Events (Wintersemester 2017/18)
Date  Lecturer  Title  Room 

16.01.2018 10:30 Uhr 
Rishabh Gvalani Imperial College London 
Oberseminar: Phase transitions for the McKeanVlasov equation on the torus 
Hörsaal SeMath, Pontdriesch 1416 

Past Events
Date  Lecturer  Title  Room 

18.07.2017 14:00 Uhr 
Siegfried Beckus TechnionIsrael Institute of Technology 
Oberseminar: Shnol type Theorem for the Agmon ground state 
Raum 001, Pontdriesch 1416 
The celebrated Shnol theorem asserts that every polynomially bounded generalized eigenfunction for a given energy E associated with a Schrödinger operator H implies that E is in the L2spectrum of H. Later Simon rediscovered this result independently and proved additionally that the set of energies admitting a polynomially bounded generalized eigenfunction is dense in the spectrum. A remarkable extension of these results holds also in the Dirichlet setting. It has been conjectured that the polynomial bound on the generalized eigenfunction can be replaced by an object intrinsically defined by H, namely, the Agmon ground state. During the talk, we positively answer the conjecture indicating that the Agmon ground state describes the spectrum of the operator H. Specifically, we show that if u is a generalized eigenfunction for the eigenvalue E that is bounded by the Agmon ground state, then E belongs to the L2spectrum of H. Furthermore, this assertion extends to the Dirichlet setting whenever a suitable notion of Agmon ground state is available. 

18.07.2017 10:30 Uhr 
Xian Liao University of Bonn 
Oberseminar: Conserved energies for the onedimensional cubic nonlinear Schrödinger equations 
Hörsaal SeMath, Pontdriesch 1416 
In this talk I will present the derivation of the conserved energies which are equivalent to the H^snorms of the solutions of the onedimensional cubic nonlinear Schrödinger equations (NLS), that is, all the H^snorms (with some lower bound for s) of the solutions are conserved a priori: This is done in the recent exciting work by KochTataru. I will also present briefly my recent progress with Professor Koch for the GrossPitaevskii equation (GP): (GP) is defocusing (NLS) but with a non standard constraint on the solution q at infinity: q > 1 at infinity. Technically this talk will be divided into three parts. In the introduction part, I will start with a rough statement about the conserved energies for (NLS) and (GP), and then introduce the essential notation: the transmission coefficient, and the three technical tools: the Hopf algebra, the frequencyrescaled norms and the superharmonic functions on the upper half plane. Then I will explain how to formulate the conserved energies by use of the transmission coefficient and how to show its equivalence to the H^snorms by use of the technical tools: This is done by KochTataru for (NLS). Finally for the GrossPitaevskii equation (GP) we will see that the non standard constraint at infinity causes essential new difficulties in the analysis. 

11.07.2017 10:30 Uhr 
Jean Bellissard University of Münster, retired from Georgia Institute of Technology 
Special Joint Analysis Seminar (Math+Physics): A Toy Model for Viscosity 
Hörsaal SeMath, Pontdriesch 1416 
A short review of the temperature behavior of liquids viscosity will be provided. The concept of anankeon as a new degree of freedom will be described and its relation with elastic degrees of freedom discussed. Then a simplistic solvable model, based on a Stochastic Markov dynamics, will be proposed and the solution explained and discussed. One consequence is the prediction that in a certain subclass of liquids, there is a bifurcation leading to a new time scale, the Maxwell time, which is liable to explain the exponential increase of the viscosity near the liquidsolid transition. A comparison with numerical simulations using molecular dynamics will be discussed. 

16.05.2017 10:30 Uhr 
Antione Hocquet TU Berlin 
Oberseminar: Finitetime singularities of the stochastic harmonic map flow on surfaces. 
Raum 001, Pontdriesch 1416 
A ferromagnetic material possesses a magnetization, which, out of equilibrium, satisfies the LandauLifshitzGilbert equation (LLG). Thermal fluctuations are taken into account by Gaussian spacetime white noise. At least in the deterministic case, there is an important parallel between this model and the socalled Harmonic Map Flow (HMF). This was originally used by geometers (in the early sixties) as a tool to build harmonic maps between two manifolds u:M>N. The case where M is two dimensional is critical, in the sense that the natural energy barely fails to give wellposedness. We do not address here the problem of the solvability of LLG driven by spacetime white noise. Instead, we consider a spatially correlated version. We show that contrary to the deterministic case, blowup of solutions happen no matter how we choose the initial data. 

23.05.2017 10:30 Uhr 
Etienne Sandier Université Paris 12 
Joint Analysis Seminar: Lower bound for energy growth of locally minimizing solutions of Δu=u(1u2) for u: ℝ3→ℝ2 
Hörsaal SeMath, Pontdriesch 1416 
t.b.a. 

13.06.2017 10:30 Uhr 
Prof. Helmut Abels Universität Regensburg 
Joint Analysis Seminar: Diffuse Interface Models for TwoPhase Flows of Incompressible Fluids and Their Sharp Interface Limits 
Hörsaal SeMath, Pontdriesch 1416 
t.b.a. 

09.05.2017 10:30 Uhr 
Guido de Philippis SISSA, Triest 
Joint Analysis Seminar: On the structure of measures satisfying a PDE constraint 
Hörsaal SeMath, Pontdriesch 1416 
After a general introduction concerning the study of the interplay between PDE constraint and concentration/oscillation, I will present a general structure theorem for the singular part of Radon measure satisfying a PDE constraint. I will then present some applications. 

02.05.2017 10:30 Uhr 
David Gross Universität zu Köln 
Joint Analysis Seminar: Low rank matrix recovery, the Clifford group, and some quantum mechnics 
Hörsaal SeMath, Pontdriesch 1416 
t.b.a. 

46 April, 2017 
AachenAugsburgAppliedAnalysis Workshop 
This two and a half day event explores recent progress in applied and stochastic analysis.  Pontdriesch 1416 
Details at the webpage listed above. 

07.02.2017 14:15 Uhr 
Giuseppe Savaré University of Pavia 
Joint Analysis Seminar: Singular perturbation of gradient flows and rateindependent evolution problems 
klPhys, Schinkelstr. 2 
t.b.a. 

31.01.2017 14:15 Uhr 
Manon Baudel University of Orléans 
Oberseminar: Spectral theory for random Poincaré maps 
Raum 001, Pontdriesch 1416 
We consider stochastic differential equations, obtained by adding weak Gaussian white noise to ordinary differential equations admitting N asymptotically stable periodic orbits. To quantify the rare transitions between periodic orbits, we construct a discretetime, continuousspace Markov chain, called a random Poincaré map. We show that this process admits exactly N eigenvalues which are exponentially close to 1, and provide expressions for these eigenvalues and their left and right eigenfunctions in terms of committor functions of neighbourhoods of periodic orbits. The eigenvalues and eigenfunctions are wellapproximated by principal eigenvalues and quasistationary distributions of processes killed upon hitting some of these neighbourhoods. The proofs rely on Feynman–Kactype representation formulas for eigenfunctions, Doob’s htransform, spectral theory of compact operators, and a detailed balance property satisfied by committor functions. Joint work with Nils Berglund (Orléans). 

24.01.2017 14:15 Uhr 
Christian Mießen IMM RWTH Aachen 
Oberseminar: A massive parallel simulation approach to 2D and 3D grain growth in polycrystalline materials 
Raum 001, Pontdriesch 1416 
We developed a highly efficient simulation model for 2D and 3D grain growth and recrystallization based on the levelset method. The developed model introduces modern computational concepts to achieve excellent performance on parallel computer architectures. We found strong scalability on ccNUMA architectures. For this purpose, the model considers the application of local levelset functions at the grain level. The model was utilized to simulate ideal and nonideal grain growth in 2D and 3D with the objective to study the evolution of statistical representative volume elements in polycrystals. In addition, we simulated microstructure evolution in an anisotropic magnetic material affected by an external magnetic field. 

20.12.2016 14:15 Uhr 
Sebastian Scholtes RWTH Aachen University 
Oberseminar: Variations on geometric knot theory 
Raum 001, Pontdriesch 1416 
The talk will encompass several themes in geometric knot theory. We will talk about new geometric curvature energies and the discretisation of some established energies. For the last item, we consider different modes of variational convergence. Time allowing, we explore the connection of geometric curvature energies to discrete and metric geometry. 

