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In this episode Gudrun speaks with Nadja Klein and Moussa Kassem Sbeyti who work at the Scientific Computing Center (SCC) at KIT in Karlsruhe. Since August 2024, Nadja has been professor at KIT leading the research group Methods for Big Data (MBD) there. She is an Emmy Noether Research Group Leader, and a member of AcademiaNet, and Die Junge Akademie, among others. In 2025, Nadja was awarded the Committee of Presidents of Statistical Societies (COPSS) Emerging Leader Award (ELA). The COPSS ELA recognizes early career statistical scientists who show evidence of and potential for leadership and who will help shape and strengthen the field. She finished her doctoral studies in Mathematics at the Universität Göttingen before conducting a postdoc at the University of Melbourne as a Feodor-Lynen fellow by the Alexander von Humboldt Foundation. Afterwards she was a Professor for Statistics and Data Science at the Humboldt-Universität zu Berlin before joining KIT. Moussa joined Nadja's lab as an associated member in 2023 and later as a postdoctoral researcher in 2024. He pursued a PhD at the TU Berlin while working as an AI Research Scientist at the Continental AI Lab in Berlin. His research primarily focuses on deep learning, developing uncertainty-based automated labeling methods for 2D object detection in autonomous driving. Prior to this, Moussa earned his M.Sc. in Mechatronics Engineering from the TU Darmstadt in 2021. The research of Nadja and Moussa is at the intersection of statistics and machine learning. In Nadja's MBD Lab the research spans theoretical analysis, method development and real-world applications. One of their key focuses is Bayesian methods, which allow to incorporate prior knowledge, quantify uncertainties, and bring insights to the “black boxes” of machine learning. By fusing the precision and reliability of Bayesian statistics with the adaptability of machine and deep learning, these methods aim to leverage the best of both worlds. The KIT offers a strong research environment, making it an ideal place to continue their work. They bring new expertise that can be leveraged in various applications and on the other hand Helmholtz offers a great platform in that respect to explore new application areas. For example Moussa decided to join the group at KIT as part of the Helmholtz Pilot Program Core-Informatics at KIT (KiKIT), which is an initiative focused on advancing fundamental research in informatics within the Helmholtz Association. Vision models typically depend on large volumes of labeled data, but collecting and labeling this data is both expensive and prone to errors. During his PhD, his research centered on data-efficient learning using uncertainty-based automated labeling techniques. That means estimating and using the uncertainty of models to select the helpful data samples to train the models to label the rest themselves. Now, within KiKIT, his work has evolved to include knowledge-based approaches in multi-task models, eg. detection and depth estimation — with the broader goal of enabling the development and deployment of reliable, accurate vision systems in real-world applications. Statistics and data science are fascinating fields, offering a wide variety of methods and applications that constantly lead to new insights. Within this domain, Bayesian methods are especially compelling, as they enable the quantification of uncertainty and the incorporation of prior knowledge. These capabilities contribute to making machine learning models more data-efficient, interpretable, and robust, which are essential qualities in safety-critical domains such as autonomous driving and personalized medicine. Nadja is also enthusiastic about the interdisciplinarity of the subject — repeatedly changing the focus from mathematics to economics to statistics to computer science. The combination of theoretical fundamentals and practical applications makes statistics an agile and important field of research in data science. From a deep learning perspective, the focus is on making models both more efficient and more reliable when dealing with large-scale data and complex dependencies. One way to do this is by reducing the need for extensive labeled data. They also work on developing self-aware models that can recognize when they're unsure and even reject their own predictions when necessary. Additionally, they explore model pruning techniques to improve computational efficiency, and specialize in Bayesian deep learning, allowing machine learning models to better handle uncertainty and complex dependencies. Beyond the methods themselves, they also contribute by publishing datasets that help push the development of next-generation, state-of-the-art models. The learning methods are applied across different domains such as object detection, depth estimation, semantic segmentation, and trajectory prediction — especially in the context of autonomous driving and agricultural applications. As deep learning technologies continue to evolve, they’re also expanding into new application areas such as medical imaging. Unlike traditional deep learning, Bayesian deep learning provides uncertainty estimates alongside predictions, allowing for more principled decision-making and reducing catastrophic failures in safety-critical application. It has had a growing impact in several real-world domains where uncertainty really matters. Bayesian learning incorporates prior knowledge and updates beliefs as new data comes in, rather than relying purely on data-driven optimization. In healthcare, for example, Bayesian models help quantify uncertainty in medical diagnoses, which supports more risk-aware treatment decisions and can ultimately lead to better patient outcomes. In autonomous vehicles, Bayesian models play a key role in improving safety. By recognizing when the system is uncertain, they help capture edge cases more effectively, reduce false positives and negatives in object detection, and navigate complex, dynamic environments — like bad weather or unexpected road conditions — more reliably. In finance, Bayesian deep learning enhances both risk assessment and fraud detection by allowing the system to assess how confident it is in its predictions. That added layer of information supports more informed decision-making and helps reduce costly errors. Across all these areas, the key advantage is the ability to move beyond just accuracy and incorporate trust and reliability into AI systems. Bayesian methods are traditionally more expensive, but modern approximations (e.g., variational inference or last layer inference) make them feasible. Computational costs depend on the problem — sometimes Bayesian models require fewer data points to achieve better performance. The trade-off is between interpretability and computational efficiency, but hardware improvements are helping bridge this gap. Their research on uncertainty-based automated labeling is designed to make models not just safer and more reliable, but also more efficient. By reducing the need for extensive manual labeling, one improves the overall quality of the dataset while cutting down on human effort and potential labeling errors. Importantly, by selecting informative samples, the model learns from better data — which means it can reach higher performance with fewer training examples. This leads to faster training and better generalization without sacrificing accuracy. They also focus on developing lightweight uncertainty estimation techniques that are computationally efficient, so these benefits don’t come with heavy resource demands. In short, this approach helps build models that are more robust, more adaptive to new data, and significantly more efficient to train and deploy — which is critical for real-world systems where both accuracy and speed matter. Statisticians and deep learning researchers often use distinct methodologies, vocabulary and frameworks, making communication and collaboration challenging. Unfortunately, there is a lack of Interdisciplinary education: Traditional academic programs rarely integrate both fields. It is necessary to foster joint programs, workshops, and cross-disciplinary training can help bridge this gap. From Moussa's experience coming through an industrial PhD, he has seen how many industry settings tend to prioritize short-term gains — favoring quick wins in deep learning over deeper, more fundamental improvements. To overcome this, we need to build long-term research partnerships between academia and industry — ones that allow for foundational work to evolve alongside practical applications. That kind of collaboration can drive more sustainable, impactful innovation in the long run, something we do at methods for big data. Looking ahead, one of the major directions for deep learning in the next five to ten years is the shift toward trustworthy AI. We’re already seeing growing attention on making models more explainable, fair, and robust — especially as AI systems are being deployed in critical areas like healthcare, mobility, and finance. The group also expect to see more hybrid models — combining deep learning with Bayesian methods, physics-based models, or symbolic reasoning. These approaches can help bridge the gap between raw performance and interpretability, and often lead to more data-efficient solutions. Another big trend is the rise of uncertainty-aware AI. As AI moves into more high-risk, real-world applications, it becomes essential that systems understand and communicate their own confidence. This is where uncertainty modeling will play a key role — helping to make AI not just more powerful, but also more safe and reliable. The lecture "Advanced Bayesian Data Analysis" covers fundamental concepts in Bayesian statistics, including parametric and non-parametric regression, computational techniques such as MCMC and variational

Gudrun talks with Polyxeni Spilioti at Aarhus university about spectral geometry. Before working in Aarhus Polyxeni was a postdoctoral researcher in the group of Anton Deitmar at the University of Tübingen. She received her PhD from the University of Bonn, under the supervision of Werner Mueller after earning her Master's at the National and Technical University of Athens (Faculty of Applied Mathematics and Physics). As postdoc she was also guest at the MPI for Mathematics in Bonn, the Institut des Hautes Etudes Scientifiques in Paris and the Oberwolfach Research Institute for Mathematics. In her research she works on questions like: How can one obtain information about the geometry of a manifold, such as the volume, the curvature, or the length of the closed geodesics, provided that we can study the spectrum of certain differential operators? Harmonic analysis on locally symmetric spaces provides a powerful machinery in studying various invariants, such as the analytic torsion, as well as the dynamical zeta functions of Ruelle and Selberg. References and further information P. Spiliotti: Ruelle and Selberg zeta functions on compact hyperbolic odd dimensional manifolds PhD thesis, Bonn, 2015. Greek Women in Mathematics Website Celebration of Greek Women in mathematics, May 12 2022 Greek women in mathematics - First podcast episode Eberhard Zeidler on Wikipedia Podcasts A. Pohl: Quantenchaos, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 79, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2016.

