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04.06.2018 16:00 Aleksandr Aravkin, Washington Research Foundation, USA:
Fast methods for nonsmooth nonconvex problems using variable projectionMI 02.06.011 (Boltzmannstr. 3, 85748 Garching)

Classic inverse problems are formulated using smooth penalties and regularizations. However, nonsmooth and nonconvex penalties/regularizers have proved to be extremely useful in underdetermined and noisy settings. Problems with these features also arise naturally when modeling complex physical and chemical phenomena; including PDE-constrained optimization, phase retrieval, and structural resolution of bio-molecular models. We propose a new technique for solving a broad range of nonsmooth, nonconvex problems. The technique is based on a relaxed reformulation, and can be implemented on a range of problems in a simple and scalable way. In particular, we typically need only solve least squares problems, as well as implement custom separable operators. We discuss the problem class, reformulation and algorithms, and give numerous examples of very promising numerical results in different applications.

04.06.2018 16:30 Stein Andreas Bethuelsen (TU Munich) :
TBAB 252 (Theresienstr. 39, 80333 München)

TBA

07.06.2018 15:45 Michael Kniely (IST Austria):
Material Design for Optimal Excitation Induced Charge Transfer in Photovoltaic DevicesMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

This talk is concerned with a novel approach in the context of material design for (organic) photovoltaics. We consider a quantum-mechanical model for a prescribed distribution of positive charges (atomic cores) and a corresponding set of orbitals describing the negative charges (electrons). In the ground state, all orbitals up to HOMO are occupied and all higher orbitals starting from LUMO are unoccupied. By a light-induced excitation, the electronic system may end up in the first excited state where HOMO is unoccupied but LUMO is occupied. Our aim is to maximize this light-induced spatial charge transfer from HOMO to LUMO as a function of the underlying nuclear charge distribution. Concerning optimal charge transfer, we will review a general existence proof for the corresponding mathematical optimization problem. Numerical simulations are carried out for a 1D chain of atoms and illustrate the applicability of this approach. This work is part of a joint project with Gero Friesecke.

07.06.2018 16:30 Prof. Dr. Arnaud Le Ny (Universite Paris-Est):
TBA2.01.10 (Parkring 11, 85748 Garching-Hochbrück)

TBA

07.06.2018 17:15 Ulrich Pinkall (TU Berlin) :
A Weierstrass representation for 2D elasticity MI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

We study a class of elastic energy functionals for maps between planar domains (among them the so-called squared distance functional) whose critical points (elastic maps) allow a far more complete theory than one would expect from general elasticity theory. For some of these functionals elastic maps even admit a "Weierstrass representation" in terms of holomorphic functions, reminiscent of the one for minimal surfaces. We also prove a global uniqueness theorem that does not seem to be known in other situations.

08.06.2018 14:00 Organisatoren: Noam Berger, Diane Conache, Nina Gantert, Silke Rolles, Sabine Jansen:
Women in Probability 2018MI 00.07.014 (Boltzmannstr. 3, 85748 Garching)

Sprecherinnen sind: Fabienne Castell, Karen Habermann, Irene Marcovici, Sara Merino-Aceituno, Francesca Nardi, Ellen Powell, Ellen Saada, Kristina Schubert

09.06.2018 09:00 Organisatoren: Noam Berger, Diane Conache, Nina Gantert, Silke Rolles, Sabine Jansen:
Women in Probability 2018MI 00.07.014 (Boltzmannstr. 3, 85748 Garching)

Sprecherinnen sind: Fabienne Castell, Karen Habermann, Irene Marcovici, Sara Merino-Aceituno, Francesca Nardi, Ellen Powell, Ellen Saada, Kristina Schubert

12.06.2018 15:30 Guillaume Carlier (Université Paris Dauphine & John von Neumann Professor@TUM):
Optimizing over convex functions: motivations and challengesMI 02.06.011 (Boltzmannstr. 3, 85748 Garching)

Optimization problems subject to a convexity constraint on the admissible profiles arise in a variety of contexts in aerodynamics, economics, geometry, shape optimization, mass transport.... They are challenging because discretizing convex functions or shapes is in general very costly and naive algorithms maybe inconsistent. In this survey talk, after describing some applications and theoretical results I will review some tractable numerical approaches to these problems.