13.12.2016 14:15 Uhr 
Giovanni Di Fratta CMAP, Ecole Polytechnique 
Oberseminar: Thin convex shells in micromagnetics 
Raum 001, Pontdriesch 1416 
The talk is devoted to the Γdevelopment analysis of the micromagnetic energy functional, when the domain occupied by the nanomagnet is a thin shell generated by a bounded and convex smooth surface. Indeed, recently a significant interest to nanomagnets with curved shape has appeared. In particular, spherical shells are currently of great interest due to their capability to support skyrmion solutions which can be stabilized by curvature effects only, in contrast to the planar case where the intrinsic DzyaloshinskyMoriya interaction is required. It is well established that the effects of the demagnetizing field operator can be reduced to an effective easysurface anisotropy for planar thin shells whose thickness is much less than the size of the system. More precisely, in G. Gioia and R. D. James (Micromagnetics of very thin films. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 453(1956):213–223, 1997) it is shown that the effects of the demagnetizing field operator can be reduced to an effective easysurface anisotropy for planar thin shells. A generalization of this result can be found in G. Carbou (Thin layers in micromagnetism. Mathematical Models and Methods in Applied Sciences, 11(09):1529–1546, 2001) where, for thin shells generated by extruding surfaces whose closure is diffeomorphic to the closed unit disk of R^2, the asymptotic behavior of the minimizers of the micromagnetic energy functional is investigated. In V. Slastikov (Micromagnetics of thin shells. Mathematical Models and Methods in Applied Sciences, 15(10):1469–1487, 2005) a Γconvergence analysis is performed on pillowlike thin shells. In all the cited cases the investigation leaves out very interesting scenarios like the spherical one which cannot be easily recovered by simply gluing local patches. In this talk we present, in the spirit of the theoretical framework presented in G. Anzellotti and S. Baldo (Asymptotic development by Γconvergence. Applied mathematics and optimization, 27(2):105–123, 1993), a Γdevelopment analysis of the micromagnetic energy functional when the shell is generated, like in the case of a sphere, by a bounded and convex smooth surface. 

06.12.2016 14:15 Uhr 
John M. Ball University of Oxford 
Joint Analysis Seminar: The mathematics of liquid crystals 
klPhys, Schinkelstr. 2 
t.b.a. 

02.12.2016 14:15 Uhr 
Sören Bartels Universität Freiburg 
Mathematisches Kolloquium: Approximation of large bending problems 
Hörsaal SeMath, Pontdriesch 1416 
The development of polymer structures suggests various new applications in the area of nanotechnology. The controlled fabrication of related devices and nanotools leads however to many difficulties. Numerical simulations can contribute to improving this. In the talk we discuss the mathematical modeling and reliable computation of large bilayer bending effects. Deformations are described via a nonlinear bending energy subject to a pointwise isometry constraint. We devise finite element discretizations using discrete Kirchhoff triangles and show accuracy of approximations via Gammaconvergence of the discretized functionals. The practical energy minimization is based on a semiimplicit discretization of a related gradient flow. Selfavoidance of deformations is not included in the model and appears to be relevant only in some situations. We present first results concerning the convergent computation of selfavoiding inextensible curves using a tangentpoint functional. 

18.11.2016 14:15 Uhr 
Stefan Müller Universität Bonn 
Mathematisches Kolloquium: The mathematics of packing, crumpling and folding 
Hörsaal SeMath, Pontdriesch 1416 
A number of questions in physics and biology involve the problem of packing thin elastic objects in a container in an optimal way, e.g. with minimal elastic energy. In this lecture I will discuss precise mathematical formulations of some of these problems, recent results and open conjectures 

17.11.2016 11:00 Uhr 
Zisis N. Sakellaris Athen 
Oberseminar: Minimization of Curvature in Conformal Geometry 
Raum 001, Pontdriesch 1416 
t.b.a. 

15.11.2016 14:15 Uhr 
Qiji J. Zhu Western Michigan University 
Joint Analysis Seminar: Variational methods in the presence of symmetry 
klPhys, Schinkelstr. 2 
t.b.a. 

25.10.2016 14:15 Uhr 
Gero Friesecke TU München 
Joint Analysis Seminar: Inferring atomic structure from Xray diffraction patterns 
klPhys, Schinkelstr. 2 
t.b.a. 

05.07.2016 10:45 Uhr 
Andrea Mondino ETH Zürich 
Joint Analysis Seminar: Nonsmooth spaces with Ricci curvature lower bounds 
Hörsaal SeMath, Pontdriesch 1416 
The idea of compactifying the space of Riemannian manifolds satisfying Ricci curvature lower bounds goes back to Gromov in the '80s and was pushed by Cheeger and Colding in the '90s who investigated the structure of the spaces arising as GromovHausdorff limits of smooth Riemannian manifolds satisfying Ricci curvature lower bounds. A completely new approach via optimal transportation was proposed by LottVillani and Sturm almost ten years ago; with this approach one can a give a precise meaning of what means for a non smooth space to have Ricci curvature bounded from below by a constant. This approach has been refined in the last years by a number of authors and a number of fundamental tools have now been established (for instance the Bochner inequality, the splitting theorem, etc.), permitting to give further insights in the theory. In the seminar I will give an overview of the topic. In the talk, after a brief introduction to the topic I will present some recent results. 

14.06.2016 10:45 Uhr 
Camilla Nobili University of Basel 
Oberseminar: Bounds on turbulent convection 
Raum 001, Pontdriesch 1416 
We present some recent results regarding the RayleighBénard convection. In a first part we deal with the infinite Prandtl number limit of the Boussinesq equations and we introduce the temperature background field method in order to find upper bounds on the average upward heat transport. Inspired by the seminal result of Doering, Otto and Westdickenberg (née Reznikoff) in 2007 we characterized all admissible background profiles and we show that the upper bound of Otto and Seis 2013 is optimal within this method. In the second part we consider fluids with finite Prandtl number and we present a new upper bound on the Nusselt number which catches a transition in the phase space (Pr, Ra). 

07.06.2016 10:45 Uhr 
Robert L. Jerrard University of Toronto 
Joint Analysis Seminar: Leapfrogging vortex rings for the three dimensional GrossPitaevskii equation 
Hörsaal SeMath, Pontdriesch 1416 
TBA 

24.05.2016 10:45 Uhr 
Eric A. Carlen Rutgers University 
Joint Analysis Seminar: The structure of near minimizers of a nonlocal free energy functional 
Hörsaal SeMath, Pontdriesch 1416 
The GatesPentroseLebowitz free energy functional is a nonlocal analog of the phenomenological van der Waals free energy function. Unlike the local van der Waals functional, it arises in the continuum limit of lattice gas models. As in many statistical mechanical models in which free energy functionals are large deviations functional, one is interested not only in the absolute minimizers, but also the near minimizers. In classical work on the near minimizers of the van der Waals functional, the coarea formula and the quantitative isoperimetric inequality play a crucial role. We present joint work with Maggi on a nonlocal quantitative isoperimetric inequality, and discuss its application to the description of near minimizers of the GatesPentroseLebowitz free energy functional in work with Carvalho, Esposito, Marra and Lebowitz. 

03.05.2016 10:45 Uhr 
Yuriy Mokrousov FZ Jülich 
Oberseminar: Topological Spintronics: guided by abinitio research 
Raum 001, Pontdriesch 1416 
Currently, solid state physics experiences a revolution associated with the advent of novel topological concepts. It was realized that, as by magic, many of the wellknown phenomena can suddenly be intuitively understood following abstract mathematical ideas which tell us that the dynamics of electrons in solids is directly related to topology of the spaces in which they live. This revolution has completely changed the landscape of spintronics, which deals with the interplay between spin and charge of electrons, leading to predictions of novel, topological states of matter such as topological insulators and magnetic skyrmions. In my talk, on simple but important examples, I will explain how the topological standpoint can be utilized for the prediction of novel effects related to electron dynamics, and lead to quantitative description of these effects in most complex materials. 

26.04.2016 10:45 Uhr 
Dorin Bucur Université de Savoie 
Joint Analysis Seminar: Optimal shapes and isoperimetric inequalities for spectral functionals 
Hörsaal SeMath, Pontdriesch 1416 
In this talk I will discuss isoperimetric inequalities involving the spectrum of the Laplace operator (of FaberKrahn or SaintVenant type) seen from the perspective of shape optimization. I will focus on problems involving the spectrum of the RobinLaplacian and the Steklov problem, and show techniques developed around the MumfordShah functional in image segmentation theory can be used to prove such inequalities. 