One of the reasons we started this podcast in 2013 was to provide a more realistic picture of mathematics and of the way mathematicians work. On Nov. 19 2021 Gudrun talked to Stephanie Anne Salomone who is Professor and Chair in Mathematics at the University of Portland. She is also Director of the STEM Education and Outreach Center and Faculty Athletic Representative at UP. She is an Associate Director of Project NExT, a program of the Mathematical Association of America that provides networking and professional development opportunities to mathematics faculty who are new to our profession. She is a wife and mother of three boys, Milo (13), Jude (10), and Theodore (8). This conversation started on Twitter in the summer of 2021. There Stephanie (under the twitter handle @SitDownPee) and @stanyoshinobu Dr. Stan Yoshinobu invited their fellow mathematicians to the following workshop: Come help us build gender equity in mathematics! Picture a Mathematician workshop led by @stanyoshinobu Dr. Stan Yoshinobu and me, designed for men in math, but all genders welcome. Gudrun was curious to learn more and followed the provided link: Workshop Abstract Gender equity in the mathematical sciences and in the academy broadly is not yet a reality. Women (and people of color, and other historically excluded groups) are confronted with systemic biases, daily experiences, feelings of not being welcome or included, that in the aggregate push them out of the mathematical sciences. This workshop is designed primarily for men in math (although all genders are welcome to participate) to inform and inspire them to better see some of the key issues with empathy, and then to take action in creating a level-playing field in the academy. Workshop activities include viewing “Picture a Scientist” before the workshop, a 2-hour synchronous workshop via zoom, and follow-up discussions via email and Discord server. *All genders welcome AND this workshop is designed for men to be allies. This idea resonated strongly with Gudrun's experiences: Of course women and other groups which are minorities in research have to speak out to fight for their place but things move forward only if people with power join the cause. At the moment people with power in mathematical research mostly means white men. That is true for the US where Stephanie is working as well as in Germany. Allyship is a concept which was introduced by people of colour to name white people fighting for racial justice at their side. Of course, it is a concept which helps in all situations where a group is less powerful than another. Men working for the advancement of non-male mathematicians is strictly necessary in order for equality of chances and a diversity of people in mathematics to be achieved in the next generation. And to be clear: this has nothing to do with counting heads but it is about not ruining the future of mathematics as a discipline by creating obstacles for mathematicians with minoritized identities. The important question is: How is it possible to educate men and especially powerful white men to become allies? The idea of this first workshop designed by Stephanie and Stan was to invite men already interested in learning more and to build a basis with the documentary Picture a scientist (2020). SYNOPSIS PICTURE A SCIENTIST chronicles the groundswell of researchers who are writing a new chapter for women scientists. Biologist Nancy Hopkins, chemist Raychelle Burks, and geologist Jane Willenbring lead viewers on a journey deep into their own experiences in the sciences, ranging from brutal harassment to years of subtle slights. Along the way, from cramped laboratories to spectacular field stations, we encounter scientific luminaries - including social scientists, neuroscientists, and psychologists - who provide new perspectives on how to make science itself more diverse, equitable, and open to all. (from the webpage) In this film there are no mathematicians, but the situations in sciences and mathematics are very similar and for that it lends itself to show the situation. In the podcast conversation Gudrun and Stephanie talk about why and in what way the documentary spoke to them. The huge and small obstacles in their own work as women mathematicians which do not make them feel welcome in a field they feel passionate about. The film shows what happens to women in Science. It shows also men in different roles. Obviously there are the bullies. Then there are the bystanders. There are universities which allow women to be hired and give them the smallest space available. But there are also men who consider themselves friends of their female collaegues who cannot believe that they did not notice how the behaviour of other men (and their own behavior in not taking a side). Seeing this play out over the course of the film is not a comfortable watch, and perhaps because of this discomfort, we hope to build empathy. On the other hand, there is a story of women scientists who noticed that they were not treated as well as their male colleagues and who found each other to fight for office space and the recognition of their work. They succeded a generation ago. The general idea of the workshop was to start with the documentary and to talk about different people and their role in the film in order to take them as prototypical for roles which we happen to observe in our life and which we might happen to play. This discussion in groups was moderated and guided in order to make this a safe space for everyone. Stephanie spoke about how we have to let men grow into their responsibility to speak out against a hostile atmosphere at university created mostly by men. In the workshop it was possible to first develop and then train for possible responses in situations which ask for men stepping in as an ally. The next iteration of the workshop Picture a Mathematician will be on May 11. Biography: Stephanie Salomone earned her Ph.D. in Mathematics from UCLA in 2005 and joined the faculty at the University of Portland that year. She serves as Professor and Chair of Mathematics and Director of the STEM Education and Outreach Center at UP, as well as the Faculty Athletic Representative. She is an Associate Director of Project NExT, a national professional development program for new higher-education mathematics faculty. She was the PI on the NSF REFLECT program, advancing the use of evidence-based practices in STEM teaching at UP and the use of peer-observation for formative assessment of teaching, and has managed a combined $1.6 million as the PI on a subaward of the Western Regional Noyce Alliance grant and as PI of the NSF Noyce Program at UP. She is on the Board of Directors for Saturday Academy, a local 501c3 whose mission is to engage children in hands-on STEM learning. Dr. Salomone is the recipient of UP’s 2009 Outstanding Teaching Award and the recipient of the 2019 Oregon Academy of Sciences Outstanding Educator in STEM Higher Education Award. Literature and further information Allyship: What It Means to Be an Ally, Tulane university, School of social work Guide to allyship Ernest, Reinholz, and Shah: Hidden Competence: women’s mathematical participation in public and private classroom spaces, Educ Stud Math 102, 153–172 (2019). https://doi.org/10.1007/s10649-019-09910-w J.R. Cimpian, T.H. Kimand, Z.T. McDermott: Understanding persistent gender gaps in STEM, Science 368, Issue 6497, 1317-1319 (2020). https://doi.org/10.1126/science.aba7377 S.J. Ceci and W.M. Williams: Understanding current causes of women’s underrepresentation in science PNAS 108 3157–3162 (2011). https://doi.org/10.1073/pnas.1014871108 Inquirybased learning site Equatiy and teaching math Blog post by Stan Yoshinobu Podcasts Mathematically uncensored Podcast

