Dezember 2016

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### 01.12.2016 15:45 Hans Wilhelm Alt (TUM) :The entropy principle revisitedMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

Thermodynamics is one of the most challenging topics in mathematical theory and theoretical physics. The notion of entropy is now ~150 years old and by its importance it is not surprising that up to today the entropy principle is present in different versions. But all are based on the second law of thermodynamics. I will give a short survey of the history of thermodynamics, and show how the entropy principle is used in mathematics: It gives equality restrictions on the terms in the considered differential equations, and also inequalities which determine the structure of the system. Therefore it is more than just a method to get a-priori estimates. At the end I will show that the fact that the entropy has to be an objective scalar indicate that one has to take the trace in the second moment equation, which is the well-known energy equation.

### 01.12.2016 16:30 Andreas Obersteiner:Zahlensinn und seine Grenzen - Studien mit mathematisch qualifizierten ErwachsenenA 027 (Theresienstr. 39, 80333 München)

Eine Voraussetzung für Zahlensinn, den flexiblen Umgang mit Zahlen, ist die Fähigkeit, Zahlsymbolen schnell ihre Größeninformation entnehmen zu können. Beispielsweise lässt sich das Ergebnis der Addition ?7/8 + 12/13? ohne Rechnung abschätzen, wenn man schnell sieht, dass der Wert beider Brüche in etwa 1 beträgt. Während die überwiegende Mehrheit der Schülerinnen und Schüler einen ausgeprägten Zahlensinn für natürliche Zahlen entwickelt, haben viele Schülerinnen und Schüler mit Brüchen enorme Schwierigkeiten. Typische Fehler basieren auf der Sichtweise von Brüchen als zwei getrennte Zahlen, was etwa zu der Annahme führt, dass 5/9 größer als 3/4 sei, da der erste Bruch aus den größeren Komponenten besteht. Studien zeigen, dass auch ältere Schüler und selbst Erwachsene bei bestimmten Aufgaben zu Fehlentscheidungen tendieren. Solche Fehlentscheidungen sind möglicherweise nicht nur durch mangelndes Verständnis für Brüche zu erklären. Psychologische Theorien über Intuition und Bias gehen davon aus, dass auch automatisiertes Wissen über natürliche Zahlen eine Rolle spielen könnte. Im Vortrag werden Studien vorgestellt, in denen mathematisch versierte Erwachsene, darunter Mathematiker an einer Universität, Aufgaben zu rationalen und irrationalen Zahlen bearbeiteten. Unter Analyse von Lösungsraten, Reaktionszeiten und Blickbewegungen wird der Frage nachgegangen, ob sich auch bei diesen Personen typische Verhaltensmuster finden lassen, und ob sich Grenzen des Zahlensinns zeigen.

### 01.12.2016 17:15 Giacomo Canevari (University of Oxford):Defects in nematic shells: a discrete-to-continuum approachMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

Nematic shells are the datum of a surface coated with a thin film of liquid crystals. Liquid crystals are composed by rod-shaped molecules, which tend to align to each other, locally. The interaction between the molecules and the surface induces topological defects, that is, regions of rapid changes in the orientation of the molecules that carry a topological charge. In this talk, we consider a (simplified) discrete model for nematic shells, where the molecules sit at the vertices of a triangular mesh, and study defects in the limit as the mesh parameter tend to zero. This is joint work with Antonio Segatti (Università di Pavia, Italy).

### 02.12.2016 14:00 Prof. Dr. Anton Schiela (Universität Bayreuth):Some well-known and not so well-known properties of semi-smooth Newton methodsGebäude 33, Raum 1401 (Werner-Heisenberg-Weg 39, 85577 Neubiberg)

Due to their local convergence properties semi-smooth Newton methods have become very popular in the last few years. In particular, there are non-trivial local results available for some infinite-dimensional problems which suggest their application. While local theory is very nice and clean, globalization of semi-smooth Newton methods is rather delicate. In this talk we would like to present some ideas, concerning both aspects.

### 06.12.2016 18:00 Jean-Paul Allouche (CNRS, Paris):Automatic sequences: between order and chaosA 027 (Theresienstr. 39, 80333 München)

Between "ordered sequences" (e.g., periodic ones) and "chaotic sequences" (e.g., random sequences) there is some room for intermediate sequences that are neither periodic nor really "random". Among these neither/nor sequences, a class called "automatic sequences" has many interesting properties and occurs in several distinct fields in mathematics, computer science, or physics.

Let us write down the (beginning of the) most famous automatic sequence, namely the "Prouhet-Thue-Morse" sequence. Can we immediately see patterns in it? $0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 . . .$ We will propose a "promenade" among automatic sequences showing some of their properties in number theory (transcendency of numbers and of series), in harmonic analysis (deterministic sequences having the same behavior as "random" sequences), in theoretical computer science (repetitions in infinite words, Hanoi tower, finite automata, cellular automata), and in physics (one dimensional Ising model, quasicrystals). A brief allusion to the use of automatic sequences in music will conclude the talk.

