findet jeweils ab 16:15 Uhr im Raum 611 statt.
Sommer 2018  Sommer 2023
Datum  Sprecher  Herkunft  Titel/Bemerkungen 

05. Juli 2023  Christian Scharrer 
Bonn  
27. Juni 2023 (Beginn 14:15 Uhr im Banachraum)  Klaus Widmayer  Zürich/Wien 
On the stability of a point charge for the VlasovPoisson system ================================================== We consider the dynamics of the repulsive VlasovPoisson equations near a point charge, addressing the question of its stability: For solutions which start as small, smooth and suitably localized perturbations of a point charge we capture the precise asymptotic behavior. Building on optimal decay estimates, this is revealed to be a modified scattering dynamic. Our analysis relies on the Hamiltonian/symplectic structure of the equations, and makes use of an exact integration of the linearized equation through angleaction coordinates. This is joint work with Jiaqi Yang (ICERM) and Benoit Pausader (Brown University). 
21. Juni 2023  Dominic Breit  TU Clausthal  
14. Juni 2023  
06. Juni 2023 (Beginn 14:15 Uhr im Banachraum)  Jacobus Portegies  TU Eindhoven 
(Semi)continuity of Krasnoselskii eigenvalues under convergence of the underlying spaces ================================================== The general question in this talk is whether eigenvalues of operators defined on geometric spaces converge as these spaces converge to a limit space. Because the operators that we consider are often nonlinear, we need proper generalizations of eigenvalues, such as Krasnoselskii eigenvalues. I'll describe how to obtain continuity for eigenvalues of the Laplace operator defined on CD(K,N) spaces under measured GromovHausdorff convergence, and I will explain how to get semicontinuity of Krasnoselskii eigenvalues under volume flat convergence. The talk contains results from joint works with Luigi Ambrosio, Shouhei Honda, Jeff Jauregui and Raquel Perales. 
23. Mai 2023 (Beginn 14:15 Uhr im Banachraum)  Sebastian Hensel 
Bonn 
Stability of planar multiphase mean curvature flow beyond circular topology change ================================================== A classical result of GageHamilton and Grayson asserts that any smooth, closed and simple curve in the plane evolving by mean curvature flow (MCF) shrinks to a point in finite time and becomes circular in the process. We establish a weakstrong stability result beyond the time of such circular topology change: any weak (i.e., BV) solution of planar multiphase MCF starting sufficiently close to a smooth, closed and simple curve evolving by MCF has to stay close to it for all times.