In March 2018 Gudrun had a day available in London when travelling back from the FENICS workshop in Oxford. She contacted a few people working in mathematics at the University College London (ULC) and asked for their time in order to talk about their research. In the end she brought back three episodes for the podcast. This is the second of these conversations. Gudrun talks to Marta Betcke. Marta is associate professor at the UCL Department of Computer Science, member of Centre for Inverse Problems and Centre for Medical Image Computing. She has been in London since 2009. Before that she was a postdoc in the Department of Mathematics at the University of Manchester working on novel X-ray CT scanners for airport baggage screening. This was her entrance into Photoacoustic tomography (PAT), the topic Gudrun and Marta talk about at length in the episode. PAT is a way to see inside objects without destroying them. It makes images of body interiors. There the contrast is due to optical absorption, while the information is carried to the surface of the tissue by ultrasound. This is like measuring the sound of thunder after lightning. Measurements together with mathematics provide ideas about the inside. The technique combines the best of light and sound since good contrast from optical part - though with low resolution - while ultrasound has good resolution but poor contrast (since not enough absorption is going on). In PAT, the measurements are recorded at the surface of the tissue by an array of ultrasound sensors. Each of that only detects the field over a small volume of space, and the measurement continues only for a finite time. In order to form a PAT image, it is necessary to solve an inverse initial value problem by inferring an initial acoustic pressure distribution from measured acoustic time series. In many practical imaging scenarios it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. Then numerical models of wave propagation can be used within the variational image reconstruction framework to find a regularized least-squares solution of an optimization problem. Assuming homogeneous acoustic properties and the absence of acoustic absorption the measured time series can be related to the initial pressure distribution via the spherical mean Radon transform. Integral geometry can be used to derive direct, explicit inversion formulae for certain sensor geometries, such as e.g. spherical arrays. At the moment PAT is predominantly used in preclinical setting, to image tomours and vasculature in small animals. Breast imaging, endoscopic fetus imaging as well as monitoring of perfusion and drug metabolism are subject of intensive ongoing research. The forward problem is related to the absorption of the light and modeled by the wave equation assuming instanteneous absorption and the resulting thearmal expansion. In our case, an optical ultrasound sensor records acoustic waves over time, i.e. providing time series with desired spacial and temporal resolution. Given complete data, then one can mathematically reverse the time direction and find out the original object. Often it is not possible to collect a complete data due to e.g. single sided access to the object as in breast imaging or underlying dynamics happening on a faster rate than one can collect data. In such situations one can formulate the problem in variational framework using regularisation to compensate for the missing data. In particular in subsampling scenario, one would like to use raytracing methods as they scale linearly with the number of sensors. Marta's group is developing flexible acoustic solvers based on ray tracing discretisation of the Green's formulas. They cannot handle reflections but it is approximately correct to assume this to be true as the soundspeed variation is soft tissue is subtle. These solvers can be deployed alongside with stochastic iterative solvers for efficient solution of the variational formulation. Marta went to school in Poland. She finished her education there in a very selected school and loved math due to a great math teacher (which was also her aunt). She decidede to study Computer Sciences, since there she saw more chances on the job market. When moving to Germany her degree was not accepted, so she had to enrol again. This time for Computer Sciences and Engineering at the Hamburg University of Technology. After that she worked on her PhD in the small group of Heinrich Voss there. She had good computing skills and fit in very well. When she finished there she was married and had to solve a two body problem, which brought the couple to Manchester, where a double position was offered. Now both have a permanent position in London. References M. Betcke e.a.: Model-Based Learning for Accelerated, Limited-View 3-D Photoacoustic Tomography IEEE Transactions on Medical Imaging 37, 1382 - 1393, 2018. F. Rullan & M. Betcke: Hamilton-Green solver for the forward and adjoint problems in photoacoustic tomography archive, 2018. M. Betcke e.a.: On the adjoint operator in photoacoustic tomography Inverse Problems 32, 115012, 2016. doi C. Lutzweiler and D. Razansky: Optoacoustic imaging and tomography - reconstruction approaches and outstanding challenges in image performance and quantification, Sensors 13 7345, 2013. doi: 10.3390/s130607345 Podcasts G. Thäter, K. Page: Embryonic Patterns, Gespräch im Modellansatz Podcast, Folge 161, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018. F. Cakoni, G. Thäter: Linear Sampling, Conversation im Modellansatz Podcast, Episode 226, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2019. G. Thäter, R. Aceska: Dynamic Sampling, Gespräch im Modellansatz Podcast, Folge 173, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018. S. Fliss, G. Thäter: Transparent Boundaries. Conversation in the Modellansatz Podcast episode 75, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. S. Hollborn: Impedanztomographie. Gespräch mit G. Thäter im Modellansatz Podcast, Folge 68, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2015. M. Kray, G. Thäter: Splitting Waves. Conversation in the Modellansatz Podcast episode 62, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. F. Sayas, G. Thäter: Acoustic scattering. Conversation in the Modellansatz Podcast episode 58, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015.

This is the third of three conversation recorded during the Conference on mathematics of wave phenomena 23-27 July 2018 in Karlsruhe. Gudrun is in conversation with Anne-Sophie Bonnet-BenDhia from ENSTA in Paris about transmission properties in perturbed waveguides. The spectral theory is essential to study wave phenomena. For instance, everybody has experimented with resonating frequencies in a bathtube filled with water. These resonant eigenfrequencies are eigenvalues of some operator which models the flow behaviour of the water. Eigenvalue problems are better known for matrices. For wave problems, we have to study eigenvalue problems in infinite dimension. Like the eigenvalues for a finite dimensional matrix the Spectral theory gives access to intrinisic properties of the operator and the corresponding wave phenomena. Anne-Sophie is interested in waveguides. For example, optical fibres can guide optical waves while wind instruments are guides for acoustic waves. Electromagnetic waveguides also have important applications. A practical objective is to optimize the transmission in a waveguide, even if there are some perturbations inside. It is known that for certain frequencies, there is no reflection by the perturbations but it is not apriori clear how to find these frequencies. Anne-Sophie uses complex analysis for that. The idea is to complexify the (originally real) coordinates by analytic extension. It is a classic idea for resonances that she adapts to the problem of transmission. This mathematical method of complex scaling is linked to the method of perfectly matched layers in numerics. It is used to solve problems set in unbounded domains on a computer by finite elements. Thanks to the complex scaling, she can solve a problem in a bounded domain, which reproduces the same behaviour as in the infinite domain. Finally, Anne-Sophie is able to get numerically a complex spectrum of frequencies, related to the quality of the transmission in a perturbed waveguide. The imaginary part of the complex quantity gives an indication of the quality of the transmission in the waveguide. The closer to the real axis the better the transmission. References A-S. Bonnet-BenDhia, L. Chesnel and V. Pagneux:Trapped modes and reflectionless modes as eigenfunctions of the same spectral problem Proceedings of the Royal Society A, 2018, doi 10.1098/rspa.2018.0050 A-S. Bonnet-BenDhia: Mathematical and numerical treatment of plasmonic waves at corners of metals and metamaterials Emerging Topics in Optics, IMA, Minneapolis, 2017 A-S. Bonnet-BenDhia, L. Chesnel and S. Nazarov: Perfect transmission invisibility for waveguides with sound hard walls Journal de Mathématiques Pures et Appliquées, 2017, doi 10.1016/j.matpur.2017.07.020 A.-S. Bonnet-BenDhia e.a.: A method to build non-scattering perturbations of two-dimensional acoustic waveguides Math. meth. appl. sci., vol. 40, pp. 335–349, 2015 doi 10.1002/mma.3447 Podcasts S. Fliss, G. Thäter: Transparent Boundaries. Conversation in the Modellansatz Podcast episode 75, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. M. Kray, G. Thäter: Splitting Waves. Conversation in the Modellansatz Podcast episode 62, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. F. Sayas, G. Thäter: Acoustic scattering. Conversation in the Modellansatz Podcast episode 58, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015.

