of Ginzburg-Landau m-armed spiral waves have been investigated extensively. However, most spiral waves are unstable and thereby rarely visible in experiments and numerical simulations. In this talk I selectively stabilize certain significant classes of unstable spiral waves within circular and spherical geometries. As a result, stable spiral waves with an arbitrary number of arms are obtained for the first time. The tool for stabilization is the symmetry-breaking control triple method, which is an equivariant generalization of the widely applied Pyragas control to the setting of PDEs.

This is joint work with Jia-Yuan Dai (National Chung Hsing University, Taiwan) and Babette de Wolff (Vrije Universiteit Amsterdam, Netherlands).**18.05.2022, 15:15 Uhr, Ulmenstr. 69, Haus 3, HS 326/327**(Hybrid-Veranstaltung)

**Dipl.-Ing. Alexander Steinicke, PhD**(Montanuniversitaet Leoben)**"From Stochastic Differential Equations to Piecewise Lipschitz Functions"**

Abstract**16.02.2022, 15:15 Uhr**, Online-Veranstaltung

**Prof. Dr. Jan Sieber**(University of Exeter, UK)**"Delay differential equations - numerical treatment and the case of large delay"**

Abstract: Delay differential equations (DDEs), in which some of the arguments enter with a time delay, but which otherwise look like ordinary differential equations, occupy a place somewhere between ordinary differential equations and partial differential equations (PDEs) with one space dimension. This is noticeable when implementing numerical methods, especially for finding equilibria, periodic solutions and the spectra of the linear DDEs. When the delay becomes large the limiting behaviour of some periodic oscillations approaches that of patterns in PDEs. A particular example are "temporal dissipative solitions" periodic pulses caused by delayed feedback into an excitable system.

(Joint work with Serhiy Yanchuk, Stefan Ruschel, Matthias Wolfrum)**12.01.2022, 15:15 Uhr**, Online-Veranstaltung

**Prof. Dr. Ivan Veselić**(Technische Universität Dortmund)**"Uncertainty relations and applications"**

Abstract: Uncertainty relations or unique continuation estimates for various classes of functions are investigated in several fields of mathematical analysis. They have also a number of interesting applications, among them those in mathematical physics and the theory of partial differential equations. While in other areas uncertainty implies less knowledge or weaker mathematical results, in these cases uncertainty principles in fact improve our knowledge about certain mathematical objects.

The talk aims at shedding a bit of light on these aspects of uncertainty principles.**15.12.2021, 16:00 Uhr**(Uhrzeit aktualisiert am 09.12.), Online-Veranstaltung

**Prof. Dr. Wilhelm Stannat**(TU Berlin)**"Mean-field approach to Bayesian estimation of Markovian signals"**

Abstract: Estimating Markovian signals X from noisy observations is an important problem in the natural and engineering sciences. Within the Bayesian approach the underlying mathematical problem essentially consists in the (stochastic) analysis of the conditional law of X with a view towards its efficient numerical approximation.

In this talk I will discuss mean-field type descriptions of the conditional law of X, when X is the solution of a stochastic differential equation, and present recent results on corresponding ensemble-based numerical approximations.

The talk is based on joint work with T. Lange, S. Pathiraja and S. Reich.

References:

[1] S. Pathiraja, S. Reich, W. Stannat: McKean-Vlasov SDEs in nonlinear filtering,

SIAM J. Control Optim. 59 (2021), no. 6, 4188–4215.

[2] S. Pathiraja, W. Stannat: Analysis of the feedback particle filter with diffusion

map based approximation of the gain, Foundations of Data Science 3 (2021): 615-645.