9. Mai 2023 (Beginn 14:15 Uhr im Banachraum)  Paul Dario  Paris 
Rigidity of harmonic functions on the supercritical percolation cluster ================================================== We study the behavior of harmonic functions on the infinite cluster in supercritical Bernoulli bond percolation. Most of the results which have been proved on these functions assert that they behave similarly to the harmonic functions on the lattice Zd (a typical example is the Liouville theorem on the percolation cluster). In this talk, we will be interested in the differences between harmonic functions on the lattice and on the percolation cluster through some specific properties. In this direction, we prove that there cannot exist a Lipschitz harmonic function on the percolation cluster. This property is false on the lattice as the function x > x_1 is both 1Lipschitz and harmonic. We will review some of the known results on harmonic functions on the percolation cluster and discuss some ideas of the proof. This is joint work with A. BouRabee and W. Cooperman. 
03. Mai 2023  Anna Balci 
Bielefeld 
Maximal Regularity for Equations with Degenerate Weights ================================================== We study local and global maximal regularity estimates for elliptic equations with degenerate weights. We show that higher integrability of the gradients can be obtained by imposing a local small oscillation condition on the weight and a local small Lipschitz condition on the boundary of the domain. Our results are new in the linear and nonlinear case. We show by example that the relation between the exponent of higher integrability and the smallness parameters is sharp even in the linear or the unweighted case. We study the regularity of the weighted Laplacian and pLaplacian with degenerate elliptic matrixvalued weights. We establish a novel logarithmic BMOcondition on the weight that allows to transfer higher integrability of the data to the gradient of the solution.The talk is based on joint works with Lars Diening, Raffaella Giova, Antonia Passarelli di Napoli, SunSig Byun and HoSik Lee. 
25. April 2023 (Beginn 14:15 Uhr im Banachraum)  Antonio Tribuzio  Bonn 
Energy scaling of singularperturbation models involving higherorder laminates ================================================== Motivated by the appearance of complex microstructures in the modelling of shapememory alloys, we study the energy scaling behaviour of some Nwell problems with surface energy given by a singular higherorder term. In the case of absence of gauge invariances (e.g. with respect to the action of SO(n) or Skew(n)), we provide an ansatzfree lower bound which relies on a bootstrap argument in Fourier space and gives evidence of the higher order of lamination involved. The upper bound is provided by iterated branching constructions. 
03. Februar 2023 (Beginn 12:00 Uhr in Raum M511)  Alexandre GirodrouxLavigne  Paris 
Homogenization of stiff inclusions through network approximation ================================================== The homogenization of a conductive medium randomly perforated with inclusions of infi 
17. Januar 2023 (Beginn 12:15 Uhr in Raum M611) 
Konstantinos Zemas  Münster 
Homogenization of nonlinear randomly perforated materials under minimal assumptions on the geometry ================================================== In this work we combine and generalize earlier works of GiuntiHöferVelazquez (on the homogenization of the Poisson equation in random critically perforated domains) and AnsiniBraides (on a variational approach for the more general nonlinear vectorial problem in the periodic setting), each one in the direction of the other. Namely, we show that under similar general assumptions on the geometry of the random perforations as the ones posed in the work of GiuntiHöfer and Velazquez, the stochastic analogue of the result of AnsiniBraides holds true, with an average deterministic nonlinear capacitaryterm appearing in the Γlimit. This is joint, ongoing work with Caterina Zeppieri and Lucia Scardia. 
11. Januar 2023 (Beginn 14:15 Uhr in Raum M511) 
Mitia Duerinckx 
Effective viscosity of dilute suspensions ================================================== This talk is devoted to the largescale rheology of systems of suspended particles in a Stokes fluid. After reviewing recent results on the definition of the effective viscosity of such systems in terms of homogenization theory, I will focus on its asymptotic expansion in dilute regime. I will present a new, optimal proof of Einstein's viscosity formula for the firstorder expansion and show how to pursue the asymptotic expansion to higher orders. The essential difficulty originates in the longrange nature of hydrodynamic interactions: these require suitable renormalizations, which will be systematically captured by means diagrammatic expansions. This is based on joint work with A.Gloria. 

29. November 2022 (Beginn 12:15 Uhr im Banachraum) 
Fabian Rupp 
Wien 
Multiplicity and curvature ================================================== A classical inequality of Li and Yau gives a lower bound on the Willmore energy of a surface in terms of its multiplicity at an arbitrary point. We discuss recent extensions to other curvaturedependent bending energies, such as Euler's elastic energy or the CanhamHelfrich functional. Additionally, we illustrate applications to geometric flows and the regularity of minimizers. 
16. November 2022 
Matteo Capoferri und Mikhail Cherdantsev 
A new paradigm for the spectral theory of systems ================================================== I will present a new approach to the spectral theory of systems of PDEs on closed manifolds, developed in a series of recent papers by Dmitri Vassiliev (UCL) and myself, based on the use of pseudodifferential projections. Emphasis will be placed on ideas and motivation; the talk will include a brief historical overview of the development of the subject area. ================================================== Highcontrast random composites: homogenisation framework and new spectral phenomena ================================================== We study the homogenisation problem for elliptic operators with highcontrast random coefficients describing a twophase composite with the heterogeneity scale $\epsilon$ made up of small inclusions randomly distributed in a matrix component. It is assumed that the coefficients of the operator are of order one in the matrix component and of order $\epsilon^2$ in the inclusions (socalled double porosity scaling). Highcontrast composites receive special attention in scientific community due to the bandgap structure of their spectrum. In this talk I will give an introduction to the highcontrast setting followed by an overview of our recent results in the topic and some ongoing work. 