In den nächsten Wochen bis zum 20.2.2020 möchte Anna Hein, Studentin der Wissenschaftskommunikation am KIT, eine Studie im Rahmen ihrer Masterarbeit über den Podcast Modellansatz durchführen. Dazu möchte sie gerne einige Interviews mit Ihnen, den Hörerinnen und Hörern des Podcast Modellansatz führen, um herauszufinden, wer den Podcast hört und wie und wofür er genutzt wird. Die Interviews werden anonymisiert und werden jeweils circa 15 Minuten in Anspruch nehmen. Für die Teilnahme an der Studie können Sie sich bis zum 20.2.2020 unter der Emailadresse [email protected] bei Anna Hein melden. Wir würden uns sehr freuen, wenn sich viele Interessenten melden würden. In the coming weeks until February 20, 2020, Anna Hein, student of science communication at KIT, intends to conduct a study on the Modellansatz Podcast within her master's thesis. For this purpose, she would like to conduct some interviews with you, the listeners of the Modellansatz Podcast, to find out who listens to the podcast and how and for what purpose it is used. The interviews will be anonymous and will take about 15 minutes each. To participate in the study, you can register with Anna Hein until 20.2.2020 at [email protected] . We would be very pleased if many interested parties would contact us. This is the second of three conversation recorded Conference on mathematics of wave phenomena 23-27 July 2018 in Karlsruhe. Gudrun is in conversation with Mariana Haragus about Benard-Rayleigh problems. On the one hand this is a much studied model problem in Partial Differential Equations. There it has connections to different fields of research due to the different ways to derive and read the stability properties and to work with nonlinearity. On the other hand it is a model for various applications where we observe an interplay between boyancy and gravity and for pattern formation in general. An everyday application is the following: If one puts a pan with a layer of oil on the hot oven (in order to heat it up) one observes different flow patterns over time. In the beginning it is easy to see that the oil is at rest and not moving at all. But if one waits long enough the still layer breaks up into small cells which makes it more difficult to see the bottom clearly. This is due to the fact that the oil starts to move in circular patterns in these cells. For the problem this means that the system has more than one solutions and depending on physical parameters one solution is stable (and observed in real life) while the others are unstable. In our example the temperature difference between bottom and top of the oil gets bigger as the pan is heating up. For a while the viscosity and the weight of the oil keep it still. But if the temperature difference is too big it is easier to redistribute the different temperature levels with the help of convection of the oil. The question for engineers as well as mathematicians is to find the point where these convection cells evolve in theory in order to keep processes on either side of this switch. In theory (not for real oil because it would start to burn) for even bigger temperature differences the original cells would break up into even smaller cells to make the exchange of energy faster. In 1903 Benard did experiments similar to the one described in the conversation which fascinated a lot of his colleagues at the time. The equations where derived a bit later and already in 1916 Lord Rayleigh found the 'switch', which nowadays is called the critical Rayleigh number. Its size depends on the thickness of the configuration, the viscositiy of the fluid, the gravity force and the temperature difference. Only in the 1980th it became clear that Benards' experiments and Rayleigh's analysis did not really cover the same problem since in the experiment the upper boundary is a free boundary to the surrounding air while Rayleigh considered fixed boundaries. And this changes the size of the critical Rayleigh number. For each person doing experiments it is also an observation that the shape of the container with small perturbations in the ideal shape changes the convection patterns. Maria does study the dynamics of nonlinear waves and patterns. This means she is interested in understanding processes which change over time. Her main questions are: Existence of observed waves as solutions of the equations The stability of certain types of solutions How is the interaction of different waves She treats her problems with the theory of dynamical systems and bifurcations. The simplest tools go back to Poincaré when understanding ordinary differential equations. One could consider the partial differential equations to be the evolution in an infinite dimensional phase space. Here, in the 1980s, Klaus Kirchgässner had a few crucial ideas how to construct special solutions to nonlinear partial differential equations. It is possible to investigate waterwave problems which are dispersive equations as well as flow problems which are dissipative. Together with her colleagues in Besancon she is also very keen to match experiments for optical waves with her mathematical analysis. There Mariana is working with a variant of the Nonlinear Schrödinger equation called Lugiato-Lefever Equation. It has many different solutions, e.g. periodic solutions and solitons. Since 2002 Mariana has been Professor in Besancon (University of Franche-Comté, France). Before that she studied and worked in a lot of different places, namely in Bordeaux, Stuttgart, Bucharest, Nice, and Timisoara. References V.A. Getling: Rayleigh-Bénard Convection Structures and Dynamics, Advanced Series in Nonlinear Dynamics, Volume 11, World Scientific, Oxford (1998) P. H. Rabinowitz: Existence and nonuniqueness of rectangular solutions of the Bénard problem. Arch. Rational Mech. Anal. (1968) 29: 32. M. Haragus and G. Iooss: Local bifurcations, center manifolds, and normal forms in infinite-dimensional dynamical systems. Universitext. Springer-Verlag London, Ltd., London; EDP Sciences, Les Ulis, 2011. Newell, Alan C. Solitons in mathematics and physics. CBMS-NSF Regional Conference Series in Applied Mathematics, 48. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1985. Y. K. Chembo, D. Gomila, M. Tlidi, C. R. Menyuk: Topical Issue: Theory and Applications of the Lugiato-Lefever Equation. Eur. Phys. J. D 71 (2017). Podcasts S. Fliss, G. Thäter: Transparent Boundaries. Conversation in the Modellansatz Podcast episode 75, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. M. Kray, G. Thäter: Splitting Waves. Conversation in the Modellansatz Podcast episode 62, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. F. Sayas, G. Thäter: Acoustic scattering. Conversation in the Modellansatz Podcast episode 58, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015.

In den nächsten Wochen bis zum 20.2.2020 möchte Anna Hein, Studentin der Wissenschaftskommunikation am KIT, eine Studie im Rahmen ihrer Masterarbeit über den Podcast Modellansatz durchführen. Dazu möchte sie gerne einige Interviews mit Ihnen, den Hörerinnen und Hörern des Podcast Modellansatz führen, um herauszufinden, wer den Podcast hört und wie und wofür er genutzt wird. Die Interviews werden anonymisiert und werden jeweils circa 15 Minuten in Anspruch nehmen. Für die Teilnahme an der Studie können Sie sich bis zum 20.2.2020 unter der Emailadresse [email protected] bei Anna Hein melden. Wir würden uns sehr freuen, wenn sich viele Interessenten melden würden. In the coming weeks until February 20, 2020, Anna Hein, student of science communication at KIT, intends to conduct a study on the Modellansatz Podcast within her master's thesis. For this purpose, she would like to conduct some interviews with you, the listeners of the Modellansatz Podcast, to find out who listens to the podcast and how and for what purpose it is used. The interviews will be anonymous and will take about 15 minutes each. To participate in the study, you can register with Anna Hein until 20.2.2020 at [email protected] . We would be very pleased if many interested parties would contact us. This is the first of three conversation recorded Conference on mathematics of wave phenomena 23-27 July 2018 in Karlsruhe. Gudrun talked to Fioralba Cakoni about the Linear Sampling Method and Scattering. The linear sampling method is a method to reconstruct the shape of an obstacle without a priori knowledge of either the physical properties or the number of disconnected components of the scatterer. The principal problem is to detect objects inside an object without seeing it with our eyes. So we send waves of a certain frequency range into an object and then measure the response on the surface of the body. The waves can be absorbed, reflected and scattered inside the body. From this answer we would like to detect if there is something like a tumor inside the body and if yes where. Or to be more precise what is the shape of the tumor. Since the problem is non-linear and ill posed this is a difficult question and needs severyl mathematical steps on the analytical as well as the numerical side. In 1996 Colton and Kirsch (reference below) proposed a new method for the obstacle reconstruction problem in inverse scattering which is today known as the linear sampling method. It is a method to solve the above stated problem, which scientists call an inverse scattering problem. The method of linear sampling combines the answers to lots of frequencies but stays linear. So the problem in itself is not approximated but the interpretation of the response is. The central idea is to invert a bounded operator which is constructed with the help of the integral over the boundary of the body. Fioralba got her Diploma (honor’s program) and her Master's in Mathematics at the University of Tirana. For her Ph.D. she worked with George Dassios from the University of Patras but stayed at the University of Tirana. After that she worked with Wolfgang Wendland at the University of Stuttgart as Alexander von Humboldt Research Fellow. During her second year in Stuttgart she got a position at the University of Delaware in Newark. Since 2015 she has been Professor at Rutgers University. She works at the Campus in Piscataway near New Brunswick (New Jersey). References F. Cakoni, D. Colton and H. Haddar, Inverse Scattering Theory and Transmission Eigenvalues, CBMS-NSF Regional Conference Series in Applied Mathematics, 88, SIAM Publications, 2016. F. Cakoni, D. Colton, A Qualitative Approach to Inverse Scattering Theory, Springer, Applied Mathematical Series, Vol. 188, 2014. T. Arens: Why linear sampling works, Inverse Problems 20 163-173, 2003. https://doi.org/10.1088/0266-5611/20/1/010 A. Kirsch: Characterization of the shape of a scattering obstacle using the spectral data of the far field operator, Inverse Problems 14 1489-512, 1998 D. Colton, A. Kirsch: A simple method for solving inverse scattering problems in the resonance region, Inverse Problems 12 383-93, 1996. Podcasts S. Fliss, G. Thäter: Transparent Boundaries. Conversation in the Modellansatz Podcast episode 75, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. M. Kray, G. Thäter: Splitting Waves. Conversation in the Modellansatz Podcast episode 62, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. F. Sayas, G. Thäter: Acoustic scattering. Conversation in the Modellansatz Podcast episode 58, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015.