### 07.12.2016 11:00 Dr. Jiehua Chen (TU Berlin):Teams in Online Scheduling Polls: Game-Theoretic AspectsMI 02.04.011 (Boltzmannstr. 3, 85748 Garching)

Consider an important meeting to be held in a team-based organization. Taking availability constraints into account, an online scheduling poll is used to decide upon the exact time of the meeting. Decisions are to be taken during the meeting, therefore each team wants to maximize its relative attendance in the meeting (that is, the proportional number of its participating team members).

We introduce a corresponding game, where each team can declare (in the scheduling poll) a lower total availability, in order to improve its relative attendance---the pay-off. We are especially interested in situations where teams can form coalitions:

1. We provide an efficient algorithm that, given a coalition, finds an optimal way for each team in the coalition to improve its pay-off. 2. In contrast, we show that deciding whether a coalition with improvement exists is NP-hard. 3. We also study the existence of Nash equilibria: Finding Nash equilibria for various small sizes of teams and coalitions can be done in polynomial time while it is coNP-hard if the coalition size is unbounded.

* This is a joint work with Robert Bredereck, Rolf Niedermeier, Svetlana Obraztsova, and Nimrod Talmon.

### 07.12.2016 16:00 Christiane Fuchs:Understanding Biological Processes using Stochastic Modelling: Gaining Information from Uncertainty144 (Ludwigstr. 33, 80539 München)

The molecular biology of life seems inaccessibly complex. It is subject to random variation and not exactly predictable. Still, mathematical models and statistical inference pave the way towards the understanding of biolog- ical mechanisms. In contrast to deterministic models, stochastic processes capture the randomness of natural phenomena and result in more reliable predictions of cellular dynamics. Stochastic models and their parameter es- timation have to take into account the nature of molecular-biological data, including experimental techniques, measurement error and high dimension- ality.

This talk presents according modelling and estimation techniques and their applications: the identification of differently regulated cells from heteroge- neous populations using mixed models; parameter estimation for stochastic differential equations using computer-intensive Markov chain Monte Carlo techniques; and the realistic description of dynamical processes using Markov models with discrete-continuous state space.

### 08.12.2016 16:15 Dr. Frits Veerman (University of Edinburgh):Breathing pulses in singularly perturbed reaction-diffusion systems02.12.20 (Boltzmannstr. 3, 85748 Garching)

Pulse solutions in reaction-diffusion systems can exhibit a wide range of interesting dynamics. The dynamical behaviour of such solutions in example systems has been explored using numerical simulations; however, analytical understanding is often lacking. We study the weakly nonlinear stability of pulses in general singularly perturbed reaction-diffusion systems near a Hopf bifurcation, using a centre manifold expansion in function space. We present a general framework to obtain leading order expressions for the (Hopf) centre manifold expansion for scale separated, localised structures. Using the scale separated structure of the underlying pulse, directly calculable expressions for the Hopf normal form coefficients are obtained in terms of solutions to classical Sturm–Liouville problems. The developed theory is used to establish the existence of breathing pulses in a slowly nonlinear Gierer-Meinhardt system, and is confirmed by direct numerical simulation.

### 08.12.2016 16:30 Thomas Vogel:h-Prinzipien: Alte und neue BeispieleA 027 (Theresienstr. 39, 80333 München)

Unter einem h-Prinzip versteht man eine bestimmte Herangehensweise, Existenz- und Eindeutigkeitsprobleme in der Differentialgeometrie oder -topologie zu lösen. Wir diskutieren klassische Beispiele, sowie neuere Entwicklungen, insbesondere aus der Theorie der Kontaktstrukturen.

### 12.12.2016 14:15 Patrick Cheridito, Ph.D. (ETH Zürich):Variable annuities with high water mark withdrawal benefitBC1 2.02.01 (Parkring 11, 85748 Garching)

We develop a continuous-time model for variable annuities that allow for periodic withdrawals proportional to the high water mark of the underlying account value as well as early surrender of the policy. We derive the Hamilton--Jacobi--Bellman equation characterizing the value of such a contract and the worst case policy holder behavior from an issuer's perspective. Based on these results, we construct a dynamic trading strategy which super-hedges the contract. To treat the problem numerically, we develop a semi-Lagrangian scheme based on a discretization of the underlying noise process.

### 12.12.2016 15:00 Dr. Hajo Holzmann (Uni Marburg):Scoring functions for forecast evaluation and the role of the information setBC1 2.02.01 (Parkring 11, 85748 Garching)

Scoring functions are an essential tool to evaluate point forecasts, and scoring rules to evaluate probabilistic forecasts. We start by reviewing some recent results on the construction of scoring functions and scoring rules. Point forecasts are issued on the basis of certain information. If the forecasting mechanisms are correctly specified, a larger amount of available information should lead to better forecasts. We show how the effect of increasing the information set on the forecast can be quantified by using strictly consistent scoring functions, and also discuss the role of the information set for evaluating probabilistic forecasts by using strictly proper scoring rules. Further, a method is proposed to test whether an increase in a sequence of information sets leads to distinct, improved $h$-step point forecasts. For the value at risk (VaR), we show that increasing the information set will result in VaR forecasts which lead to smaller expected shortfalls, unless an increase in the information set does not change the VaR forecast. The effect is illustrated in simulations and applications to stock returns for unconditional versus conditional risk management as well as univariate modeling of portfolio returns versus multivariate modeling of individual risk factors.

