Juni 2017

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### 01.06.2017 15:00 Benjamin Gess (MPI Leipzig):Well-posedness by noise for scalar conservation lawsRoom 2004, 1st floor, Building L1 (Universitätsstr. 14, 86159 Augsburg)

In certain cases of (linear) partial differential equations random perturbations have been observed to cause regularizing effects, in some cases even producing the uniqueness of solutions. In view of the long-standing open problems of uniqueness of solutions for certain PDE arising in fluid dynamics such results are of particular interest. In this talk we will extend some known results concerning the well-posedness by noise for linear transport equations to the nonlinear case.

### 01.06.2017 16:30 Luigi Bianchi (TU Berlin):Structure function and energy dissipation for a dyadic model of turbulenceRoom 2004, 1st floor, Building L1 (Universitätsstr. 14, 86159 Augsburg)

Dyadic models for turbulence provide a simplified description of the turbulent energy cascade of three-dimensional Euler equation for fluids. In this talk I will introduce a generalization of the original tree-indexed dyadic model by Katz and Pavlović, and discuss some of its interesting properties, in particular concerning the phenomenon of (anomalous) energy dissipation and the structure function with its connection to intermittency.

### 01.06.2017 16:30 Rudi Weikard:On the Inverse Resonance ProblemA 027 (Theresienstr. 39, 80333 München)

Inverse spectral and scattering problems are a classical subject in mathematical physics. In this talk we present a particular variant: the inverse resonance problem in one dimension, particularly for the Schrödinger equation. In addition to the uniqueness question we investigate which information may be contained from finite noisy data. This is of interest, since, in practical settings, one cannot expect to obtain all the necessary data and, in any case, recovery algorithms cannot make use of all data even if they were available.

Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.

### 08.06.2017 15:45 Lisa Beck (Universität Augsburg):On the Neumann problem related to convex, variational integrals of linear growthMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

We study the minimization of functionals of the form

$$w \mapsto \int_\Omega [ f(|\nabla w|) - T_0 \cdot \nabla w ] \, dx$$

with a strictly convex integrand $f$ of linear growth and a regular vector-field $T_0$, among all functions in the Sobolev space $W^{1,1}$. Equivalently, we may study weak solutions to the associated Euler--Lagrange system subject to a Neumann-type boundary constraint. Due to the lack of weak compactness properties of the space $W^{1,1}$, the existence of solutions does not follow in a standard way by the direct method in the calculus of variations. While for the Dirichlet problem, where prescribed boundary values are imposed, solutions exist only in a suitably generalized sense via relaxation to the space of functions of bounded variations, the Neumann problem turns out to be always solvable in $W^{1,1}$, under a sharp and natural boundedness condition on $T_0$.

The results presented in this talk are based on a joined project with Miroslav Bulíček (Prag) and Franz Gmeineder (Oxford).

### 08.06.2017 17:15 Markus Mittnenzweig (WIAS Berlin):Gradient flow structures for quantum master equationsMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

Quantum master equations of Lindblad type are frequently used to model the dynamics of open quantum systems. We will show that, in the case of detailed balance, all Lindblad operators entropic gradient flows with respect to the relative von Neumann entropy. The corresponding Riemannian metric for the density matrices can be viewed as a non-commutative analog of the 2-Wasserstein metric for probability distributions. We will give applications to thermodynamic consistent modelling of quantum dot semiconductor devices.

### 09.06.2017 10:30 Kathryn Spalding (Loughborough University, UK):Lyapunov spectrum of Markov and Euclid treesMI 02.06.011 (Boltzmannstr. 3, 85748 Garching)

We introduce the set $\mathbb{X}$ of the most irrational numbers, and examine their connection to the Markov equation. We introduce Markov triples and the Markov tree, and relate this to the dual tree to the Farey tessellation of the upper half-plane. We then study the Lyapunov exponents $\Lambda(x)$ for Markov dynamics as a function of a path in the tree determined by $x\in \mathbb RP^1$, describing the Markov triples and their "tropical" version, Euclid triples. Finally, we will describe some properties of the Lyapunov spectrum, particularly when restricted to the set $\mathbb{X}$.