Gudrun talks to Anna Geyer. Anna is Assistant professer at TU Delft in the Mathematical Physics group at the Delft Institute of Applied Mathematics. She is interested in the behaviour of solutions to equations which model shallow water waves. The day before (04.07.2019) Anna gave a talk at the Kick-off meeting for the second funding period of the CRC Wave phenomena at the mathematics faculty in Karlsruhe, where she discussed instability of peaked periodic waves. Therefore, Gudrun asks her about the different models for waves, the meaning of stability and instability, and the mathematical tools used in her field. For shallow water flows the solitary waves are especially fascinating and interesting. Traveling waves are solutions of the form representing waves of permanent shape f that propagate at constant speed c. These waves are called solitary waves if they are localized disturbances, that is, if the wave profile f decays at infinity. If the solitary waves retain their shape and speed after interacting with other waves of the same type, we say that the solitary waves are solitons. One can ask the question if a given model equation (sometimes depending on parameters in the equation or the size of the initial conditions) allows for solitary or periodic traveling waves, and secondly whether these waves are stable or unstable. Peaked periodic waves are an interesting phenomenon because at the wave crest (the peak) they are not smooth, a situation which might lead to wave breaking. For which equations are peaked waves solutions? And how stable are they? Anna answers these questions for the reduced Ostrovsky equation, which serves as model for weakly nonlinear surface and internal waves in a rotating ocean. The reduced Ostrovsky equation is a modification of the Korteweg-de Vries equation, for which the usual linear dispersive term with a third-order derivative is replaced by a linear nonlocal integral term, representing the effect of background rotation. Peaked periodic waves of this equation are known to exist since the late 1970's. Anna presented recent results in which she answers the long standing open question whether these solutions are stable. In particular, she proved linear instability of the peaked periodic waves using semi-group theory and energy estimates. Moreover, she showed that the peaked wave is unique and that the equation does not admit Hölder continuous solutions, which implies that the reduced Ostrovsky equation does not admit cusps. Finally, it turns out that the peaked wave is also spectrally unstable. This is joint work with Dmitry Pelinovsky. For the stability analysis it is really delicate how to choose the right spaces such that their norms measure the behaviour of the solution. The Camassa-Holm equation allows for solutions with peaks which are stable with respect to certain perturbations and unstable with respect to others, and can model breaking waves. Anna studied mathematics in Vienna. Adrian Constantin attracted her to the topic of partial differential equations applied to water waves. She worked with him during her PhD which she finished in 2013. Then she worked as Postdoc at the Universitat Autònoma de Barcelona and in Vienna before she accepted a tenure track position in Delft in 2017. References A. Geyer, D.E. Pelinovsky: Spectral instability of the peaked periodic wave in the reduced Ostrovsky equations, submitted (arXiv) A. Geyer, D.E. Pelinovsky: Linear instability and uniqueness of the peaked periodic wave in the reduced Ostrovsky equation, SIAM J. Math. Analysis, 51 (2019) 1188–1208 A. Geyer, D.E. Pelinovsky: Spectral stability of periodic waves in the generalized reduced Ostrovsky equation, Lett. Math. Phys. 107(7) (2017) 1293–1314 R. Grimshaw, L. Ostrovsky, V. Shrira, et al.: Long Nonlinear Surface and Internal Gravity Waves in a Rotating Ocean, Surveys in Geophysics (1998) 19: 289. A. Constantin, W. Strauss: Stability of peakons, Commun. Pure Appl. Math. 53 (2000) 603–610. F. Natali, D.E. Pelinovsky: Instability of H1-stable peakons in the Camassa-Holm equation, submitted (arXiv) Related Podcasts X. Liao, G. Thäter: Nonhomogenous Fluids, Conversation in the Modellansatz Podcast, Episode 189, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2018. M. Lopez-Fernandez, G. Thäter: Convolution Quadrature, Conversation in the Modellansatz Podcast, Episode 133, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2017. S. Fliss, G. Thäter: Transparent Boundaries, Conversation in the Modellansatz Podcast episode 075, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. F. Sayas, G. Thäter: Acoustic scattering, Conversation in the Modellansatz Podcast episode 058, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. E. Zuazua, G. Thäter: Waves Conversation in the Modellansatz Podcast episode 054, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015.

Gudrun talks with Changjing Zhuge. He is a guest in the group of Lennart Hilbert and works at the College of applied sciences and the Beijing Institute for Scientific and Engineering Computing (BISEC) at the Beijing University of Technology. He is a mathematician who is interested in system biology. In some cases he studies delay differential equations or systems of ordinary differential equations to characterize processes and interactions in the context of cancer research. The inbuilt delays originate e.g. from the modeling of hematopoietic stem cell populations. Hematopoietic stem cells give rise to other blood cells. Chemotherapy is frequently accompanied by unwished for side effects to the blood cell production due to the character of the drugs used. Often the production of white blood cells is hindered, which is called neutropenia. In an effort to circumvent that, together with chemotherapy, one treats the patient with granulocyte colony stimulating factor (G-CSF). To examine the effects of the typical periodic chemotherapy in generating neutropenia, and the corresponding response of this system to given to G-CSF Changjing and his colleagues studied relatively simple but physiologically realistic mathematical models for the hematopoietic stem cells. And these models are potential for modeling of other stem-like biosystems such as cancers. The delay in the system is related to the platelet maturation time and the differentiation rate from hematopoietic stem cells into the platelet cell. Changjing did his Bachelor in Mathematics at the Beijing University of Technology (2008) and continued with a PhD-program in Mathematics at the Zhou-Peiyuan Center for Applied Mathematics, Tsinghua University, China. He finished his PhD in 2014. During his time as PhD student he also worked for one year in Michael C Mackey's Lab at the Centre for Applied Mathematics in Bioscience and Medicine of the McGill University in Montreal (Canada). References C. Zhuge, M.C. Mackey, J. Lei: Origins of oscillation patterns in cyclical thrombocytopeniaJournal of Theoretical Biology 462,432-445, 2019. C. Zhuge, X. Sun, J. Lei: On positive solutions and the Omega limit set for a class of delay differential equations. Discrete and Continuous Dynamical Systems - Series B, 18(9), 2487~2503, 2013. C. Zhuge, M.C. Mackey, J. Lei: Neutrophil dynamics in response to chemotherapy and G-CSF Journal of Theoretical Biology 293, 111-120 2012.Podcasts L. Hilbert, G. Thäter: Zellkerne, Gespräch im Modellansatz Podcast, Folge 206, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2019. M. Gonciarz, G. Thäter: Portrait of Science, Gespräch im Modellansatz Podcast, Folge 197, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2019. G. Thäter, K. Page: Embryonic Patterns, Gespräch im Modellansatz Podcast, Folge 161, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018. L. Adlung, G. Thäter, S. Ritterbusch: Systembiologie, Gespräch im Modellansatz Podcast, Folge 39, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2016. Omega Tau-Podcast 072: Forschung in der Zellbiologie, 2011. J. Schmoranze, I. Wessolowski: Beim Herrn der Mikroskope – AMBIO Core Facility, Sciencekompass Podcast, Episode 009 B, 2017.