Reference: Holzmann, H., Eulert, M. (2014) The role of the information set for forecasting -- with applications to risk management. Annals of Applied Statistics 8, 595-621

### 12.12.2016 16:15 Dr. Carsten Chong (TU München):Contagion in Financial Systems: A Bayesian Network Approach BC1 2.02.01 (Parkring 11, 85748 Garching)

We develop a structural default model for interconnected financial institutions in a probabilistic framework. For all possible network structures we characterize the joint default distribution of the system using Bayesian network methodologies. Particular emphasis is given to the treatment and consequences of cyclic financial linkages. We further demonstrate how Bayesian network theory can be applied to detect contagion channels within the financial network, to measure the systemic importance of selected entities on others, and to compute conditional or unconditional probabilities of default for single or multiple institutions.

### 13.12.2016 14:15 Richard D. James (University of Minnesota):Atomistically inspired origamiMI 02.06.011 (Boltzmannstr. 3, 85748 Garching)

“Objective Structures” are structures generated as orbits of discrete groups of isometries. We comment on their unexpected prevalence in nanoscience, materials science and biology and also explain why they arise in a natural way as distinguished structures in quantum mechanics, molecular dynamics and continuum mechanics. The underlying mathematical idea is that the isometry group that generates the structure matches the invariance group of the differential equations. Their characteristic features in molecular science imply highly desirable features for macroscopic structures, particularly 4D structures that deform. We illustrate the latter by constructing some “objective origami” structures.

### 15.12.2016 15:00 Bastian von Harrach (Goethe-Universität Frankfurt am Main):Inverse problems and medical imagingRoom 2004, 1st floor, Building L1 (Universitätsstr. 14, 86159 Augsburg)

Medical diagnosis has been revolutionized by noninvasive imaging methods such as computerized tomography (CT) and magnetic resonance imaging (MRI). These great technologies are based on mathematics. If the patient's interior was known then we could numerically simulate the outcome of physical measurements performed on the patient. Medical imaging requires solving the corresponding inverse problem of determining the patient's interior from the performed measurements. In this talk, we will give an introduction to inverse problems in medical imaging, and discuss the mathematical challenges in newly emerging techniques such as electrical impedance tomography (EIT), where electrical currents are driven through a patient to image its interior. EIT leads to the inverse problem of determining the coefficient in a partial differential equation from (partial) knowledge of its solutions. We will describe recent mathematical advances on this problem that are based on monotonicity relations with respect to matrix definiteness and the concept of localized potentials.

### 15.12.2016 16:30 Guido Schneider (Universität Stuttgart):Limits of the Klein Gordon Zakharov system and generalizationsRoom 2004, 1st floor, Building L1 (Universitätsstr. 14, 86159 Augsburg)

The Klein Gordon Zakharov system describes waves in plasma. Various singular limits are considered for this system. It is the goal of this talk to discuss the validity of the regular limit systems, i.e. to prove that the regular limit systems make correct predictions about the dynamics of the original system. It turns out that there are modifications of the Klein Gordon Zakharov system for which such a formal approximation makes wrong predictions.

### 15.12.2016 16:30 Jean-Louis Colliot-Thélène :Gegenwärtige Entwicklungen des Lürothschen ProblemsA 027 (Theresienstr. 39, 80333 München)

Wenn man die Lösungen einer algebraischen Gleichung f(x1; : : : ; xn) = 0 in mehreren Variabeln parametrisieren kann, kann man sie eindeutig parametrisieren? Wenn das der Fall ist, dann sagt man, dass die Gleichung eine razionale Hyperfäche definiert. In dem Fall von zwei Variablen lautet die Antwort Ja (Satz von Lüroth, 1875). In dem Fall von drei Variabeln, bei algebraischen Gleichungen mit komplexen Koeffizienten, lautet die Antwort auch Ja (Castelnuovo, 1894). Im Jahre 1972 wurde eine negative Antwort in höheren Dimension gegeben. Zu der Zeit wurden drei sehr verschiedene Methoden benutzt (Clemens-Griffiths, Iskovskikh-Manin, Artin-Mumford). 1995 erschien eine wichtige neue Methode (Kollar). In den letzten drei Jahren ist eine weitere Methode entwickelt worden, zuerst von C. Voisin, dann mit Varianten von verschiedenen Autoren. Mittels dieser Methode ist die Nichtrazionalitat und - sogar besser - die Nichtstabilrazionalität einer ganzen Menge von Hyperflächen festgestellt worden.

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