[3] T. Lange, W. Stannat: Mean field limit of Ensemble Square Root Filters - discrete

and continuous time, Foundations of Data Science 3 (2021): 563-588.**17.11.2021, 15:15 Uhr, Ulmenstr. 69, Haus 3, HS 326/327**(Hybridveranstaltung)

**Prof. Constantinos Siettos**(University of Naples Federico II, Italy)**"Numerical Solution of Nonlinear PDEs and Stiff Problems of ODEs with Random Projection Networks and Extreme Learning Machines"**

Abstract: We use a class of machine learning the so-called Random Projections Networks and Extreme Learning Machines to numerically solve nonlinear partial differential equations (PDEs) and stiff problems of ODEs. For our demonstrations, we study several benchmark problems, namely (a) the Rober and Van-der Pol ODEs and, (b) the one-dimensional viscous Burgers and, the one- and two-dimensional Bratu PDEs. We also show how one can expolit the proposed methodology to construct bifurcation diagrams past limit points. The numerical efficiency of the proposed numerical machine learning scheme is compared against well established numerical analysis methods such as the adaptive Runge-Kutta ode45 and the ode15s a variable-step, variable-order solver based on the numerical differentiation formulas for solving the ODEs and central finite differences (FD) and Finite-element (FEM) methods for solving PDEs. We show that the proposed machine learning framework, regarding the solution of ODEs yields good numerical approximation accuracy without being affected by the stiffness, thus outperforming in same cases the ode45 and ode15s integrators, while regarding the solution of PDEs outperforms FD and importantly FEM for medium to large sized grids in terms of computational times and numerical accuracy.**13.10.2021, 15:15 Uhr**, Online-Veranstaltung

**Dr. Paolo Di Tella**(University of Rostock)**"On Martingale Representation Theorems"**

Abstract: A central result in Stochastic Analysis is the martingale representation theorem of the Brownian motion. In this talk we are going to present classical result and extensions of the Brownian martingale representation theorem in more general contexts. We shall then present some applications to mathematical finance.**14.07.2021**, 1**5:15 Uhr**, Online-Veranstaltung

**Prof. Kim Knudsen**(Technical University of Denmark)**"Electromagnetic imaging – mathematical analysis and computations"**

Abstract:

In this talk we will look at inverse problems related to electromagnetic imaging. One example is Electrical Impedance Tomography (EIT), mathematically known as the Calderón problem, where the goal is to identify a body’s interior electrical conductivity distribution from measurements of voltages and currents on the surface of the body. This problem is severely ill-posed and requires heavy regularization techniques to be implemented before allowing for image reconstruction even with low resolution and contrast.

Recently, novel hybrid imaging methods such as Acousto-Electric Tomography and Magnetic Resonance EIT have appeared. These approaches exploit different coupled physical phenomena and therefore hold promise for much more accurate and stable methods than EIT.

From a mathematical analysis and computational perspective we consider the three different examples; we will formulate the relevant models, pose fundamental questions and give (partial) answers.**16.06.2021, 15:15 Uhr**, Online-Veranstaltung

**Prof. Dr. Bernd Sturmfels**(Direktor am Max-Planck-Institut für Mathematik in den Naturwissenschaften Leipzig; Professor University of California at Berkeley)**"3264 Conics in a Second"**

Abstract: Enumerative algebraic geometry counts the solutions to certain geometric constraints. Numerical algebraic geometry determines these solutions for any given instance. This lecture illustrates how these two fields complement each other, especially in the light of emerging new applications. We start with a gem from19th century geometry, namely the 3264 conics that are tangent to five given conics in the plane. This topic was featured in the January 2020 issue of the Notices of the American Mathematical Society. We conclude with an application in statistics, namely maximum likelihood estimation for linear Gaussian covariance models.**17.06.2020, 15:00 Uhr**, Online-Veranstaltung

**Prof. Dr. Bernold Fiedler**(FU Berlin)**"Good to be late, precisely"**

Abstract**13.05.2020, 15:15 - 16:15 Uhr**, Online-Veranstaltung

**Prof. Dr. Armin Iske**(Universität Hamburg)**"Kernel-based approximation methods for data analysis and machine learning"**

Abstract**15.04.2020, 15:00 - 16:00 Uhr**, Online-Veranstaltung

**Prof. Dr. Reinhard Racke**(Universität Konstanz)**"Exponentielle Stabilität für thermoelastische Systeme — die Multiplikatormethode"**