19.04.2016 14:00 Uhr 
Carina Geldhauser Universität Bonn 
Special Seminar: The $L^2$ gradient flow of the double well potential and a related interacting particle system 
Raum 001, Pontdriesch 1416 
We consider the forwardbackward parabolic equation $u_t = \left( W'(u_x)\right)_X$ with periodic boundary conditions in one space dimension, where $W$ is a double well potential. This equation is the formal $L^2$ gradient flow of the nonconvex potential $W(p) = \frac{1}{4} (1p^2)^2$, which is a priori illposed. The first part of the talk will show how regularisation by discretisation in space can be used to prove existence of solutions of the equation for a special class of initial data. In the second part of the talk, we view such discreteinspace schemes as systems of particles driven by the potential $W$ and add a perturbation by independent Brownian motions to their dynamics. We address the question how many particles are allowed to interact with each other such that the resulting interacting particle system converges as $h\to 0$ to a wellposed stochastic PDE. If time allows, we will state some results on the longtime behaviour of solutions to the limit SPDE. This talk combines results obtained in collaboration with Giovanni Bellettini, Anton Bovier and Matteo Novaga. 

19.04.2016 10:45 Uhr 
Melanie Rupflin University of Oxford 
Oberseminar: Flowing to minimal surfaces 
Raum 001, Pontdriesch 1416 
For maps from surfaces there is a close connection between the area functional and Dirichlet energy and thus also between their critical points. As such, one way to try to find critical points of the Area is to consider a gradient flow of the Dirichlet energy, which not only evolves a map but also the domain metric in order to find a map that is not only harmonic but also (weakly) conformal and thus a (branched) minimal immersion. In this talk I will discuss the construction of such a flow, the Teichmueller harmonic map flow, and explain in particular how this flow decomposes any given initial map into one or more branched minimal immersions. 

09.02.2016 14:15 Uhr 
Emanuele Spadaro MPI MIS Leipzig 
Oberseminar: An epiperimetric inequality for the thin obstacle problem 
Raum 001, Pontdriesch 1416 
I will discuss some recent results on the thin obstacle problem (also known as the scalar Signori problem). This is a classical problem in the calculus of variations and, in its simplest form, it consists in minimizing the Dirichlet energy among all functions that are constrained to have a positive trace on a hyperplane. Despite the long tradition, many questions concerning the regularity of the solutions remain still open. In this talk, our focus is on the rate of converge of the solutions to their unique blowup limits near certain points of the free boundary. Following the pioneering work by G. Weiss on the classical obstacle problem, we prove an "epiperimetric inequality" a la Reifenberg, which closely resembles the one firstly shown in the '60s in the study of the regularity of minimal surfaces. This is a joint work with M. Focardi of the University of Florence. 

26.01.2016 14:15 Uhr 
Alexander Lytchak University of Cologne 
Joint Analysis Seminar: Classical Plateau Problem in metric spaces 
klPhys 
TBA 

19.01.2016 14:15 Uhr 
Florian Nolte Universität Heidelberg 
Oberseminar: Domains in ferromagnetic films with perpendicular anisotropy 
Raum 001, Pontdriesch 1416 
We consider a regime of ultrathin ferromagnetic films with strong anisotropy and easy axis pointing out of the film plane. Experiments show the formation of various domain patterns such as socalled bubble or maze domains. We aim to explain some of these patterns using an energy minimization approach  starting from the full threedimensional micromagnetic model, we identify a reduced regime and derive the asymptotic behavior of the energy in the framework of $\Gamma$convergence. Our analysis indicates that the typical length scale of domains grows exponentially as a function of the inverse thickness of the plate. 

15.12.2015 14:15 Uhr 
Laure SaintRaymond Pierre et Marie Curie University (Paris VI) 
Joint Analysis Seminar: From systems of particles to kinetic and fluid models 
klPhys 
TBA 

11.12.2015 14:15 Uhr 
Tim Laux MPI MIS Leipzig 
Oberseminar: Convergence of thresholding schemes for geometric flows 
Raum 001, Pontdriesch 1416 
The thresholding scheme, a time discretization for meancurvature flow was introduced by Meriman, Bence and Osher in 1992. In the talk we present new convergence results for modern variants of this scheme, in particular in the multiphase case with arbitrary surface tensions. The first result establishes convergence towards a weak formulation of meancurvature flow in the BVframework of sets of finite perimeter. The proof is based on the interpretation of the thresholding scheme as a minimizing movement scheme by Esedoglu and Otto in 2014. This interpretation means that the thresholding scheme preserves the structure of (multiphase) meancurvature flow as a gradient flow w. r. t. the total interfacial energy. More precisely, the thresholding scheme is a minimizing movement scheme for an energy that $\Gamma$converges to the total interfacial energy. In this sense, our proof is similar to the convergence results of Almgren, Taylor and Wang in 1993 and Luckhaus and Sturzenhecker in 1995, which establish convergence of a more academic minimizing movement scheme. Like the one of Luckhaus and Sturzenhecker, ours is a conditional convergence result, which means that we have to assume that the timeintegrated energy of the approximation converges to the timeintegrated energy of the limit. This is a natural assumption, which is however not ensured by the compactness coming from the basic estimates. We will also discuss new convergence results for volumepreserving meancurvature flow and forced meancurvature flow.


24.11.2015 14:15 Uhr 
Tim Sullivan University of Warwick 
Joint Analysis Seminar: Brittleness and robustness of Bayesian inference 
klPhys 
The flexibility of the Bayesian approach to uncertainty, and its notable practical successes, have made it an increasingly popular tool for uncertainty quantification. The scope of application has widened from the finite sample spaces considered by Bayes and Laplace to very highdimensional systems, or even infinitedimensional ones such as PDEs. It is natural to ask about the accuracy of Bayesian procedures from several perspectives: e.g., the frequentist questions of wellspecification and consistency, or the numerical analysis questions of stability and wellposedness with respect to perturbations of the prior, the likelihood, or the data. This talk will outline positive and negative results (both classical ones from the literature and new ones due to the authors and others) on the accuracy of Bayesian inference. There will be a particular emphasis on the consequences for high and infinitedimensional complex systems. In particular, for such systems, subtle details of geometry and topology play a critical role in determining the accuracy or instability of Bayesian procedures. Joint work with Houman Owhadi and Clint Scovel (Caltech). 

10.11.2015 14:15 Uhr 
Eduard Feireisl Academy of Sciences of the Czech Republic 
Joint Analysis Seminar: On solvability of certain problems in fluid mechanics involving inviscid fluids 
klPhys 
We present a general method of "construction" of solutions to systems of partial differential equations describing the motion of inviscid fluids. The method is based on a variable coefficients version of the oscillatory lemma proved in the context of the incompressible Euler system by C. De Lellis and L. Székelyhidi. Several specific examples of fluid systems including the Korteweg fluid models, quantum fluids, the EulerFourier system, and the SavageHutter model will be presented. We also discuss suitable admissibility criteria to ensure wellposedness of these problems. 

03.11.2015 14:15 Uhr 
Benjamin Berkels RWTH Aachen 
Oberseminar: Variational approaches for image segmentation and registration 
Raum 001, Pontdriesch 1416 
Image segmentation and registration are two of the fundamental image processing problems. Segmentation is to decompose an image into disjoint regions that are roughly homogeneous in a suitable sense. If three or more regions are sought, one speaks of multiphase segmentation. We first review how to find global minimizers of the nonconvex binary MumfordShah model to solve the classical twophase segmentation problem. Then, we propose a novel method for multiphase segmentation of images based on the MumfordShah model and highdimensional local feature vectors. While the method was developed for the segmentation of extremely noisy crystal images based on localized Fourier transforms, the resulting framework is not tied to specific feature descriptors. For instance, using local spectral histograms as features, it allows for robust texture segmentation. Image registration is the task of transforming two or more images into a common coordinate system. After a short introduction to variational image registration, we discuss how a series of hundreds of noisy scanning transmission electron microscopy (STEM) images can be registered to obtain an improved image that enables subpicometer precision measurements of atom positions surpassing the quality attainable by single shot STEM images. Particular challenges here are input data with a low signaltonoise ratio and periodic structures. Finally, nonrigid approaches in the context of medical imaging are discussed. 