02.November 2022 
Marco Bravin 
Delft 
A connection between homogenisation of compressible NavierStokes and fluidstructure problems ================================================== In this talk I will present some recent improvements in the study of homogenisation of compressible viscous fluid in the case of tiny holes and the connection with fluid structure problems. In particular I highlight a situation where the fluid + rigid body problem has more flexibility respect to case of the fluid alone. This flexibility helps us to deduce new ideas to study the case of the fluid alone. 
29. September 2022 (Beginn: 14:15 Uhr im Raum M611) 
Andreas Kirsch  Karlsruhe 
The factorization method in inverse scattering theory 
08. Juni 2022  Georgiana Chatzigeorgiou 
Up to the boundary regularity for BVPs governed by Fully Nonlinear Operators ================================================== We introduce the notion of viscosity solutions for second order fully nonlinear elliptic/parabolic equations. A viscosity solution, u, is defined through the condition that whenever a test function, φ, touches u from below/above at a point then φ should be a classical super/subsolutions of the equation at this point. Since u is apriori merely continuous, it is natural to study whether the equation finally impose any regularizing effects on u. We start by giving an overview of the theory that have been developed the last decades on the interior regularity properties of viscosity solutions, introducing the main tools used, namely the ABP and Harnack inequalities. Then we shall concentrate on oblique derivative problems (where the oblique derivative condition is understood only in the viscosity sense as well) and discuss about the up to the boundary (first order) Hölder regularity of the solutions giving quantitative bounds for the corresponding Hölder norms in terms of the data. 

09. Februar 2022  Christopher Irving 
Regularity results for LegendreHadamard elliptic systems ================================================== I will discuss the regularity of solutions to quasilinear systems satisfying a LegendreHadamard ellipticity condition. For such systems it is known that weak solutions may which fail to be C^1 in any neighbourhood, so we cannot expect a general regularity theory. However if we assume an apriori regularity condition of the solutions we can rule out such counterexamples. Focusing on solutions to EulerLagrange systems, I will present an improved regularity results for solutions whose gradient satisfies a suitable BMO / VMO condition. Ideas behind the proof will be presented in the interior case, and global consequences will also be discussed. 

08. Februar 2022 (Beginn 14:15 Uhr)  Roberta Marziani 
Münster 
Asymptotic analysis of singularly perturbed elliptic functionals & application to stochastic homogenization. ================================================== In this talk we introduce a general class of singularlyperturbed elliptic functionals Fε and we study their asymptotic behaviour as the perturbation parameter ε > 0 vanishes. Under suitable 
02. Februar 2022  Richard Schubert 
Bonn 
An L^1 based approach to optimal relaxation of gradient flows: bumplike solutions of the 1D CahnHilliard equation ================================================== In the beginning we will review the classical approaches to obtain exponential or algebraic rates of convergence towards minimizers of the energy in the case of gradient flows in (strictly) convex energy landscapes. We will discuss advantages and disadvantages of this method generalized to mildly nonconvex energies and in particular try to understand in which cases this approach yields optimal rates. In the second part of the talk we will consider a more robust, but related method that relies on L^1type distances instead of the "natural" distance associated to the gradient flow. By means of example we will consider the CahnHilliard equation in one dimension and look at solutions with two transition layers. Here, in contrast to the case of one transition layer, the longtime limit is not fixed by mass conservation and in order to control the dynamics, a detailed understanding of the movement of the transition layers is needed. This talk is based on joint work with Sarah Biesenbach and Maria G. Westdickenberg 
01. Februar 2022 (Beginn 14:15 Uhr) 
Jakob Fuchs 
Bonn 
The Thresholding Scheme for the Mean Curvature Flow of Mean Convex Sets ================================================== Merriman, Bence and Osher's thresholding scheme is a 
08. Dezember 2021  Juan Velazquez 
Bonn 
Oscillatory solutions of coagulationfragmentation equations 
01. Dezember 2021  Fatima Zohra Goffi 
The effective characterization of metamaterials with nonlocal constitutive relations 