For the full programme of the SFB Colloquium see: http://www.discretization.de/en/events/14/

14.06.2018 15:00 André Schlichting (Universität Aachen):
A non-local Fokker-Planck equation related to nucleation and coarseningRoom 2004, 1st floor, Building L1 (Universitätsstr. 14, 86159 Augsburg)

In this talk we consider a Fokker-Planck equation modeling nucleation of clusters very similar to the classical Becker-Döring equation. The main feature of the equation is the dependence of the driving vector field and boundary condition on a non-local order parameter related to the excess mass of the system. In this way the equation has formally the structure of a McKean-Vlasov equation, but with a non-local boundary condition. We briefly discuss the well-posedness and regularity properties of the Cauchy-Problem. Here the main difficulty is to improve basic a priori regularity properties of the non-local order parameter. The main part of the talk focuses on the longtime behavior of the system. The system possesses a free energy, which strictly decreases along the evolution and leads to a gradient structure involving boundary conditions. We generalize the standard entropy method based on suitable weighted logarithmic Sobolev inequalities and interpolation estimates. In this way, we obtain an explicit characterization of the convergence to equilibrium with algebraic or even exponential rates depending on the particular assumptions on the vector fields, diffusivity and initial data. (joint work with J. Conlon)

14.06.2018 16:30 Franz Gmeineder (Universität Bonn):
Regularity theory for functionals on BD - from convexity to symmetric-rank-one convexityRoom 2004, 1st floor, Building L1 (Universitätsstr. 14, 86159 Augsburg)

Linear growth functionals (such as the minimal surface functional) are usually minimised over the space BV of functions of bounded variation. However, if we pass to the vectorial case and replace the full by the symmetric gradient, then Ornstein's Non-Inequality rules out coerciveness of linear growth functionals on BV. We are thereby lead to examine generalised minima over the space BD of functions of bounded deformation: For such maps the symmetric distributional gradients are finite Radon measures. In this talk I aim to give a comprehensive regularity analysis for generalised minimisers both in the convex and the symmetric-semiconvex framework. The results presented therein are partially obtained in collaboration with J. Kristensen (Oxford).

18.06.2018 16:15 Annalisa Iuorio (TU Wien):
Geometric Singular Perturbation Analysis of a Model for Micro-Electro Mechanical Systems (MEMS)MI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

Many technological devices commonly used today rely on Micro-Electro Mechanical Systems (MEMS). These are defined as very small structures combining electrical and mechanical components on a common substrate to perform several tasks. Their application in various fields such as medicine, transport industry and communications has raised considerable scientific interest.

The aim of this talk is to give a general introduction on the electrostatic-elastic case, where an elastic membrane is allowed to deflect above a ground plate under the action of an electric potential. This situation can be mathematically described by a parabolic PDE with a particular nonlinear source term that can lead to the “touchdown phenomenon”. Mathematically, touchdown causes non existence of steady states and/or finite time blow-up of solutions. A recently proposed model depending on a small “regularization” parameter ε is introduced, where considering additional insulating effects allows to avoid singularities. We use tools from geometric singular perturbation theory and blow-up methods to study the bifurcation of steady-state solutions, emphasizing the interplay between the parameters appearing in the model. In particular, we focus our attention on the singular limit as these small parameters tend to zero.

25.06.2018 16:30 Dr. Christian Mönch (Universität Mannheim):
TBAB 252 (Theresienstr. 39, 80333 München)

TBA

28.06.2018 15:45 TBA:
TBAMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

28.06.2018 17:15 Geneviève Dusson (University of Warwick):
TBAMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)