13.10.2015 15:00 Uhr 
Stavros Komineas University of Crete 
Oberseminar: Dynamics of skyrmions in chiral ferromagnets 
Raum 001, Pontdriesch 1416 
We will give a description of the dynamics of topological and nontopological solitons in ferromagnetic films. We study materials with a DzyaloshinskiiMoriya interaction and easyaxis anisotropy. Our analysis is based on an important link between topology and dynamics which is established through the construction of unambiguous conservation laws. In particular, we study the motion of a topological skyrmion with skyrmion number Q=1 and a nontopological skyrmionium with Q=0 under the influence of an applied field gradient (which plays the role of a force). The Q=1 skyrmion undergoes Hall motion perpendicular to the direction of the field gradient with a drift velocity proportional to the gradient. In contrast, the nontopological Q=0 skyrmionium is accelerated in the direction of the field gradient, thus exhibiting ordinary Newtonian motion. When the applied field is switched off the Q=1 skyrmion is spontaneously pinned around a fixed guiding center, whereas the Q=0 skyrmionium moves with constant velocity v. We give a numerical calculation of a skyrmionium traveling with any constant velocity v that is smaller than a critical velocity vc. 

14.07.2015 14:00 Uhr 
John McCuan Georgia Tech 
Oberseminar: Numerical limits of stability for cylindrical pendent drops 
Raum 001, Pontdriesch 1416 
Cylindrical pendent drops are a hybrid between pendent drops and horizontal liquid bridges in a downward gravity field. They are somewhat remarkable for admitting discontinuous stable families indexed by increasing volume and stable drops with volume larger than some unstable drops adhering to the same support geometry in particular. This feature, among others, complicates the stability analysis, and while some stability properties of these drops can be rigorously proved, some assertions presently depend on numerical calculations. In this talk I will describe the basic stability behavior distinguishing between rigorous and numerical results and giving particular emphasis to some recently discovered fine properties exposed by the numerics. Time permitting, I will discuss details of our numerical approach and some technical aspects relying on asymptotic analysis. 

23.06.2015 14:00 Uhr 
Patrick Dondl Durham University 
Oberseminar: Motion of interfaces in random media: pinning and some applications 
Raum 001, Pontdriesch 1416 
We consider the evolution of an interface, subject to a driven mean curvature flow, in a random environment. The environment is modeled by a nonlinear, random, forcing term in the evolution equation and describes localized obstacles which are harder to penetrate by the interface. First we will consider a the problem of pinning a nearly flat interface in such a random field of obstacles, proving existence of a stationary solution of the evolution equation by a combination of percolation results and sub and supersolution techniques. This leads to the emergence of a hysteresis that does not vanish for slow loading, even though the local evolution law is viscous (in particular, the velocity of the interface in the model is linear in the driving force). We will then apply some of these ideas to solutions of Landaude Gennes' theory of nematic liquid crystals in the sharp interface limit, considering the evolution of interfaces with spherical initial conditions. 

02.06.2015 14:00 Uhr 
Benjamin Schlein University of Zurich 
Joint Analysis Seminar: Nonsmooth differential geometry. Abstract at Instmath event page. 
Hörsaal SeMath, Pontdriesch 1416 
Abstract at Instmath event page. 

12.05.2015 14:00 Uhr 
Karlheinz Gröchenig University of Vienna 
Joint Analysis Seminar: Deformation of Gabor systems. Abstract at Instmath event page. 
Hörsaal SeMath, Pontdriesch 1416 
Abstract at Instmath event page. 

05.05.2015 14:00 Uhr 
Aldo Pratelli University of ErlangenNürnberg 
Joint Analysis Seminar: On the approximation of Sobolev homeomorphisms. Abstract at Instmath event page. 
Hörsaal SeMath, Pontdriesch 1416 
Abstract at Instmath event page. 

21.04.2015 14:00 Uhr 
Nicola Gigli University Pierre et Marie Curie (Paris VI) 
Joint Analysis Seminar: Nonsmooth differential geometry. Abstract at Instmath event page. 
Hörsaal SeMath, Pontdriesch 1416 
Abstract at Instmath event page. 

03.03.2015 14:00 Uhr 
Yuko Nagase Osaka City University Advanced Mathematical Institute (OCAMI) 
Oberseminar: Analysis of a CahnHilliard/AllenCahn equation 
Raum 001, Pontdriesch 1416 
In this talk I will present some analyses of a CahnHilliard/AllenCahn equation which was introduced by Karali and Katsoulakis. The limit evolution of the equation under a suitable scaling is also mean curvature flow, similarly to the AllenCahn equation but a different coefficient constant appears, which speeds up the mean curvature flow. We will show some analyses, that is, existence of solution and asymptotic behaviors. As next step, we will consider a stochastic version of the equation. I will present some recent known results of the existence of solution and related results. 

10.02.2015 15:00 Uhr 
Peter Hornung TU Dresden 
Oberseminar: The Willmore functional on isometric immersions 
Raum 001, Pontdriesch 1416 
In this talk we present some results about the (generalised) Kirchhoff plate functional from nonlinear elasticity. This functional is obtained by restricting the classical Willmore functional to the class of isometric immersions of a fixed 'reference' Riemannian manifold.


20.01.2015 16:00 Uhr 
Laurent Demanet MIT 
Joint Analysis Seminar: 1930s analysis for 2010s signal processing: recent progress on the superresolution question. Abstract at Lehrstuhl C event page. 
Hörsaal SeMath, Pontdriesch 1416 
Abstract at Lehrstuhl C event page. 

13.01.2015 16:00 Uhr 
Alexei N. Bogdanov IFW Dresden 
Special seminar: Chiral skyrmions: rigorous solutions and physical applications 
Hörsaal SeMath, Pontdriesch 1416 
Two dimensional chiral magnetic vortices or skyrmions represent areas of reverse magnetization localized into tubes with the diameters of nanoscale sizes. Importantly that in most of nonlinear physical systems such multidimensional static solitonic states are unstable and collapse spontaneously under the influence of external or internal perturbations. In condensed matter systems lacking inversion symmetry two and threedimensional localized states (skyrmions) are stabilized by a specific mechanism imposed by handedness of the underlying structure [1]. This single out condensed matter systems with intrinsic and induced chirality (noncentrosymetric magnetic crystals, multiferroics, ferroelectrics, and liquid crystals) into a particular class of materials where skyrmions can be induced and manipulated.


06.01.2015 16:00 Uhr 
Felix Otto MPI for Mathematics in the Sciences 
Joint Analysis Seminar: A regularity theory for elliptic equations with random coefficients. Abstract at Lehrstuhl C event page. 
Hörsaal SeMath, Pontdriesch 1416 
Abstract at Lehrstuhl C event page. 

18.11.2014 16:00 Uhr 
Martin Rumpf University of Bonn 
Joint Analysis Seminar: Time Discrete Geodesics on Image Manifolds. Abstract at Lehrstuhl C event page. 
Hörsaal SeMath, Pontdriesch 1416 
The abstract is posted at http://www.mathc.rwthaachen.de/news/home/. 

11.11.2014 15:00 Uhr 
Jens Rademacher University of Bremen 
Oberseminar: Pattern formation in simple spintronic device models with aligned fields. 
Raum 001, Pontdriesch 1416 
The selforganized emergence of spatiotemporal patterns is a ubiquitous phenomenon in nonlinear processes on large homogeneous domains. In this talk a class of LandauLifshitzGilbertSlonczewski equations is studied from this viewpoint, highlighting various aspects of the theory. The model describes magnetization dynamics in the presence of an applied field and a spin polarized current. Here we consider the case of axial symmetry and focus on coherent structure solutions that occur due to the symmetry. This is joint work with Christof Melcher (RWTH). 

04.11.2014 18:00 Uhr 
Angela Stevens University of Münster 
Colloquium: Mathematical Modeling of Structure Formation in Cellular Systems due to Cell Motion 
Hörsaal III 
Chemotaxis  directed cell motion due to attractive,
mostly diffusible, signals  is a common mechanism
for pattern and structure formation in developmental
cell systems. Related mathematical models are partial
differential equations of crossdiffusion type.
Signals for cell communication can also be more localized
(e.g. within the socalled extra cellular matrix).
In this case mathematical models of partial
differential equations coupled with ordinary differential equations
result.
Pattern formation of both kinds of models differ and are discussed.
Also mathematically different techniques are required to analyze
these models w.r.t. their pattern forming behavior.
Further, there are connections with selfattracting reinforced random
walks, which will also be discussed.