Abstract: Anhand der Wärmeleitungsgleichung bzw. der gedämpften Wellengleichung wird die Energie- bzw. Multiplikatormethode bei Evolutionsgleichungen vorgestellt, ebenso ein Zusammenhang zur Fourierreihenentwicklung bzw. zur Fouriertransformation, letzteres am Beispiel thermoelastischer Platten. Numerische Resultate unterstreichen die analytisch erhaltenen Abschätzungen.**13.11.2019, 15:15 Uhr, HS 326/327 (Ulmenstr. 69, Haus 3)**

**Prof. Dr. Markus Reiß**(HU Berlin)**"Statistics for stochastic PDEs"**

Abstract: For a broader audience we shall introduce to basic stochastic ordinary and partial differential equations (SODEs/SPDEs) and consider statistical estimation of the coefficients in these equations. We shall encounter a fundamental difference for drift estimation for SODEs/SPDEs. Then we consider the specific problem of estimating the space-dependent diffusivity of a stochastic heat equation from time-continuous observations with space resolution*h*. This will be achieved by a localised Maximum-Likelihood approach. The rather counterintuitive convergence result and its efficiency as*h -> 0*will be discussed in detail. (joint work with Randolf Altmeyer, Berlin)**16.10.2019, 15:15 Uhr, HS 326/327 (Ulmenstraße 69, Haus 3)**

**Prof. Dr. Peter E. Kloeden**(Universität Tübingen)**"Random ordinary differential equations and their numerical approximation"**

Random ordinary differential equations (RODEs) are pathwise ordinary differential equations that contain a stochastic process in their vector field functions. They have been used for many years in a wide range of applications, but have been very much overshadowed by stochastic ordinary differential equations (SODEs). The stochastic process could be a fractional Brownian motion or a Poisson process, but when it is a diffusion process then there is a close connection between RODEs and SODEs through the Doss-Sussmann transformation and its generalisations, which relate a RODE and an SODE with the same (transformed) solutions. RODEs play an important role in the theory of random dynamical systems and random attractors.

Classical numerical schemes such as Runge-Kutta schemes can be used for RODEs but do not achieve their usual high order since the vector field does not inherit enough smoothness in time from the driving process. It will be shown how, nevertheless, various kinds of Taylor-like expansions of the solutions of RODES can be obtained when the stochastic process has Hölder continuous or even measurable sample paths and then used to derive pathwise convergent numerical schemes of arbitrarily high order. The use of bounded noise and an application in biology will be considered.

Xiaoying Han and P. E. Kloeden,

Random Ordinary Differential Equations and their Numerical Solution,

Springer Nature Singapore, 2017.**10.07.2019, 15:15 Uhr, HS 326/327 (Ulmenstr. 69, Haus 3)**

**Prof. Dr. Frank Vallentin**(Universität zu Köln)**"Über das Färben geometrischer Graphen (Chromatic numbers of geometric graphs)"**

Abstract: A classical problem in discrete geometry (due to Hadwiger and Nelson) is to find the minimal number of colors one needs to color all points in the Euclidean plane so that no two points which are distance 1 apart receive the same color. Similar geometric coloring problems can be posed in the context of the hyperbolic plane, n-dimensional Euclidean spaces, n-dimensional spheres, or coloring the Voronoi tessellation of n-dimensional lattices. In this talk I will present a theoretical framework in which all these geometric coloring problems (assuming that the color classes are measurable sets) can be conveniently studied with the help of harmonic analysis and convex optimization.**15.05.2019, 15:00 Uhr, HS 326/327 (Ulmenstr. 69, Haus 3)**

**Prof. Dr. Petra Wittbold**(Universität Duisburg-Essen)**"Time-fractional stochastic conservation laws"**

Abstract**19.06.2019, 13:00 Uhr, HS 326/327 (Ulmenstr. 69, Haus 3)**

**Prof. Dr. Michael Dellnitz**(University of Paderborn, Germany)**"Glimpse of the Infinite – on the Approximation of the Dynamical**

Behavior for Delay and Partial Differential Equations"

Abstract: Over the last years so-called set oriented numerical methods have been developed for the analysis of the long-term behavior of finite-dimensional dynamical systems. The underlying idea is to approximate the corresponding objects of interest – for instance global attractors or related invariant measures – by box coverings which are created via multilevel subdivision techniques. That is, these techniques rely on partitions of the (finite-dimensional) state space, and it is not obvious how to extend them to the situation where the underlying dynamical system is infinite-dimensional.