### 09.06.2017 14:15 Prof. Dr. Vlada Limic (Département de Mathématiques, Université Paris Sud):The secret of excursions of Bs - 1/2s² + ... + ts as t increasesH13 Dep. Mathematik (Cauerstr. 11, 91058 Erlangen)

After many years the speaker’s thoughts return to the near-critical random graphs and the multiplicative coalescent. The secret announced in the title is far form being well- understood. However recent progress on the (near-critical) random graph encoding via the so-called simultaneous breadth-first walks, and the much richer excursion mosaic processes are encouraging. The purpose of the talk is to explain these recent findings, and put them in perspective in terms of the limiting extreme eternal multiplicative coale- scent processes.

### 09.06.2017 15:30 Prof. Dr. Leif Döring (Mathematical Institute, Universität Mannheim):Skorohod Embedding Problem for Lévy ProcessesH13 Dep. Mathematik (Cauerstr. 11, 91058 Erlangen)

For a given probability distribution, the classical Skorohod Embedding Problem consists of finding (if possible) a stopping time so that a Brownian motion at the stopping time has a the prescribed distribution. Many solutions have been found and applied in diffe- rent contexts. We discuss the analogue question for Lévy process and derive necessa- ry/sufficient conditions for the existence of a solution. An explicit construction is derived using time-change theory for Markov processes.

### 09.06.2017 16:00 Narcis Miguel Baños (Universitat de Barcelona, Spanien):Diffusive properties of chaotic orbits in the presence of accelerator modes in low dimensional conservative systemsMI 02.06.011 (Boltzmannstr. 3, 85748 Garching)

In this talk we will deal with the dynamics in chaotic zones of 2D and 3D conservative systems.

Concerning the 2D case, we will discuss the effect of stability islands on the statistical properties of the Chirikov standard map. The islands under study surround Accelerator Modes: periodic orbits of the map when it is considered on a torus that are unbounded orbits when the map is lifted to the cylinder. The observed phenomena will be related to geometrical dynamical structures and available limit models.

We will end by briefly discussing how to translate this study to the 3D setting: the construction of a proper volume preserving model, which is the analogous to stability islands in this context and which is the effect of the latter in the diffusive properties of the chosen model.

This based in joint work with J. D. Meiss (UC Boulder), C. Sim\'o (UB) and A. Vieiro (UB).

### 09.06.2017 17:00 Prof. Dr. Roman Kotecký (Mathematics Institute of Warwick):Emergence of long cycles for random interchange process on hypercubesH13 Dep. Mathematik (Cauerstr. 11, 91058 Erlangen)

Motivated by phase transitions in quantum spin models, we study random permutations of vertices (induced by products of uniform independent random transpositions on edges) in the case of high-dimensional hypercubes. We establish the existence of a transition accompanied by emergence of cycles of diverging lengths. (Joint work with Piotr Miło´s and Daniel Ueltschi.)

### 12.06.2017 16:00 Timo Schlüter (Universität Mainz):Fractional moment estimates for interacting diffusions2.01.10 (Parkring 11, 85748 Garching-Hochbrück)

Let (fXi(t)gi2Zd )t0 be the system of interacting diusions on [0;1) dened by dXi(t) = X j2Zd a(i; j)[Xj(t)

### 12.06.2017 17:00 Dr. Andrej Depperschmidt (Erlangen) :Recombination as a tree-valued process along the genome2.01.10 (Parkring 11, 85748 Garching-Hochbrück)

In Moran models the genealogy at a single locus of a constant size $N$ population in equilibrium is given by the well-known Kingman's coalescent. When considering multiple loci under recombination, the ancestral recombination graph encodes the genealogies at all loci. For a continuous genome we study the tree-valued process of genealogies along the genome in the limit $N\to\infty$. Encoding trees as metric measure spaces, we show convergence to a tree-valued process. Furthermore we discuss some mixing properties of the resulting process.

This is joint work with Etienne Pardoux and Peter Pfaffelhuber.