28.10.2014 16:00 Uhr 
Camillo DeLellis University of Zurich 
Joint Analysis Seminar: Dissipative continuous solutions of the incompressible Euler equations with Onsagercritical spatial regularity. Abstract at Lehrstuhl C event page. 
Hörsaal SeMath, Pontdriesch 1416 
The abstract is posted at http://www.mathc.rwthaachen.de/news/home/. 

13.10.2014 16:00 Uhr 
Martin Hairer Warwick University 
Joint Analysis Seminar: Weak universality of the KPZ equation. (Note this talk is on a Monday!) Abstract at Lehrstuhl C event page. 
Hörsaal SeMath, Pontdriesch 1416 
The abstract is posted at http://www.mathc.rwthaachen.de/news/home/. 

15.07.2014 16:00 Uhr 
Zdzislaw Brzezniak University of York 
Joint Analysis Seminar: See Lehrstuhl C event page 
I 
The abstract is posted at http://www.mathc.rwthaachen.de/news/home/. 

08.07.2014 15:00 Uhr 
Lucia Scardia University of Glasgow 
Oberseminar: POSTPONED  SG 11 
The seminar is postponed. A new date will be announced next semester. 

01.07.2014 16:00 Uhr 
Felix Schulze University College London 
Joint Analysis Seminar: See Lehrstuhl C event page 
I 
The abstract is posted at http://www.mathc.rwthaachen.de/news/home/. 

17.06.2014 16:00 Uhr 
Massimo Fornasier TU Muenchen 
Joint Analysis Seminar: See Lehrstuhl C event page 
I 
The abstract is posted at http://www.mathc.rwthaachen.de/news/home/. 

13.05.2014 16:00 Uhr 
Changyou Wang University of Kentucky 
Joint Analysis Seminar: CANCELLED 
I 
06.05.2014 16:00 Uhr 
Mauro Maggioni Duke University 
Joint Analysis Seminar: See Lehrstuhl C event page 
I 
The abstract is posted at http://www.mathc.rwthaachen.de/news/home/. 

29.04.2014 15:00 Uhr 
Paola Pozzi University of DuisburgEssen 
Oberseminar: On the elastic flow for open curves  SG 11 
In this talk I will discuss a longtime existence result for the elastic flow of open curves in $\mathbb{R}^n$. 

15.04.2014 15:00 Uhr 
Lukas Döring MPI Leipzig 
Oberseminar: Reduced models for domain walls in soft ferromagnetic films  SG 11 
Depending on material parameters and sample dimensions, soft ferromag netic films exhibit various kinds of domain walls (transition layers between neighboring domains of constant magnetization). In the first part of the talk, we present a reduced model for a single domain wall at the crossover from symmetric to asymmetric wall types in an infinitely extended film. The reduced model captures the optimal splitting of the wall into an asymmetric, strayfield free core and logarithmically decaying, symmetric wall tails (obtained via Gamma conver gence, joint work with R. Ignat and F. Otto). In the second part, we consider periodic domain patterns for which the wall width is not only confined by material anisotropy but also the neighboring wall tails. Using methods similar to the singlewall case, we derive a reduced model that describes the influence of the tail interaction on the splitting into the core and tails. Moreover, it yields a prediction for the increased rotation of the magnetization towards magnetic fields applied along the wall normal direction. 

04.02.2014 15:00 Uhr (Note there is a second talk this day) 
Barbara Niethammer University of Bonn 
Joint Analysis Seminar: Phase transitions in a nonlocal FokkerPlanck equation with multiple time scales  Fo 3 
Please join us for coffee afterwards at 16:00 in room 114 in the Main Building. 

04.02.2014 16:45 Uhr (Note special time) 
Alexander Mielke Weierstrass Institute for Applied Analysis and Stochastics (WIAS) 
Joint Analysis Seminar: On gradient structures for reactiondiffusion systems  Fo 3 
Please join us for coffee beforehand at 16:00 in room 114 in the Main Building. 

28.01.2014 15:00 Uhr 
Peter Sternberg Indiana University 
Oberseminar: Minimizers of a nonlocal isoperimetric problem in thin domains  Fo 3 
The nonlocal isoperimetric problem arises as a limit of the OhtaKawasaki model for diblock copolymers. As a variational problem, it takes the form of a competition between a local term favoring low surface area and a nonlocal term favoring high oscillation. In this talk I will survey some of the previous activity on this problem (of which there is a lot) and then focus on a recent result by Massimiliano Morini and me in the setting of thin domains where we can identify the global minimizer for all values of the coefficient of nonlocality. 

07.01.2014 15:00 Uhr 
Thierry Gallay University of Grenoble 
Joint Analysis Seminar: Distribution of energy and convergence to equilibria in extended dissipative systems  Fo 3 
We study the local energy dissipation in gradientlike nonlinear partial differential equations on unbounded domains. Our basic assumption, which happens to be satisfied in many classical examples, is a pointwise upper bound on the energy flux in terms of the energy dissipation rate. Under this hypothesis, we derive a simple and general bound on the integrated energy flux which implies that, in low space dimensions, our ``extended dissipative system'' has a gradientlike dynamics in a suitable averaged sense. In particular, we can estimate the time spent by any trajectory outside a neighborhood of the set of equilibria. As an application, we study the longtime behavior of solutions to the twodimensional NavierStokes equation in an infinite cylinder. This talk is based on a collaboration with S. Slijepcevic (Zagreb, Croatia).


10.12.2013 15:00 Uhr 
Didier Bresch University of Savoie 
Joint Analysis Seminar: Mathematical topics around shallowwater type equations  Fo 3 


29.11 30.11.2013  Analysis Day 
Speaker and schedule information for this two day event  


19.11.2013 15:30 Uhr 
Martina Hofmanova MPI Leipzig 
Oberseminar: The concept of kinetic solutions and wellposedness for stochastic conservation laws  SG 11 
Many basic equations in physiscs can be written in the form of
conservation law. However, as it is common in the field of PDEs and
SPDEs, classical or strong solutions do not exist in general and, on the
other hand, weak solutions are not unique. The notion of kinetic
formulation and kinetic solution turns out to be a very convenient tool to
overcome these difficulties.


05.11.2013 15:30 Uhr 
Peter Bella MPI Leipzig 
Oberseminar: Wrinkling of a Stretched Annular Elastic Thin Sheet  Identification of the Optimal Scaling Law for the Ground State Energy  SG 11 
In [Bella & Kohn: Wrinkles as the result of compressive stresses in an annular thin film, to appear in CPAM] we identified the optimal scaling law of the minimum of the elastic energy of a stretched annular thin elastic sheet. In this talk I will describe the next step towards the understanding of this problem  I will identify the optimal prefactor in the scaling law. Moreover, I show that this prefactor can be characterized as a minimum of a much simpler (scalar) variational problem. 

17.12.2013 15:30 Uhr 
Filip Rindler University of Warwick 
Oberseminar: Directional oscillations, concentrations, and compensated compactness via microlocal compactness forms  SG 11 
Microlocal compactness forms (MCFs) are a new tool to study oscillations and concentrations in L^pbounded sequences of functions. Decisively, MCFs retain information about the location, value distribution, and direction of oscillations and concentrations, thus extending both the theory of (generalized) Young measures and the theory of Hmeasures. Since in L^pspaces oscillations and concentrations precisely discriminate between weak and strong compactness, MCFs allow to quantify the difference between these two notions of compactness. The definition involves a Fourier variable, whereby also differential constraints on the functions in the sequence can be investigated easily. Furthermore, pointwise restrictions are reflected in the MCF as well, paving the way for applications to Tartar's framework of compensated compactness; consequently, we establish a new weaktostrong compactness theorem in a "geometric" way. Moreover, the hierarchy of oscillations with regard to slow and fast scales can be investigated as well since this information is also is reflected in the generated MCF. 

22.10.2013 15:00 Uhr 
Massimo Fornasier Technical University München 
CANCELLED!: Joint Analysis Seminar on Quasilinear compressed sensing  Fo 3 
Unfortunately this talk was cancelled due to illness. Please feel free to join anyway for coffee at 14:15 in room 114 in the Main Building. 

16.07.2013 18:00 Uhr 
Stanley Alama McMaster University 
Kolloquium: Vortices and the GinzburgLandau Functional  Hörsaal III 
The GinzburgLandau model is a widely used tool for describing the physical state of superconductors, superfluids, or BoseEinstein condensates. It also appears in particle physics as the Abelian Higgs model. GinzburgLandau is a rich source of interesting phenomena in the calculus of variations and in the study of singularities in solutions to partial differential equations. In this talk, I will start with the basics of GinzburgLandau vortices, beginning with the classical results of BethuelBrezisHélein. Then I will present some theorems on vortex lines for the 3D GinzburgLandau model, in the context of Gammaconvergence. Finally, I will present an overview of some recent results on the effect of anisotropy in the mathematical study of superconductors. Anisotropic models are important for the understanding of the hightemperature superconductors, and they present some interesting mathematical results and challenges. 