In June 2019 Gudrun talked with Serena Carelli. Serena is member of the Research Training Group (RTG) Simet, which is based in Karlsruhe, Ulm and Offenburg. It started its work in 2017 and Gudrun is associated postdoc therein. The aim of that graduate school is to work on the better understanding of Lithium-ion batteries. For that it covers all scales, namley from micro (particles), meso (electrodes as pairs) to macro (cell) and involves scientists from chemistry, chemical engineering, material sciences, electro engineering, physics and mathematics. The group covers the experimental side as well as modeling and computer simulations. Serena is one of the PhD-students of the program. She is based in Offenburg in the group of Wolfgang Bessler (the deputy speaker of the RTG). Her research focusses on End-of-life prediction of a lithium-ion battery cell by studying the mechanistic ageing models of the graphite electrode among other things. Mathematical modelling and numerical simulation have become standard techniques in Li-ion battery research and development, with the purpose of studying the issues of batteries, including performance and ageing, and consequently increasing the model-based predictability of life expectancy. Serena and others work on an electrochemical model of a graphite-based lithium-ion cell that includes combined ageing mechanisms: Electrochemical formation of the solid electrolyte interphase (SEI) at the anode, breaking of the SEI due to mechanical stress from volume changes of the graphite particles, causing accelerated SEI growth, gas formation and dry-out of the electrodes, percolation theory for describing the loss of contact of graphite particles to the liquid electrolyte, formation of reversible and irreversible Li plating. The electrochemistry is coupled to a multi-scale heat and mass transport model based on a pseudo-3D approach. A time-upscaling methodology is developed that allows to simulate large time spans (thousands of operating hours). The combined modeling and simulation framework is able to predict calendaric and cyclic ageing up to the end of life of the battery cells. The results show a qualitative agreement with ageing behavior known from experimental literature. Serena has a Bachelor in Chemistry and a Master's in Forensic Chemistry from the University of Torino. She worked in Spain, the Politécnico de Torino and in Greece (there she was Marie Curie fellow at the Foundation for Research and Technology - Hellas) before she decided to spend time in Australia and India. References Serena's Linked in site A. Latz & J. Zausch: Thermodynamic consistent transport theory of Li-ion batteries, Journal of Power Sources 196 3296--3302, 2011. T. Seger: Elliptic-Parabolic Systems with Applications to Lithium-Ion Battery Models, Doktorarbeit Universität Konstanz, 2013. M. Kespe & H. Nirschl: Numerical simulation of lithium-ion battery performance considering electrode microstructure, International Journal of Energy Research 39 2062-2074, 2015. J.-M. Tarascon & M. Armand: Issues and challenges facing rechargeable lithium batteries, Nature 414 359-367, 2001. W.G. Bessler: Elektrische Energiespeicherung mit Batterien und Brennstoffzellen, Forschung im Fokus, Hochschule Offenburg (2018). Podcasts A. Jossen: Batterien, Gespräch mit Markus Völter im Omega Tau Podcast, Folge 222, 2016. J. Holthaus: Batterien für morgen und übermorgen, KIT.Audio Podcast, Folge 2, 2016. D. Breitenbach, U. Gebhardt, S. Gaedtke: Elektrochemie, Laser, Radio, Proton Podcast, Folge 15, 2016. M. Maier: Akkumulatoren, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 123, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017. V. Auinger: Optimale Akkuladung, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 160, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018.

Gudrun met Magdalena Gonciarz in Dresden. They sat down in a very quiet Coffeeshop in Dreikönigskirche and talked about their experiences as scientists giving science an image. Magda started Portrait of science in 2016 with two objectives: to show that science is a process with many contributors at all carreer levels and to have a get-away from a demanding PhD-project, to express her creativity and have tangible results. The person who pointed Gudrun in Magda's direction is Lennart Hilbert, a former co-worker of Magda in Dresden who is now working at KIT on Computational Architectures in the Cell Nucleus (he will be a podcast guest very soon). On the Portrait of Science page one can find photographs of people from Dresden's Life Science campus. Apart from the photographs, one can also find their stories. How and why did they become scientists? What do they do, what are they passionate about? Magda invites us: "Forget the tubes and Erlenmeyer flasks. Science is only as good as the people who do it. So sit back, scroll down and get to know them looking through the lens of Magdalena Gonciarz. Have you ever wondered what kind of people scientists are? Would you like to know what are they working on? What drives and motivates them - spending days in the basement without the sun? Portrait of Science project aims at uncovering more about people who contribute to science at all levels - Research Group Leaders, Postdocs, PhD Students, Staff Scientists and Technicians. All of them are vital for progress of scientific research and all of them are passionate people with their own motivations." When she started the Portrait of Science project, Magda challenged herself to take more pictures. She wanted to show the real people behind science and their personality. This was a creative task, quite different from her work as scientist - done with comparably little time. On top of taking the pictures, interviewees were asked to fill out a questionaire to accompany the story told by the photographs. Surprisingly, the stories told by her co-workers turned out to be quite inspiring. The stories told have shown the passion and the diverse motivations. People mentioned their failures as well. There were stories about accidents and their crucial role in carreers, about coincidence of finding a fascinating book or the right mentor - even as far back as in early childhood sometimes. Sharing ups and downs and the experience that there is a light at the end of the tunnel was a story she needed and which was worth to be shared. Knowing how hard scientific work can be, and how multiple friends and colleagues struggled more than she herself, Magda still strongly feels that it is useful to show that this is not a private and unique experience, but probably a part of the life of every scientist. This struggle can be overcome with time, effort, and help. Magda comes from Poland. During her Master's studies, she had an opportunity to do a research placement at the University of Virginia. During that time she felt welcomed as part of a scientific community in which she wanted to stay. It was a natural decision to proceed with a PhD. She applied to the very prestigious Dresden International Graduate School for Biomedicine and Bioengineering and joined the biological research on proteins and their modifications in the lab of Jörg Mansfeld. After finishing her project, she decided to leave academia. Since 2018 she works for a learning and training agency CAST PHARMA and is involved in producing e-Learning solutions for pharmaceutical companies. Magda also talked a bit about her PhD research. As we all know, genes code for proteins. However, one protein can exist in multiple different forms with multiple varying functions. A protein can be post-translationallly modified, i.e., modified after it is created in order to e.g., be relocated, have different interaction partners or become activated or destroyed in a manner of minutes. Recently, modern methods such as mass spectrometry, made it possible to see the multitude of post-translationally modified forms of proteins and allowed further research with the use of biochemistry or imaging techniques to gain insight into functions of these modifications, e.g., at different stages of the cell life. Gudrun and Magda also talked about the challenge to make a broader audience understand what the particular research topic is all about. It is hard to refer to things we cannot see. It is often easier for people with more translatable research to connect it to various diseases, e.g., cancer but still creates a challenge for those working with more basic issues such as developmental biology. What Magda took from her time in academia is much more than her results and her part in the basic research story. She feels that curiosity and quick learning skills are her superpowers. She is able to become familiar with any topic in a short amount of time. She can manage multiple parts of a project. Also she learned resilience and how to deal with challenges and failures on a daily basis, which can prove to be helpful in all areas of life. At the moment, she is still making plans whether to continue the Portrait of Science in the future, maybe in a changed format. Podcasts A. Leßmöllmann: Wissenschaftskommunikation, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 130, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017. C. Rojas-Molian: Rage of the Blackboard, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 121, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017.