### 13.06.2017 16:30 Ion Nechita (TU München):On some uses of random matrices in quantum information theoryMI 03.10.011 (Boltzmannstr. 3, 85748 Garching)

I will review the theory of random quantum states and random quantum channels. I will then discuss recent progress to the question of additivity of the minimum output entropy of quantum channels coming from new random examples. The abstract illustrates my plan for the talk: for half an hour, my plan is to be fairly general and to present several random matrix models, without giving too many details. For the second half of the talk, I plan to discuss in detail a model for random quantum channels coming from Haar unitary matrices and show that these channels violate the additivity of the minimum output entropy. Please let me know what you think about all this.

### 19.06.2017 16:30 Dr. Asja Fischer (Universität Bonn):"Towards biologically plausible deep learning"B 251 (Theresienstr. 39, 80333 München)

"In recent years (deep) neural networks got the most prominent models for supervised machine learning tasks. They are usually trained based on stochastic gradient descent where backpropagation is used for the gradient calculation. While this leads to efficient training, it is not very plausible from a biological perspective.

We show that Langevin Markov chain Monte Carlo inference in an energy-based model with latent variables has the property that the early steps of inference, starting from a stationary point, correspond to propagating error gradients into internal layers, similar to backpropagation. Backpropagated error gradients correspond to temporal derivatives with respect to the activation of hidden units. These lead to a weight update proportional to the product of the presynaptic firing rate and the temporal rate of change of the postsynaptic firing rate. Simulations and a theoretical argument suggest that this rate-based update rule is consistent with those associated with spike-timing-dependent plasticity. These ideas could be an element of a theory for explaining how brains perform credit assignment in deep hierarchies as efficiently as backpropagation does, with neural computation corresponding to both approximate inference in continuous-valued latent variables and error backpropagation, at the same time."

### 19.06.2017 16:30 Sascha Desmettre:Generalized Pareto processes and liquidityB 349 (Theresienstr. 39, 80333 München)

Motivated by the modeling of liquidity risk in fund management in a dynamic setting, we propose and investigate a class of time series models with generalized Pareto marginals: the autoregressive generalized Pareto process (ARGP), a modified ARGP (MARGP) and a thresholded ARGP (TARGP). These models are able to capture key data features apparent in fund liquidity data and reflect the underlying phenomena via easily interpreted, low-dimensional model parameters. We establish stationarity and ergodicity, provide a link to the class of shot-noise processes, and determine the associated interarrival distributions for exceedances. Moreover, we provide estimators for all relevant model parameters and establish consistency and asymptotic normality for all estimators (except the threshold parameter, which as usual must be dealt with separately). Finally, we illustrate our approach using real-world fund redemption data, and we discuss the goodness-of-fit of the estimated models.

### 20.06.2017 14:15 Caroline Moosmüller, University of Passau:Iterative refinement processes for manifold-valued dataMI 02.06.011 (Boltzmannstr. 3, 85748 Garching)

We consider iterative refinement processes which operate on discrete data and produce a smooth curve or surface in the limit. Most results on such processes, also called subdivision schemes, concern data in vector spaces and rules which are linear. We are interested in studying manifold-valued data and refinement rules which are solely defined by the intrinsic geometry of the underlying manifold. In this talk we focus on a particular class of subdivision schemes, called Hermite schemes. These algorithms successively refine discrete point-vector data and, via a limit process, produce a curve and its derivatives. We give an introduction to linear Hermite subdivision schemes and present adaptations to manifolds using geodesics and parallel transport. Furthermore, we analyse the resulting nonlinear algorithms with respect to convergence and C1 smoothness.

### 20.06.2017 15:30 Rayan Saab, University of California, San Diego:Near-optimal quantization and encoding under various measurement modelsMI 02.06.011 (Boltzmannstr. 3, 85748 Garching)

In the era of digital computation, data acquisition consists of a series of steps. A sampling or measurement process is typically followed by quantization, or digitization, which allows digital storage and transmission of data. In turn, quantization is often followed by encoding, or compression, to efficiently represent the quantized data. In this talk, we discuss quantization and encoding schemes for a variety of measurement processes, along with their associated reconstruction algorithms.

