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Spring Semester 2017
Note: The highlighted event marks the next occurring event and events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.
Date / Time  Speaker  Title  Location  

31 January 2017 15:1516:15 
Prof. Dr. David Kinderlehrer Carnegie Mellon University 
The gradient flow of microstructure  HG G 43  
Abstract: A central problem of microstructure is to develop technologies capable of producing an arrangement, or ordering, of the material, in terms of mesoscopic parameters like geometry and crystallography, appropriate for a given application. Is there such an order in the first place? We describe the emergence of the grain boundary character distribution (GBCD), a statistic that details texture evolution, and illustrate why it should be considered a material property. The theory relies on mass transport and entropy methods, and as a consequence we seek to identify it as a gradient flow in the sense of Ambrosio, Gigli, and Savaré. In this way, the empirical texture statistic is revealed as a solution of a FokkerPlanck type equation whose limit behavior is a Boltzmann distribution, which, is in fact, observed in simulation. The development exposes the question of how to understand the circumstances under which a harvested empirical statistic is a property of the underlying process. (joint work with P. Bardsley, K. Barmak, E. Eggeling, M. Emelianenko, Y. Epshteyn, X.Y. Lu and S. Ta’asan)  
7 March 2017 15:1516:15 
Prof. Dr. Rosario Mingione Università degli studi di Parma 
Nonstandard growth conditions, double phase functionals and regularity  HG G 43  
Abstract: Regularity problems for nonuniformly elliptic operators are delicate, since they cannot be classified in a single family, but they rather show very different features and problematic aspects. I will give a brief summary of some results in this direction.  
14 March 2017 15:1516:15 
Prof. Dr. Jan Metzger Universität Potsdam 
On the uniqueness of small surfaces minimizing the Willmore functional subject to a small area constraint (CANCELLED)  HG G 43  
Abstract: We consider the Willmore functional for surfaces immersed in a compact Riemannian manifold M and study minimizers subject to a small area constratint. We show that if the scalar curvature of M has a nondegenerate maximum then for small enough area these minimizers are unique. This is joint work with Tobias Lamm and Felix Schulze.  
21 March 2017 15:1516:15 
Dr. Xavier RosOton University of Texas at Austin 
Regularity of free boundaries in obstacle problems  HG G 43  
Abstract: We present a brief overview of the regularity theory for free boundaries in different obstacle problems. We describe how a monotonicity formula of Almgren plays a central role in the study of the regularity of the free boundary in some of these problems. Finally, we explain new strategies which we have recently developed to deal with cases in which monotonicity formulas are not available.  
28 March 2017 15:1516:15 
Prof. Dr. Melanie Rupflin University of Oxford 
Title T.B.A.  HG G 43  
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5 April 2017 14:0015:00 
Prof. Dr. Max Fathi Université de Toulouse 
Gradient flows and scaling limits for interacting particle systems  HG G 19.1  
Abstract: In this talk, I will explain how the gradient flow framework for Markov chains on finite spaces that was introduced in 2011 by Maas and Mielke can be combined with the SandierSerfaty theorem on convergence of gradient flows to study scaling limits for interacting particle systems on lattices. The talk will be focused on the case of the simple exclusion process. Joint work with Marielle Simon (INRIA Lille).  
25 April 2017 15:1516:15 
Prof. Dr. Matteo Bonforte Universidad Autónoma de Madrid 
Nonlinear and Nonlocal Degenerate Diffusions on Bounded Domains  HG G 43  
Abstract:
We investigate quantitative properties of nonnegative solutions $u(t,x)\ge 0$ to the nonlinear fractional diffusion equation, $\partial_t u + \mathcal{L} F(u)=0$ posed in a bounded domain, $x\in\Omega\subset \mathbb{R}^N$\,, with appropriate homogeneous Dirichlet boundary conditions. As $\mathcal{L}$ we can use a quite general class of linear operators that includes the three most common versions of the fractional Laplacian $(\Delta)^s$, $0 

2 May 2017 15:1516:15 
Dr. Stefano Spirito Università degli Studi dell'Aquila 
Lagrangian Solutions of 2D Euler equations  HG G 43  
Abstract: Lagrangian Solutions of two dimensional Euler equations are, roughly speaking, solutions for which the vorticity is transported by the flow of the velocity. In this talk I will firstly give an overview regarding the existence of Lagrangian solutions and secondly I will discuss a recent result with Gianluca Crippa, Camilla Nobili, and Christian Seis concerning the convergence of NavierStokes solutions to Lagrangian solutions of 2D Euler in the vanishing viscosity limit. A crucial point in the proof of this result is a new uniqueness theorem, interesting in its own right, for solutions of the linear continuity equation with non smooth vector field (Singular integral of an L^1 function)  
9 May 2017 15:1516:15 
Dr. Armin Schikorra Universität Freiburg 
On free boundary problems for conformally invariant variational functions  HG G 43  
Abstract: I will present a regularity result at the free boundary for critical points of a large class of conformally invariant variational functionals. The main argument is that the EulerLagrange equation can be interpreted as a coupled system, one of local nature and one of nonlocal nature, and that both systems (and their coupling) exhibit an antisymmetric structure which leads to regularity estimates.  
16 May 2017 15:1516:15 
Prof. Dr. Carlo Sinestrari Università di Roma "Tor Vergata" 
Convex ancient solutions of curvature flows  HG G 43  
Abstract: We consider compact convex hypersurfaces evolving by mean curvature flow which are ancient, that is, defined for all negative times. Solutions with these properties occur as the limit of rescalings near a singularity of a general mean convex solution of the flow. The easiest example is a shrinking sphere, but there are other known examples having an oval shape which becomes more and more eccentric for negative times. In this talk we consider various sufficient conditions which ensure that our solution is a shrinking sphere. Examples are: a uniform pinching on the principal curvatures, a growth rate assumption on the diameter, a bound on the ratio of outer and inner radius, a bound on the isoperimetric ratio. These results are in collaboration with G. Huisken. The characterization of the shrinking sphere via the uniform pinching property has been also obtained in more general contexts, such as higher codimensional mean curvature flow, or other extrinsic curvature flows (results in collaboration with S. Risa). Other related results have been obtained by R. Haslhofer and O. Hershkovits and by M. Langford and S. Lynch.  
23 May 2017 15:1516:15 
Prof. Dr. Walter Craig McMaster University 
Vortex filament dynamics  HG G 43  
Abstract: The evolution of vortex filaments in three dimensions is a central problem in mathematical hydrodynamics, appearing in questions on solutions of the Euler equations as well as in the fine structure of vortex filamentation in a superfluid. It is also a setting in the analysis of partial differential equations with a compelling formulation as a Hamiltonian dynamical systems in an infinite dimensional phase space. I will give an analysis of a system of model equations for the dynamics of nearparallel vortex filaments in a three dimensional fluid. These equations can be formulated as Hamiltonian PDEs, and the talk will describe some aspects of a phase space analysis of solutions, including the construction of periodic and quasiperiodic orbits via a version of KAM theory for PDEs, and a topological principle to count multiplicity of solutions. This is ongoing joint work with L. Corsi (Georgia Tech), C.  
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30 May 2017 14:1515:15 
Prof. Dr. Tobias Lamm KIT Karlsruhe 
Limits of alphaharmonic maps  HG G 43  
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30 May 2017 15:4516:45 
Prof. Dr. Nicos Kapouleas Brown University 
Gluing constructions for minimal surfaces and related questions  HG G 43 
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