Gudrun Talks to Sema Coşkun who at the moment of the conversation in 2018 is a Post Doc researcher at the University Kaiserslautern in the group of financial mathematics. She constructs models for the behaviour of energy markets. In short the conversation covers the questions How are classical markets modelled? In which way are energy markets different and need new ideas? The seminal work of Black and Scholes (1973) established the modern financial theory. In a Black-Scholes setting, it is assumed that the stock price follows a Geometric Brownian Motion with a constant drift and constant volatility. The stochastic differential equation for the stock price process has an explicit solution. Therefore, it is possible to obtain the price of a European call option in a closed-form formula. Nevertheless, there exist drawbacks of the Black-Scholes assumptions. The most criticized aspect is the constant volatility assumption. It is considered an oversimplification. Several improved models have been introduced to overcome those drawbacks. One significant example of such new models is the Heston stochastic volatility model (Heston, 1993). In this model, volatility is indirectly modeled by a separate mean reverting stochastic process, namely. the Cox-Ingersoll-Ross (CIR) process. The CIR process captures the dynamics of the volatility process well. However, it is not easy to obtain option prices in the Heston model since the model has more complicated dynamics compared to the Black-Scholes model. In financial mathematics, one can use several methods to deal with these problems. In general, various stochastic processes are used to model the behavior of financial phenomena. One can then employ purely stochastic approaches by using the tools from stochastic calculus or probabilistic approaches by using the tools from probability theory. On the other hand, it is also possible to use Partial Differential Equations (the PDE approach). The correspondence between the stochastic problem and its related PDE representation is established by the help of Feynman-Kac theorem. Also in their original paper, Black and Scholes transferred the stochastic representation of the problem into its corresponding PDE, the heat equation. After solving the heat equation, they transformed the solution back into the relevant option price. As a third type of methods, one can employ numerical methods such as Monte Carlo methods. Monte Carlo methods are especially useful to compute the expected value of a random variable. Roughly speaking, instead of examining the probabilistic evolution of this random variable, we focus on the possible outcomes of it. One generates random numbers with the same distribution as the random variable and then we simulate possible outcomes by using those random numbers. Then we replace the expected value of the random variable by taking the arithmetic average of the possible outcomes obtained by the Monte Carlo simulation. The idea of Monte Carlo is simple. However, it takes its strength from two essential theorems, namely Kolmogorov’s strong law of large numbers which ensures convergence of the estimates and the central limit theorem, which refers to the error distribution of our estimates. Electricity markets exhibit certain properties which we do not observe in other markets. Those properties are mainly due to the unique characteristics of the production and consumption of electricity. Most importantly one cannot physically store electricity. This leads to several differences compared to other financial markets. For example, we observe spikes in electricity prices. Spikes refer to sudden upward or downward jumps which are followed by a fast reversion to the mean level. Therefore, electricity prices show extreme variability compared to other commodities or stocks. For example, in stock markets we observe a moderate volatility level ranging between 1% and 1.5%, commodities like crude oil or natural gas have relatively high volatilities ranging between 1.5% and 4% and finally the electricity energy has up to 50% volatility (Weron, 2000). Moreover, electricity prices show strong seasonality which is related to day to day and month to month variations in the electricity consumption. In other words, electricity consumption varies depending on the day of the week and month of the year. Another important property of the electricity prices is that they follow a mean reverting process. Thus, the Ornstein-Uhlenbeck (OU) process which has a Gaussian distribution is widely used to model electricity prices. In order to incorporate the spike behavior of the electricity prices, a jump or a Levy component is merged into the OU process. These models are known as generalized OU processes (Barndorff-Nielsen & Shephard, 2001; Benth, Kallsen & Meyer-Brandis, 2007). There exist several models to capture those properties of electricity prices. For example, structural models which are based on the equilibrium of supply and demand (Barlow, 2002), Markov jump diffusion models which combine the OU process with pure jump diffusions (Geman & Roncoroni, 2006), regime-switching models which aim to distinguish the base and spike regimes of the electricity prices and finally the multi-factor models which have a deterministic component for seasonality, a mean reverting process for the base signal and a jump or Levy process for spikes (Meyer-Brandis & Tankov, 2008). The German electricity market is one of the largest in Europe. The energy strategy of Germany follows the objective to phase out the nuclear power plants by 2021 and gradually introduce renewable energy ressources. For electricity production, the share of renewable ressources will increase up to 80% by 2050. The introduction of renewable ressources brings also some challenges for electricity trading. For example, the forecast errors regarding the electricity production might cause high risk for market participants. However, the developed market structure of Germany is designed to reduce this risk as much as possible. There are two main electricity spot price markets where the market participants can trade electricity. The first one is the day-ahead market in which the trading takes place around noon on the day before the delivery. In this market, the trades are based on auctions. The second one is the intraday market in which the trading starts at 3pm on the day before the delivery and continues up until 30 minutes before the delivery. Intraday market allows continuous trading of electricity which indeed helps the market participants to adjust their positions more precisely in the market by reducing the forecast errors. References S. Coskun and R. Korn: Pricing Barrier Options in the Heston Model Using the Heath-Platen estimator. Monte Carlo Methods and Applications. 24 (1) 29-42, 2018. S. Coskun: Application of the Heath–Platen Estimator in Pricing Barrier and Bond Options. PhD thesis, Department of Mathematics, University of Kaiserslautern, Germany, 2017. S. Desmettre and R. Korn: 10 Computationally challenging problems in Finance. FPGA Based Accelerators for Financial Applications, Springer, Heidelberg, 1–32, 2015. F. Black and M. Scholes: The pricing of options and corporate liabilities. The Journal of Political Economy, 81(3):637-654, 1973. S.L. Heston: A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies, 6(2):327–343, 1993. R. Korn, E. Korn and G. Kroisandt: Monte Carlo Methods and Models in Finance and Insurance. Chapman & Hall/CRC Financ. Math. Ser., CRC Press, Boca Raton, 2010. P. Glasserman, Monte Carlo Methods in Financial Engineering. Stochastic Modelling and Applied Probability, Appl. Math. (New York) 53, Springer, New York, 2004. M.T. Barlow: A diffusion model for electricity prices. Mathematical Finance, 12(4):287-298, 2002. O.E. Barndorff-Nielsen and N. Shephard: Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. Journal of the Royal Statistical Society B, 63(2):167-241, 2001. H. Geman and A. Roncoroni: Understanding the fine structure of electricity prices. The Journal of Business, 79(3):1225-1261, 2006. T. Meyer-Brandis and P. Tankov: Multi-factor jump-diffusion models of electricity prices. International Journal of Theoretical and Applied Finance, 11(5):503-528, 2008. R. Weron: Energy price risk management. Physica A, 285(1-2):127–134, 2000. Podcasts G. Thäter, M. Hofmanová: Turbulence, conversation in the Modellansatz Podcast, episode 155, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2018. http://modellansatz.de/turbulence G. Thäter, M. J. Amtenbrink: Wasserstofftankstellen, Gespräch im Modellansatz Podcast, Folge 163, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018. http://modellansatz.de/wasserstofftankstellen S. Ajuvo, S. Ritterbusch: Finanzen damalsTM, Gespräch im Modellansatz Podcast, Folge 97, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2016. http://modellansatz.de/finanzen-damalstm K. Cindric, G. Thäter: Kaufverhalten, Gespräch im Modellansatz Podcast, Folge 45, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2015. http://modellansatz.de/kaufverhalten V. Riess, G. Thäter: Gasspeicher, Gespräch im Modellansatz Podcast, Folge 23, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2015. http://modellansatz.de/gasspeicher F. Schueth, T. Pritlove: Energieforschung, Episode 12 im Forschergeist Podcast, Stifterverband/Metaebene, 2015. https://forschergeist.de/podcast/fg012-energieforschung/

Gudrun talks to Carlos Mauricio Rojas La Rotta. They use a Skype connection since Carlos is in Berlin and Gudrun in Karlsruhe. Carlos is an electrical engineer from Colombia. His first degree is from Pontifcia Universidad Javeriana in Bogotá. For five years now he has been working at Schneider Electric in Berlin. In September 2018 Gudrun met Carlos at the EUREF-Campus in Berlin for discussing the work of Claire Harvey on her Master's thesis. The schedule on that day was very full but Gudrun and Carlos decided to have a Podcast conversation later. Carlos came to Germany as a car enthusiast. Then he got excited about the possibilities of photovoltaic energy production. For that from 2005-2007 he studied in the Carl von Ossietzky Universität in Oldenburg in the PPRE Master course Renewable Energies. When he graduated within a group of about 20 master students they found a world ready for their knowledge. Carlos worked in various topics and in different parts of Germany in the field of renewable energies. Now, at Schneider he has the unique situation, that he can combine all his interests. He develops the most modern cars, which are driving with renewable energy. In the course of his work he is also back at his original love: working with electronics, protocols and data. The work on the EUREF-Campus in Berlin started about 8-10 years ago with more questions than clear ideas. Schneider Electric is a big company with about 150.000 employees all over the world. They deal in all types of software and hardware devices for energy delivery. But the topic for Berlin was completely new: It was a test case how to construct energy sustainable districts. They started out investing in e-mobility with renewable energy and making their own offices a smart building. It is a source of a lot of data telling the story how energy is produced and consumed. At the moment they collect 1GB data per day in the office building on about 12.000 measure points into database and build this as a benchmark to compare it to other scenarios. The next step now is also to find ways to optimize these processes with limited computational possibilities. This is done with open source code on their own interface and at the moment it can optimize in the micro smart grid on the Campus. For example with 40 charging points for e-cars - consumption is planned according to production of energy. On Campus traditional batteries are used to buffer the energy, and also a bus now works on the Campus which can be discharged and is loaded without a cable! One can say: Carlos is working in a big experiment. This does not only cover a lot of new technical solutions. The Energiewende is more than putting photovoltaic and wind power out. We as a society have to change and plan differently - especially concerning mobility. Schneider Electric just started an expansion phase to the whole campus, which has a size of 5.5 ha and 2500 people working there. More than 100 charging point for e-cars will be available very soon. Podcasts C. Harvey, G. Thäter: Micro Grids, Gespräch im Modellansatz Podcast, Folge 186, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018.