We show results for classically oversampled band-limited functions, oversampled linear measurements of finite dimensional signals, and compressed sensing measurements of sparse and compressible signals. The encoding methods we discuss are practical, rely on noise-shaping quantization schemes such as Sigma-Delta quantization, and also work in the extreme case of 1-bit quantization. Moreover, they yield near-optimal approximation accuracy as a function of the bit-rate.

### 22.06.2017 15:00 Eleonora Cinti (Universität Turin:Flatness results for nonlocal phase transitions in low dimensionsRoom 2004, 1st floor, Building L1 (Universitätsstr. 14, 86159 Augsburg)

We present some recent results in the study of two, closely related, nonlocal problems: the fractional Allen-Cahn equation and fractional minimal surfaces. More precisely, we focus on the study of stable solutions, establishing sharp energy estimates, density estimates, and convergence results for blow-down sequences. As a consequence, we obtain some new classification results for stable solutions in the whole space in low dimensions. These results are contained in several works in collaboration with X. Cabré, J. Serra, and E. Valdinoci.

### 22.06.2017 16:30 Sören Bartels (Universität Freiburg):Numerical solution of nonsmooth problems and application to a problem in optimal insulationRoom 2004, 1st floor, Building L1 (Universitätsstr. 14, 86159 Augsburg)

Nonsmooth problems arise in the mathematical modeling of contact and obstacle problems, the description of plastic material behavior, and mathematical image processing. The unknown functions are typically characterized as minimizers of nondifferentiable functionals. Numerical schemes approximately solve these problems either via duality methods or classically by making use of appropriate regularizations. In the talk we discuss the discretization and iterative solution of a model problem defined on functions of bounded variation. The numerical analysis of finite element discretizations leads to reduced convergence rates which can be improved using adaptive mesh refinement. Suitable iterative solution procedures are ADMM schemes, for which we propose an automatic step size adjustment strategy, and gradient flows, for which we demonstrate the unconditional stability of a semi-implicit time discretization. The methods are applicable in the numerical determination of optimal insulating films for heat conducting bodies. Below a critical value of available insulation mass an unexpected break of symmetry occurs.

### 22.06.2017 16:30 Christian Hirsch:"Zufällige Packungen und Netzwerke im Kontinuum” A 027 (Theresienstr. 39, 80333 München)

Das Gebiet der statistischen Physik hat eindrucksvoll unter Beweis gestellt, wie elegante gitterbasierte Modelle überzeugende Erklärungsansätze für physikalisch beobachtete Phänomene bieten. In vielen Fällen scheint die Verwendung eines fixen Gitters allerdings künstlich, insbesondere wenn die räumliche Struktur von zufälligen Perturbationen gekennzeichnet ist. Dieser Zufall führt zu neuen mathematischen Herausforderungen, die im Vortrag anhand von stochastischen Modellen aus den Bereichen der Packungen und Netzwerke illustriert werden.

### 23.06.2017 09:00 Workshop: B. Bouchard, M. Frittelli, M. Maggis, S. Peng:Workshop: Recent Advances in Model Uncertainty B 349 (Theresienstr. 39, 80333 München)

For further information:

http://www.qcssc.uni-muenchen.de/news_events/workshop_modeluncertainty_2017.html

### 26.06.2017 13:00 Dr. Jonas Sauer (Max-Planck-Institut für Mathematik in den Wissenschaften, Leipzig):Time-Periodic $L^p$ Estimates for Parabolic Boundary Value ProblemsMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

We introduce a method for showing $a$ $priori$ $L^p$ estimates for time-periodic, linear, partial differential equations set in a variety of domains such as the whole space, the half space and bounded domains. The method is generic and can be applied to a wide range of problems. In the talk, I intend to demonstrate it on the Stokes equations and on parabolic boundary value problems. The latter example thus generalizes a famous result due to Agmon, Douglas and Nirenberg. The main idea is to replace the time axis with a torus in order to reformulate the problem on a locally compact abelian group and to employ Fourier analysis on this group. As a by-product, maximal $L^p$ regularity for the corresponding initial-value problem follows for many operators such as the Dirichlet Laplacian and the Stokes operator $without$ the notion of $\cal R$-boundedness. In fact, we show that maximal $L^p$ regularity for the initial value problem is even equivalent to time-periodic maximal $L^p$ regularity.