16.07.2013 15:45 Uhr 
Lia Bronsard McMaster University 
Joint Analysis Seminar: Vortices for a 2 component Ginzburg Landau system  Hörsaal V 
We study vortices in a GinzburgLandau model for a pair of complexvalued
order parameters. Multicomponent functionals have been introduced in the
context of unconventional pwave superconductors and spinor BoseEinstein
condensates to include spin coupling effects. As in the classical
GinzburgLandau model, minimizers will exhibit quantized vortices in
response to boundary conditions or applied fields. However, we show that
the interaction between the two components allows for vortices with a more
exotic core structure. Our results are based on a combination of
variational and PDE methods, blowing up around the vortex core and studying
the resulting system and its local minimizers. This is joint work with Stan
Alama and Petru Mironescu.


09.07.2013 15:30 Uhr 
Max Jensen University of Sussex 
Seminar: A Finite Element Method for HamiltonJacobiBellman equations  SG 11 
HamiltonJacobiBellman equations describe how the cost of an optimal control problem changes as problem parameters vary. This talk will address how Galerkin methods can be adapted to solve these equations efficiently. In particular, it is discussed how the convergence argument by Barles and Souganidis for finite difference schemes can be extended to Galerkin finite element methods to ensure convergence to viscosity solutions. A key question in this regard is the formulation of the consistency condition. Due to the Galerkin approach, coercivity properties of the HJB operator may also be satisfied by the numerical scheme. In this case one achieves besides uniform also strong H^1 convergence of numerical solutions on unstructured meshes. 

11.06.2013 15:30 Uhr 
Margaret Beck HeriotWatt University 
Seminar: Quasistationary states of the 2D NavierStokes equation  SG 11 
The dynamics of the 2D incompressible NavierStokes equation has two key stages: rapid convergence to certain quasistationary states, and then the slow evolution of these states as the fluid relaxes to its rest state. We provide a mathematical explanation for these multiple time scales by studying a certain family of quasistationary states, known as bars and dipoles, using techniques from the theory of infinitedimensional dynamical systems and hypocoercive operators. 

18.06.2013 15:45 Uhr 
Michael Struwe ETH 
Joint Analysis Seminar: The gradient flow for a supercritical elliptic variational problem  Hörsaal V 
TBA. Please join us for coffee beforehand at 15:15 in room 114 in the Main Building. 

04.06.2013 15:45 Uhr 
Sergio Conti Universität Bonn 
Joint Analysis Seminar: Derivation of a linetension model for dislocations in the plane  Hörsaal V 
Dislocations are topological defects in crystals which generate
longrange elastic stresses. For dislocations in the plane
the elastic interactions can be represented via a singular kernel behaving
as the H^{1/2} norm of the slip. We obtain a sharpinterface limit
within the framework of Gamma convergence in the limit of small elastic
spacing. One key ingredient is a proof of the fact that the presence of
infinitely many equivalent length scales gives strong restrictions on the
geometry of the microstructure. In particular we show that the micrustructure
must be onedimensional on most length scales, and that only few are available
for the relaxation. This talk is based on joint work with Adriana Garroni,
Annalisa Massaccesi and Stefan Müller.


28.05.2013 15:45 Uhr 
Mark Peletier University of Eindhoven 
Joint Analysis Seminar: Energydriven pattern formation via competing long and shortrange interactions  Hörsaal V 
I will discuss patterns in block copolymer melts. This is a model
system that is mathematically tractable, physically meaningful (and
experimentally accessible) and representative for a large class of
energydriven patternforming systems. Such systems show a remarkable
variety of different patterns, of which only a small fraction is well
understood.


07.05.2013 15:45 Uhr 
Giuseppe Buttazzo University of Pisa 
Joint Analysis Seminar: Optimal potentials for Schrödinger operators  Hörsaal V 
We consider the Schrödinger operator $\Delta+V(x)$ on $H^1_0(\mathcal{O})$,
where $\mathcal{O}$ is a given domain of $\mathbb{R}^d$. Our goal is to study some
optimization problems where an optimal potential $V\ge0$ has to be
determined in some suitable admissible classes and for some suitable
optimization criteria, like the energy or the Dirichlet eigenvalues.


30.04.2013 15:30 Uhr 
Angkana Rüland Universität Bonn 
Seminar: Rigidity, nonrigidity and scaling of the cubictoorthorhombic phase transition in the linear theory of elasticity  SG 11 
In this talk I present recent results on rigidity properties of the cubictoorthorhombic
phase transition in the linear theory of elasticity. Using the framework of convex
integration, it is proved that this model provides an example of a martensitic
phase transition in which already in the linear theory of elasticity no rigidity
properties can be expected without requiring additional regularity conditions
on the phase interfaces.


15.1.2013 11:00 Uhr 
Prof. Dr. Christoph Scheven Universität DuisburgEssen 
Seminar: Localizable solutions to nonlinear parabolic problems with irregular obstacles  SG 11 
The talk is concerned with parabolic obstacle problems related to the evolutionary pLaplace equation. The obstacle function may be very irregular and may also be increasing in time. In such a general situation, it was not known so far whether the solutions to such obstacle problems are localizable in the sense that the restriction of the solution on a subdomain again solves an obstacle problem. This is of course a serious problem if you are asking for local properties of a solution such as regularity. The talk will present a new existence result for localizable solutions to obstacle problems with irregular obstacles and will discuss some regularity properties of the constructed solutions. 

15.1.2013 18:00 Uhr 
Prof. Dr. Maria G. Westdickenberg RWTH Aachen 
Order and disorder: The competition between energy and entropy in randomly perturbed systems  Hörsaal III 
Abstract: Although at first glance a stochastic perturbation destroys the stability of energy minimizers, the probabilistic theory of large deviations reveals that the most likely pathways actually solve their own minimization problem. This theory—established in the mathe matical literature decades ago with the classic book of Freidlin and Wentzell—treats stochastic ordinary differential equations. Subse quently, it was confirmed that the theory generalizes naturally to stochastic partial differential equations. Recently, there has been progress in pushing large deviation theory to the limit and probing new regimes. In this talk, we will be particularly interested in the competition between energy and entropy that emerges in the case of small noise and large system size. We will present some recent results and, if time permits, give a feeling for the underlying tools. The talk is intended for a broad audience and no prior knowledge of probability theory will be assumed. 

22.01.2013 11:00 Uhr 
Prof. Dr. Günther Grün Universität ErlangenNürnberg 
Seminar: On convergent schemes for diffuse interface models for twophase flow of incompressible fluids with general mass densities  SG 11 
In this talk, we will be concerned with modeling and numerics of twophase flow of immiscible, incompressible viscous fluids with different mass densities. In contrast to the case of identical mass densities, for general mass densities it has only recently been possible to formulate diffuse interface models which are consistent with thermodynamics and for which numerical schemes satisfying energy estimates can be developed. These models may be derived e.g. by Onsager's variational principle and they consist of a momentum equation for the velocity field coupled to a CahnHilliard equation for the evolution of the order parameter. In the first part of the talk, we will discuss modeling aspects, and by a subtle discretization of the convective coupling between the flux of the phasefield and the momentum equation, we formulate a numerical scheme which is discretely consistent with thermodynamics. In the second part of the talk, we will prove its convergence in two and in three space dimensions and we present numerical simulations showing the full practicality of the approach. 

18.12.2012 11:00 Uhr 
Prof. Dr. Bernd Schmidt Uni Augsburg 
Seminar: On the passage from atomistic to continuum systems in elasticity and fracture mechanics  SG 11 
We study atomistic systems and their effective continuum counterpart in two different regimes: 1. Elastic deformations with given boundary data. Here our main aim is to relate discrete solutions of the EulerLagrange equations to solutions of the continuum equations of nonlinear elasticity. 2. crystals under uniaxial strain that may fracture. In this regime we will derive general cleavage laws from the atomistic interaction potentials. 