In this talk we will present a novel numerical framework for the computation of finite-dimensional dynamical objects for infinite-dimensional dynamical systems. Within this framework we will extend the classical set oriented numerical schemes mentioned above to the infinite-dimensional context. The underlying idea is to utilize appropriate embedding techniques for the reconstruction of global attractors in a certain finite-dimensional space. We will also illustrate our approach by the computation of global attractors both for delay and for partial differential equations; e. g. the Mackey-Glass equation or the Kuramoto-Sivashinsky equation.**10.04.2019, 17:00 Uhr, HS 326/327 (Ulmenstr. 69, Haus 3)**

**Prof. John Sheekey**(University College Dublin, Ireland)**"Finite Fields and their (less famous) cousins"**

Abstract: Finite Fields (or Galois Fields) are algebraic structures with a finite number of elements, in which all the usual rules of addition, multiplication, and division for the real numbers hold. The classic example is the integers modulo a prime, and it is well known that a finite field consisting of q elements exists precisely when q is a prime power. Furthermore it is well known that removing the assumption of commutativity of multiplication does not yield any new structures; all finite division rings are in fact fields, the Wedderburn-Dickson Theorem.

Less well-known are Finite Semifields; in a semifield, we do not assume associativity of multiplication. Non-trivial finite semifields do exist, as first shown by Dickson (1905), and there remain many open questions regarding their construction and classification. They have many interesting connections to topics such as Projective Planes, Spreads, Flocks, PN functions, and more. Recently new connections have been made with Coding Theory and Cryptography, which has lead to a renewed interest due to potential practical applications.

In this talk we will introduce the topic of finite semifields, present some of the known classifications and constructions, outline their connections to other areas of interest, and mention the main open problems.**16.01.2019, 15:15 Uhr, HS 326/327 (Ulmenstr. 69, Haus 3)**

**Prof. Dr. Christof Büskens**(Universität Bremen)**"Entwicklung ist teuer; - Mathematik unbezahlbar!**

Hochdimensionale nichtlineare Optimierung trifft industrielle Anforderungen"

Abstract: Nichtlineare Optimierung ist zu einer Schlüsseltechnologie in modernen Anwendungen geworden. Ob bei der Bestimmung neuer Kennfelder im Diesel-Abgasskandal oder dem Entwurf modellprädiktiver Regelungsverfahren, das Interesse an Lösungsmethoden für hoch- und höchstdimensionale Optimierungsprobleme ist groß.

WORHP (We Optimise Really Huge Problems) gehört zu einer neuen Generation von nichtlinearen Optimierungslösern, die sogenannte schwach-besetzte Strukturen ausnutzen. Im Gegensatz zu anderen etablierten und "gewachsen" NLP-Lösern wurde WORHP zunächst vollständig am Reißbrett entworfen und berücksichtigt aktuelle Architekturen, mathematische Entwicklungen, neue Computer- und Compilerstandards sowie industrielle Anforderungen. Hierdurch ist es möglich Probleme mit mehr als 1 Milliarde Variablen und Beschränkungen zu lösen.

Nach einer kurzen ingenieurwissenschaftlichen Motivation und einem Einblick in den aktuellen Stand zur nichtlinearen Optimierung, werden in diesem Vortrag Ideen aus der Echtzeitoptimierung ihren Weg in adaptive Regelungsverfahren finden. Abschliessend werden Anwendungen aus den Bereichen Automotive, Luft- und Raumfahrt sowie Energie vorgestellt.**12.12.2018, 15:00 Uhr, HS 326/327 (Ulmenstr. 69, Haus 3)**