24. November 2021  David GérardVaret  Paris 
Network approximation in high contrast homogenization ================================================== We will discuss the homogenization of inclusions of infinite conductivity, randomly stationary distributed inside a homogeneous conducting medium. 
17. November 2021  Leonard Kreutz 
Münster 
GEOMETRIC RIGIDITY IN VARIABLE DOMAINS ================================================== 
10. November 2021  Tim Laux  Bonn 
A new varifold solution concept for mean curvature flow: Convergence of the AllenCahn equation and weakstrong uniqueness ================================================== Weak solution concepts for mean curvature flow have been investigated since the seminal work of Brakke in the 70’s. We propose a new weak solution concept for (twophase) mean curvature flow which enjoys both (unconditional) existence and (weakstrong) uniqueness properties. These solutions are evolving varifolds, just as in Brakke's formulation, but are coupled to the phase volumes by a simple transport equation. First, we show that, in the exact same setup as in Ilmanen's proof [J. Differential Geom. 38, 417461, (1993)], any limit point of solutions to the AllenCahn equation is a varifold solution in our sense. Second, we prove that any calibrated flow in the sense of Fischer et al. [arXiv:2003.05478]  and hence any classical solution to mean curvature flow  is unique in the class of our new varifold solutions. This is in sharp contrast to the case of Brakke flows, which a priori may disappear at any given time and are therefore fatally nonunique. Finally, we propose an extension of the solution concept to the multiphase case which is at least guaranteed to satisfy a weakstrong uniqueness principle. This is joint work with Sebastian Hensel (U Bonn). 
03. November 2021  Martin Huesmann  Münster 
Optimal matching and large scale regularity theory for optimal transportation ================================================== Abstract: The optimal matching problem is one of the classical random optimization problems. The macroscopic behaviour is well understood since the work of Ajtai, Komlos, Tusnady, Talagrand and others in the 80s and early 90s. A few years ago, Caracciolo et al. proposed a new ansatz, based on a linearisation of the MongeAmpere equation to the Poisson equation, to get refined estimates for this problem. I will show how one can justify this approach in a quantitative way leading to a large scale regularity theory for the optimal transport problem. This in turn can then be used to get new information on the matching problem, like convergence to a Gaussian field which we will shortly discuss at the end of the talk. 
06. Oktober 2021 (16:15 Uhr, Raum M614) 
Eduard Feireisl  Prag 
Computing oscillatory solutions in fluid mechanics Oscillatory solutions to models of inviscid fluids may be described by probability distribution of certain phase variables in terms of the Young measure. Using the analytical results of 
08. Juli 2021 
Manuel Friedrich 
Münster 
Emergence of rigid polycrystals from atomistic systems Wenn Sie an der Veranstaltung teilnehmen wollen, dann melden Sie sich bitte bei Fiona Drees (fiona.drees@tudortmund.de) an. 
30. März 2020 
Manuel Friedrich  Münster  Equilibrium configurations for epitaxially strained films in threedimensional linear elasticity (Cancelled) 
23. März 2020  Eduard Feireisl 
Prag 
Solving illposed problems: Analysis and numerics (Cancelled) 
3. März 2020 
Marc Pegon 
Paris 
Large mass minimizers for isoperimetric problems with integrable nonlocal potentials 
2.März 2020  Sonia Fliss 
Paris 
On the analysis of periodic waveguides 
20. Januar 2020  Illia Karabash 
Dortmund 
Pareto maximization of Qfactor in photonic crystals 
13. Januar 2020  Sascha Eichmann 
Tübingen 
Minimising the CanhamHelfrich energy 
21. Oktober 2019  Yohanes Tjandrawidjaja 
Paris 
The HalfSpace Matching Method and its application to Wave Scattering in Elastic Plates 
9. Juli 2019  Koondanibha Mitra  Eindhoven 
Travelling wave and entropy solutions for twophase flow including hysteresis and dynamic pressure 
28. Januar 2019  C.J. van Duijn 
Eindhoven 
Verschoben. 
21. Januar 2019  Angkana Rüland 
Leipzig 
Uniqueness, stability and single measurement recovery for the fractional Calder\'on problem 
16. Januar 2019 (Mittwoch)  Pavel Krejci 
Prag 
Controllability of PDEs with hysteresis 