27.11.2012 15:00 (special time) 
Dr. Hans Knüpfer Universität Bonn 
Seminar: Wellposedness and lubrication approximation of the Darcy flow in the presence of a contact line  SG 11 
The propagation of a liquid drop on a plate is characterized by the evolution of the threephase contact line where air, liquid and solid meet. The region occupied by the liquid is is described by a timedependent domain with nonsmooth boundary. We address wellposedness and regularity for models for the evolution of viscous fluids. We focus on certain models for fluid propagation of viscous liquids (Darcy flow, thinfilm equation). Since the considered problems do not satisfy a maximum principle, the analysis is based on the dissipative structure of the models. 

04.12.2012 14:0015:30 Uhr 
Postdoc Day RWTH 
Seminar: Barbora Benesova, Fabio Cavalletti, Michael Gelantalis, Marc Sedjro.  Hauptgebäude 114 
Barbora Benesova: Microstructures in solids and their mathematical treatment; Fabio Cavalletti: Optimal transportation in metric measure spaces; Michael Gelantalis: Rotating vortex solutions to the GrossPitaevskii equation on S^2; Marc Sedjro: On almost axisymmetric flows with forcing terms. 

25.07.2012 15:00 Uhr 
Ermal Feleqi Universita degli Studi di Padova 
Seminar: Some aspects of Mean Field Games  SG 11 
Mean field games are a branch of game theory introduced by JM. Lasry and PL. Lions in order to model the behavior of a very large number of rational agents with a limited information (or visibility) of the game who optimize their decisions in view of the global (or macroscopic) informations available to them and that result from the actions of all agents. The perspective of applications is quite broad, e.g., in economics, finance, sociology, urban planning, engineering etc. Games with e very large number of players are approximated by a ``continuum limit'' (letting the number of the players go to infinity) in analogy with certain ``mean field'' approaches of statistical mechanics and physics, and this justifies the name. The focus on my talk will be on a class of ergodic stocastic differential games coupled only through the costs with players belonging to N different populations. (Each population consists of a large number of identical players, but the characteristics of the players vary from one population to the other.) In this case the MFG model results in a diagonal system of 2N stationary PDEs: N HamiltonJacobiBellman equations and N KolmogorovFokkerPlank linear PDEs for the final distribution of the players of each population. I will exhibit a wide range of sufficient conditions for the solvability of these systems and their rigorous (or mathematical) derivation as a `continuum limit' of certain systems of PDEs associated with games with a finite number of players as the cardinality of each population goes to infinity. In doing so, I do not only generalize previous work of Lasry and Lions by considering more general dynamics, costs and several populations, but also provide detailed proofs (which they do not in their articles). I will end my talk by indicating some perspectives for future research, most intriguing for me being the possibility of formulating a very general ``master equation'' in metric spaces of probability measures. Its mathematical interpretation, study and degree of approximation of the related games with a finite number of players seem very fascinating and promising topics to me. 

03.07.2012 11:00 Uhr 
Barbora Benesova Charles University Prague 
Seminar: Young measures on invertible matrices  SG 11 
21.06.2012 11:00 Uhr 
Xing Zhong New Jersey Institute of Technology 
Seminar: Threshold phenomena for symmetric decreasing solutions of reactiondiffusion equations  SG 11 
We study the Cauchy problem for nonlinear reactiondiffusion equations in one space dimension. By using proper energy functional and exponentially weighted functional, for symmetric decreasing initial conditions, we can prove a onetoone relation between the long time behavior of solution and the limit value of energy. Then, for a monotone increasing family of initial conditions, there exists a sharp transition between extinction and propagation. This is a joint work with Cyrill B. Muratov. 

19.06.2012 11:00 Uhr 
Dr. Greg Pavliotis Imperial College 
Seminar: Analysis and numerics for SPDEs with multiple scales  SG 11 
In this talk we will present analytical and numerical techniques for studying stochastic partial differential equations with multiple scales. After showing a rigorous homogenization theorem for SPDEs with quadratic nonlinearities, we present a numerical method for solving efficiently SPDEs with multiple scales. We then apply these analytical and numerical techniques to the stochastic KuramotoShivashinsky equation for which we show that noise induced intermittent behavior and noise induced stabilization of solutions can occur. Finally, we show how ideas from parameter estimation for diffusion processes can be used in order to obtain low dimensional coarsegrained models from time series of the SPDE (projected onto the dominant modes). This is joint work with D. Blomker and M. Hairer (analysis), A. Abdulle (numerical analysis), M. Pradas Gene, D. Tseluiko, S. Kalliadasis, D.T. Papageorgiou (stochastic KuramotoShivashinsky equation), S. Krmuscheid, S. Kalliadasis (datadriven derivation of coarsegrained models). 

12.06.2012 11:00 Uhr 
Dr. Michael Helmers Uni Bonn 
Seminar: Approximation of rotationally symmetric twocomponent bilayers  SG 11 
Models for twocomponent lipid bilayers assign an energy to a membrane that consists of an elastic part for each component and an interface term penalising component boundaries. Phase field approaches have been applied successfully to analyse such models, although many results are formal or rely on strong regularity assumptions. In the talk, we consider a surface phase field approximation of the spontaneous curvature model and study convergence to a sharp interface limit in a rotationally symmetric setting. Particular attention is paid to the regularity of limit membranes across component interfaces: exploring two different couplings between phase fields and elastic terms, we obtain either the classical model or an extension that assigns a "bending energy" also to possibly nonsmooth connections. 

05.06.2012 11:00 Uhr 
Michael Gelantalis Indiana University 
Seminar: Rotating vortex solutions to the GrossPitaevskii equation on the twosphere  SG 11 
In this talk we present some recent results concerning the existence of rotating vortex solutions to the GrossPitaevskii equation on S2. The vortices that these solutions possess follow the trajectories of certain “relative equilibria” of the pointvortex problem for all time. Similar results have been rigorously established for the GrossPitaevskii equation posed on the flat twotorus and on bounded planar domains. We adopt an approach that is based on minimizing the GinzburgLandau energy subject to an integral momentum constraint within certain symmetry classes. We also discuss the orbital stability of these solutions within a class of symmetric initial data. 

22.05.2012 11:00 Uhr 
Dr. Matthias Kurzke Uni Bonn 
Seminar: The hydrodynamic limit of the parabolic GinzburgLandau equation  SG 11 
The GinzburgLandau functional serves as a model for the formation of vortices in various physical contexts. The natural gradient flow, the parabolic GinzburgLandau equation, converges in the limit of small vortex size and finite number of vortices to a point vortex system. Passing to the limit of many vortices in this ODE, one can derive a mean field PDE, similar to the passage from point vortex systems to the 2D Euler equations with vortex sheet initial data. In the talk, I will present quantitative estimates that allow us to directly connect the parabolic GL equation to the limiting mean field PDE. This is joint work with Daniel Spirn (University of Minnesota). 

24.04.2012 11:00 Uhr 
Dr. Luca Mugnai MPI Leipzig 
Seminar: Upper bounds on coarsening rates for surface attachment limited kinetics  SG 11 
Following an approach introduced by Kohn and Otto in [Comm. Math.Phys., 2002], we prove a weak form of an upper bound on the coarsening rate for surface attachment limited kinetics which is modeled by volume preserving mean curvature flow. (This is joint work with Christian Seis, Univ. of Toronto). 

19.12.2011 ganztägig 
3Städte Seminar zur Analysis ACDortmundEindhoven 
TBA  
14.11.2011 18:00 Uhr 
Prof. Dr. Joost Hulshof, VU Amsterdam 
Kolloquium: Holefilling solutions of the porous medium equation  HS III 
Solutions of the porous medium equation have the finite speed of propagation property, exhibited by the source type solutions, which can be used as subsolutions to push the support of nontrivial nonnegative solutions outwards and force holes in the support to disappear in finite time. I will give an overview of what we know about how these holes disappear, with some emphasis on an instability result proved with Angenent, Aronson and Van den Berg. 

08.11.2011 11.00 Uhr 
Dr.Hendrik Weber, University of Warwick 
Seminar: Stochastic AllenCahn equation and Mean curvature flow  SG 11 
The AllenCahn equation is a classical model to describe the evolution of a system with two stable phases. It is wellknown that in the sharp interface limit it approximates an evolution of phase indicator functions the boundary of which performs a motion by mean curvature. In this talk we investigate the stability of this result under perturbation with a random forcing. The difficulty lies in the low regularity of this noise term that makes the application of standard analytical methods difficult. We fist discuss a simple setting where the forcing is constant in space and a smoothened white noise in time. We show that in some diagonal limit where the noise smoothing goes to zero as the interface width goes to zero the solutions converge to a forced mean curvature flow. This is shown in the framework of classical solutions via an explicit construciton of sub and supersolutions. Then we discuss the case of a stochastic transport term that is white in time and coloured in space. In this case we prove a priori bounds that imply compactness and regularity of the limiting evolution. We explain the difficulty of describing the limit. 