Gudrun talks with the Scotish engineer Claire Harvey. After already having finished a Master's degree in Product design engineering at the University of Glasgow for the last two years Claire has been a student of the Energy Technologies (ENTECH) Master program. This is an international and interdisciplinary program under the label of the European Institute of Innovation and Technology (EIT) inbetween a number of European technical universities. She spent her first year in Lisbon at Instituto Superior Técnico (IST) and the second master year at the Karlsruhe Institute of Technology (KIT). Gudrun had the role of her supervisor at KIT while she worked on her Master's thesis at the EUREF Campus in Berlin for the Startup inno2grid. Her study courses prepared her for very diverse work in the sector of renewable energy. Her decision to work with inno2grid in Berlin was based on the fact, that it would help to pave the way towards better solutions for planning micro grids and sustainable districts. Also, she wanted to see an actual micro grid at work. The office building of Schneider Electric, where the Startup inno2grid has its rooms is an experiment delivering data of energy production and consumption while being a usual office building. We will hear more about that in the episode with Carlos Mauricio Rojas La Rotta soon. Micro grids are small scale electrical grid systems where self-sufficient supply is achieved. Therefore, the integration of micro grid design within district planning processes should be developed efficiently. In the planning process of districts with decentralised energy systems, unique and customised design of micro grids is usually required to meet local technical, economical and environmental needs. From a technical standpoint, a detailed understanding of factors such as load use, generation potential and site constraints are needed to correctly and most efficiently design and implement the network. The presence of many different actors and stakeholders contribute to the complexity of the planning process, where varying levels of technical experience and disparate methods of working across teams is commonplace. Large quantities of digital information are required across the whole life-cycle of a planning project, not just to do with energetic planning but also for asset management and monitoring after a micro grid has been implemented. In the design of micro grids, large amounts of data must be gathered, there are initial optimization objectives to be met, and simulating control strategies of a district which are adapted to customer requirements is a critical step. Linking these processes - being able to assemble data as well as communicate the results and interactions of different "layers" of a project to stakeholders are challenges that arise as more cross-sector projects are carried out, with the growing interest in smart grid implementation. Claire's thesis explores tools to assist the planning process for micro grids on the district scale. Using geographical information system (GIS) software, results relating to the energetic planning of a district is linked to geo-referenced data. Layers related to energy planning are implemented - calculating useful parameters and connecting to a database where different stakeholders within a project can contribute. Resource potential, electrical/thermal demand and supply system dimensioning can be calculated, which is beneficial for clients and decision makers to visualize digital information related to a project. Within the open source program QGIS, spatial analysis and optimizations relating to the design of an energy system are performed. As the time dimension is a key part in the planning of the energy supply system of a micro grid, the data is linked to a Python simulation environment where dynamic analysis can be performed, and the results are fed back in to the QGIS project. References T. Benz et al.: Der Zellulare Ansatz. VDE, Energietechnische Gesellschaft, Frankfurt, Germany, 2015. A. Halu et al.: Data-driven modeling of solar-powered urban microgrids. Science Advances 2 (1). DOI:10.1126/sciadv.1500700, 2016. M. Giudice and E. Patti: BIM and GIS for District Modelling Politecnico di Torino, Turin, Italy, 2014. QGIS Ch. Nytsch-Geusen et al.: Sustainable and energy-efficient redevelopment of city quarters - Analytical and planning tools for energy assessment and rehabilitation of urban districts. Universität der Künste, Berlin, 2015. Podcasts Z. Ahamed, G. Thäter: Electric Vehicles on the Grid, Gespräch im Modellansatz Podcast, Folge 183, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018. G. Thäter, M. J. Amtenbrink: Wasserstofftankstellen, Gespräch im Modellansatz Podcast, Folge 163, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018. G. Thäter, B. Pousinho: Weather Generator, Gespräch im Modellansatz Podcast, Folge 148, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017.

Gudrun talks to Zaheer Ahamed about the influence of an increasing number of Electric vehicles (EV) to the electrical grid. Zaheer just finished the ENTECH Master's program. He started it with his first year at the Karlsruhe Institute for Technology (KIT) and continued in Uppsala University for the second year. Gudrun was part of the grading process of Zaheer's master thesis "Estimating Balancing Capacities of Electric Vehicles on the German and Swedish grids in 2030". The rising awareness of pollution from transport is leading to innovations within the transport sector. At the moment EVs are the leading technology. With many countries Germany and Sweden joined the so-called EV30@30 campaign, aiming for 30% of new vehicles sales to be electric by 2030. These ambitions alongside an ever increasing capacity of variable renewable energy sources (RES) in our power systems, pose a concerning challenge for Transmission systems operators (TSO) to maintain proper power system operation. Imbalances between supply and demand are undesirable in any electrical power system and with the rising popularity of EVs and RES such events are only expected to continue or increase. Fortunately, with the recent development of Vehicle to grid (V2G) concepts as well as extensive studies into the load-shifting potential of EVs, EVs presents an interesting solution for power system balancing distributed energy storage system. Zaheer's study showed that EV are capable of balancing the grid for approximately 60% of the time providing 55-60% of the total balancing energy required. However, the operation also took heavy toll on the EV’s battery performance as it could potentially reduce its life to a 1/7th of its original lifetime. References Commission Regulation (EU) 2017/1485 of 2 August 2017 on establishing a guideline on electricity transmission system operation, 2017. S. Weitemeyer e.a.: Integration of Renewable Energy Sources in future power systems: The role of storage. Renewable Energy, 75 pp.14-20, 2015. D.M.Greenwood e.a.: Frequency response services designed for energy storage. Applied Energy, 203 pp.115-127, 2017. Eurostat Database J. Schäuble e.a.: Generating electric vehicle load profiles from empirical data of three EV fleets in Southwest Germany. Journal of Cleaner Production, 150 pp.253-266, 2017. Podcasts Volker Quaschning, Tim Pritlove: Energiewende, Forschergeist 053, Stifterverband / Metaebene, 2018. V. Auinger, G. Thäter: Optimale Akkuladung, Gespräch im Modellansatz Podcast, Folge 160, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018. http://modellansatz.de/optimale-akkuladung M. Lösch, S. Ritterbusch: Smart Meter Gateway, Gespräch im Modellansatz Podcast, Folge 135, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017. http://modellansatz.de/smart-meter M. Maier, G. Thäter: Akkumulatoren, Gespräch im Modellansatz Podcast, Folge 123, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017. http://modellansatz.de/akkumulatoren D. Schumann, M. Voelter: Elektromobilität, Omega Tau Podcast 163, Makus Völter und Nora Ludewig, 2015. J. Dickmann, S. Ritterbusch: Pumpspeicherkraftwerke, Gespräch im Modellansatz Podcast, Folge 5, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2013.