The talk is based on joint works with Yasunori Maekawa and Mads Kyed.

### 26.06.2017 17:00 Jun.-Prof. Karl Worthmann:Does model predictive control work without terminal constraintsGebäude 33, Raum 1401 (Werner-Heisenberg-Weg 39, 85577 Neubiberg)

Model predictive control is nowadays a widely used advanced control technique. Firstly, due to its capability to deal with control and state constraints and, secondly, due to the simplicity of the basic idea: Measure the current state, predict and optimize over a finite time horizon, and implement the first piece of the computed input function before the process is repeated ad infinitum. Clearly, this methodology requires a sufficiently large optimization window. But is this sufficient to conclude properties like asymptotic stability of the resulting closed loop? And, if this question can be answered in the affirmative, can we quantify ''sufficiently large''? In this talk, we address these questions and explicate the answers by means of a nonholonomic robot example.

### 28.06.2017 14:30 Prof. Valentin Blomer (Universität Göttingen):Fakultätskolloquium: Eigenfunktionen auf arithmetischen Mannigfaltigkeiten MI HS 3 (Boltzmannstr. 3, 85748 Garching)

Es ist eine klassische Fragestellung, Eigenfunktionen des Laplace-Operators auf Riemannschen Mannigfaltigkeiten zu untersuchen. Vom zahlentheoretischen Standpunkt ist diese Frage vor allem interessant, wenn die Mannigfaltigkeit eine "arithmetische Struktur" besitzt, etwa in Form einer Hecke-Algebra. Ein typisches Beispiel hierfür ist die 2-Sphäre. Es werden analytische und diophantische Techniken vorgestellt, Eigenfunktionen in solchen Fällen zu untersuchen.

http://www.ma.tum.de/Mathematik/FakultaetsKolloquium#AbstractBlomer

### 28.06.2017 16:00 Prof. Frithjof Lutscher (University of Ottawa):Fakultätskolloquium: Reaction-diffusion equations with discontinuous coefficients: Derivation, analysis and applications in spatial ecologyMI HS 3 (Boltzmannstr. 3, 85748 Garching)

Reaction-diffusion equations have been applied successfully to gain insights into problems in spatial ecology for many decades. As ecologists are increasingly interested in understanding population dynamics in heterogeneous landscapes, the coefficients in these equations should be spatially dependent. While a lot of abstract theory is known for the case of smooth coefficient functions, explicit calculations are virtually impossible, and therefore the application to ecology is limited.

In this talk, I present an approach by which coefficient functions are chosen to be piecewise constant, yet novel, discontinuous matching conditions at an interface arise. I present some results and illustrate several applications of this framework to ecological problems such as population persistence, species spread and spatial pattern formation.

http://www.ma.tum.de/Mathematik/FakultaetsKolloquium#AbstractLutscher

### 29.06.2017 11:00 Ahmed Zayed (DePaul University):Energy Concentration Problem Associated with the Special Affine Fourier TransformationMI 02.08.020 (Boltzmannstr. 3, 85748 Garching)

In this talk we present the solution of the energy concentration problem for the Fourier transform that was proposed by D. Slepian, H.Landau, and H. Pollak of Bell Labs in the 1960s, and then investigate the solution of a similar problem for the special affine Fourier transformation.

### 29.06.2017 16:30 Massimo Bertolini:Rational points on elliptic curves and values of L-functions A 027 (Theresienstr. 39, 80333 München)

The problem of finding the rational solutions of cubic equations is a long-standing one and has led to fundamental open questions in modern mathematics. The aim of this talk is to recall the circle of ideas surrounding these questions and to describe some recent advances on them.