11.01.2011 
Prof. Dr. Ben Schweizer, TU Dortmund 
Kolloquium: Das NadelProblem: eine neue Methode für Homogenisierung  HS III 
19.10.2010, 14.00 Uhr 
André Schlichting, MPI Leipzig 
Ein stochastisches BeckerDöring Modell  Pfadweise Betrachtung von Kolloidwachstum  SG 11 
Wir betrachten ein Modell für Clusterwachstum, in dem die Dynamik nur durch Interaktion zwischen Monomeren und Clustern (bestehend aus mehreren Monomeren) gegeben ist. 

22.07.2010, 18.00 Uhr 
Prof. Dr. Jan Kristensen, University of Oxford 
On the problem of regularity in the calculus of Variations  HS IV 
There are by now several examples of regular variational problems that admit singular minimizers (nondifferentiable Sobolev maps, and worse) in the multidimensional vectorial case. This is in line with what one can prove: minimizers are partially regular, meaning they are smooth outside a small relatively closed subset of their domain. We refer to this set of singularities as the singular set. General measure theory easily gives that the singular set has zero Lebesgue measure, but over the years much better estimates of their size, in particular in terms of Hausdorff measures, have been derived. Still the gap between the examples provided by singular minimizers and the theoretical bounds for the size of the singular sets remains a major challenge. In this talk we give a survey of recent results on size estimanes of singular sets. 

14.07.2010, 18.15 Uhr 
Prof. Dr. Barbara Niethammer, University of Oxford 
Old and new in the analysis of Ostwald ripening  HS III 
Ostwald ripening is a fundamental process in the aging of materials, where particles of a second phase embedded in a background phase interact by diffusional mass exchange to reduce their total surface area. In the low volume fraction regime the statistics of the ripening process have been described by the classical meanfield theory by Lifshitz, Slyozov and Wagner (LSW). However, due to several shortcomings of this theory, there has been considerable interest in taking higher order effects such as fluctuations in particle densities or collision of particles into account. Several models have been discussed in the applied literature, but existing theories are still partially contradicting. I will review recent progress in the mathematical analysis of Ostwald ripening shedding light on the consistent modeling of different higher order effects and their relevance respectively. 

10.06.2010, 15.15 Uhr 
Dr. Elena Villa, University of Milan 
On the outer Minkowski content of sets. Results and applications  SG 11 
Let E be a Borel set in R^{d} and Vol(E) be its volume; denoting by E_{r}:={x ∈ R^{d}: dist(x,E) ≤ r} the parallel set of E at distance r, the limit of Vol(E_{r} \ E)/r for r which goes to zero, is called outer Minkowski content of E, provided that the limit exists finite. We give general conditions, stable under finite unions, ensuring the existence of the outer Minkowski content of Borel subsets of R^{d}. In particular we show how the value of the outer Mikowski content turns out to be closely related to the density of E at its boundary points, and how our results also apply to the study of the differentiability of the volume function of bounded sets, extending some known results in literature. In particular, we provide sufficient conditions which imply the equality between the outer Minkowski content of E and its surface measure. Such an equality is of interest in image analysis and stochastic geometry problems (estimation of mean surface densities, and evolution equations of stochastic birthandgrowth processes, for instance); some applications will be discussed in the final part of the talk. 

04.05.2010, 15.45 Uhr 
Albert Nana, LuF Mathematik 
Oberseminar: Weak solutions for fourthorder parabolic equations modeling epitaxial thin film growth  SG 11 
The aim of the present work is to establish in an appropriate function space the existence solutions of the following nonlinear parabolic problem (0.1): 

18.03.2010, 14 Uhr 
Dr. Adrian Muntean, TU Eindhoven 
Nonlinear micromacro transmission conditions for twoscale reactiondiffusion systems: Modeling and analysis  SG 11 
We study a reactiondiffusion system posed at two different spatial scales which involves nonlinear reaction and gasliquid masstransfer terms. The system incorporates a nonstandard component  a nonlinear transfer function connecting micro and macrotransport of species including thus in the model nonlinear deviations from local equilibrium configurations [usually modeled in the literature, as a faute de mieux solution, by a linear expression  the Henry's law]. We prove nonnegativity and L^\inftybounds for the active concentrations, uniqueness, and obtain globalintime existence of weak solutions via a twoscale Galerkin method. For the case of 2D macroscopic and microscopic domains, we give an a priori bound on the rate of convergence of our twoscale Galerkin scheme. This research is done in collaboration with MariaNeuss Radu (Universität Heidelberg) and Omar Lakkis (University of Sussex). 

10.11.2009, 18 Uhr 
Dr. Verena Bögelein, Universität Parma 
Kolloquium: Regularity of degenerate parabolic systems via the method of pcaloric approximation  HS III 
In this talk we are interested in the regularity of solutions to degenerate parabolic
systems. A by now classical result due to DiBenedetto states that the spacial gradients of
solutions to the parabolic pLaplacean system are Hölder continuous. It is our aim to
go somewhat beyond this result, in the sense that we consider degenerate parabolic systems
of more general structure, i.e. not necessarily having the usual quasidiagonal structure
of Uhlenbeck type. Then, by counterexamples it is clear that everywhere regularity cannot
hold in general. Nevertheless, we are able to establish a partial regularity result
stating that solutions are regular almost everywhere, i.e. except for a set of Lebesgue
measure zero. 

21.07.2009, 18 Uhr 
Dr. Roger Moser, University of Bath 
Kolloquium: Analysis aspects of polyharmonic maps  HS III 
A map between two Riemannian manifolds is called polyharmonic if it solves a certain type of variational problem. The simplest possible example is the Dirichlet energy for curves in a Riemannian manifold. Its critical points are geodesics, which are relatively easy to understand. When we study higherdimensional domains and functionals involving higher derivatives, however, then the resulting variational problems can become challenging. This is due to nonlinearities, coming from the curvature of the target space, in the underlying differential operators and in the EulerLagrage equations. We discuss a few questions and results concerning existence and regularity of solutions. 

09.06.2009, 16 Uhr 
Nicolas Condette, HU Berlin 
A Fourier Collocation Method for a Pattern Forming Gradient Flow Equation: Analysis and Simulation.  SG 11 
We are interested in the morphology of patterns arising as local minimizers of a nonconvex and nonlocal functional that exhibits a competition of interfacial and dipolar energies. Typical applications include magnetic garnet films as well as diblock copolymers. Based on a relaxed energy functional, we implement and analyze a fully discrete Fourier collocation scheme in order to approximate solutions of the associated L^2 gradient flow equation. The latter reads as a nonlinear parabolic equation in 2D space. We prove existence and uniqueness of the numerical solution and show that it converges to a solution of the initial continuous problem. We also derive some error estimates and finally perform numerical experiments aimed at illustrating the theoretical results. 

26.05.2009, 16 Uhr 
Dr. Mariya Ptashnyk, Universität Heidelberg 
Derivation of a macroscopic model for diffusive transport of stronglysorbed solute in the soil  SG 11 
One of the important questions in the soil science deals with the distribution of stronglysorbed solutes in the soil. The experiments for stronglysorbed ions, such as phosphate, show that ion bioavailability in the soil may be limited by their diffusion within the particles. A model for the diffusive transport of stronglysorbed solutes in the interparticle and intraparticle space is presented. The adsorption of solute on surfaces inside and outside soil particles is described by a nonlinear reaction. Using homogenization techniques effective macroscopic equations for the solute movement in the soil are derived. Applying the twoscale convergence, we show that the sequence of solutions of the original problem converges to the solution of the macroscopic problem. To show the convergence of the nonlinear terms on the surfaces the periodic modulation (unfolding method) is used. Solutions of the macroscopic model are compared with the data from phosphate pulse experiment. 

17.12.2008, 16 Uhr 
Dr. Kianhwa Colin Djie, Lehrstuhl I für Mathematik 
Blowup in endlicher Zeit bei einem Modell der Chemotaxis unter Berücksichtigung des volumenfüllenden Effekts  SG 11 
Wir betrachten das folgende parabolischelliptische KellerSegelModell der
Chemotaxis 