Ghent University/Maastricht University
Are almost all graphs determined by their spectrum?
In this talk we will look at the spectrum (eigenvalues) of the adjacency matrix of a graph, and ask whether the eigenvalues determine the graph. This is a difficult, but important problem which plays a special role in the famous graph isomorphism problem. It has been conjectured by van Dam and Haemers that almost every graph is determined by its spectrum. The mentioned problem has been solved for several families of graphs; sometimes by proving that the spectrum determines the graph, and sometimes by constructing nonisomorphic graphs with the same spectrum. In recent years this problem has attracted much interest. In this talk we will report on recent results concerning this conjecture.
Foliations and CR geometry
I will discuss holomorphic foliations on a complex manifold from the point of view of the exceptional minimal set conjecture. In particular I am interested in curvature conditions for the holomorphic normal bundle of the foliation. The main result is that if the holomorphic normal bundle is positive in the sense of Griffiths, then the foliation does not admit a compact invariant set that is a complete intersection of smooth real hypersurfaces. As a by-product, we obtain classification results for compact Levi-flat CR manifolds.
Discrete models for atmospheric turbulence
In this talk we introduce a discrete model for atmospheric turbulence,
which was originally derived by Helmholtz from the Euler equations.
We state some of it basic properties and show how we can derive an
effective PDE, the so-called mean field limit, from the discrete
Hamiltonian system, by using a variational principle.
Furthermore, we discuss the extension of these methods to generalized
surface quasigeostrophic models and show how tools from probability
theory can help us to get more information about turbulence phenomena.
The content of this talk is based on work in collaboration with Marco
Romito (Uni Pisa), the presentation tries to avoid technicalities and to
be accessible to a mixed audience.
Serena Guarino Lo Bianco
University of Naples Federico II
Anisotropic Variant of the BMO--type seminorms
The purpose of this talk is to present the relation between certain BMO–type seminorms and the total variation of SBV functions
Recently, Bourgain, Brezis and Mironescu introduced a new BMO–type space B ⊂ L1(Q) on the unit cube Q ⊂ ℝn, by mean of the seminorm
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where [f]𝜀 is deﬁned with a suitable maximization procedure. The space B contains BMO and the space BV of functions of bounded variation.
Later Ambrosio, Bourgain, Brezis and Figalli give a new characterization of the perimeter of sets in terms of this seminorm considering characteristic functions of sets, was studied. Further results characterizing total variation of SBV functions and norm of Sobolev functions, independent of theory of distributions, were given by Fusco, Moscariello, Sbordone.
Using a diﬀerent approach, by considering in (1), instead of cubes, covering families by translations of a given open bounded set with Lipschitz boundary, we give a representation formula of the total variation of SBV function.
Technische Universität Berlin
A Lanczos method fo Port-Hamiltonian systems
The framework of port-Hamiltonian systems (PH systems) combines both the Hamiltonian approach and the network approach, by associating with the interconnection structure of the network model a geometric structure given by a Dirac structure. A Lanczos method for non-symmetric systems of linear equations that exploits the structure of PH systems has been derived. The results from a series of parametrized numerical experiments are presented to show the numerical
stability and behavior of the solution depending on the parameters.
Johannes Guttenberg University Mainz
Extreme value theory and branching processes
After giving an overview on well known results on extreme values for sequences of independent identically distributed random variables, we turn to a class of models that exhibit a logarithmic correlation structure.
As it turns out a (sometimes hidden) branching structure helps to understand the effect of correlations. In this talk we will focus on one such model which is called branching random walk. I will explain how first and (truncated) second moment computations can be used to determine the order of the maximum.
Ludwig Maximilian University of Munich
Trees, functional inversion, and the virial expansion
Trees are ubiquitous. Probabilists may think of branching processes and ask about extinction or survival. The recursive structure of trees leads to functional equations for generating functions, of interest in analytic combinatorics. Trees also help organize power series expansions in various areas of analysis and mathematical physics, from numerics (Butcher trees) to renormalization (Gallavotti-Niccolo trees). The talk presents yet another application, namely inverse function theorems for functionals in measure spaces for which Banach inversion is not possible. Combined with cluster expansions from equilibrium statistical mechanics, the theorem allows for a rigorous derivation, in a restricted parameter regime, of density functionals used in analytic models of materials. The talk is based on joint work with Tobias Kuna and Dimitrios Tsagkarogiannis (arXiv:1906.02322 [math-ph]) and considerably improves earlier results based on Lagrange-Good inversion (J., Tate, Tsagkarogiannis, Ueltschi, CMP 2014).
Balanced manifolds or how to decorate a pumpkin
The enumeration of faces of various types of simplicial complexes is a promnent topic in algebraic, topological and geometric combinatorics. In this talk, I will first provide a short survey on what is known for general simplicial complexes, simplicial polytopes and triangulations of manifolds. In the second part, the focus lies on balanced simplicial complexes, i.e., simplicial complexes whose underlying graph permits a minimal proper coloring in the graph-theoretic sense.
Technische Universität Chemnitz
Moser iteration applied to elliptic problems with critical growth on the boundary
Technical University of Munich
Stochastic cross-diffusion systems
We investigate the well-posedness of stochastic cross-diffusion systems. Such problems arise in many application areas like fluid dynamics of mixtures, cell biology and biofilm mmodeling. Cross-diffusion occurs if the gradient in the concentration of one species induces a flux of another species. Famous examples are given by the Maxwell-Stefan systems or bacterial biofilm models. The stochastic terms quantify the lack of knowledge of certain parameters or fluctuations which occur due to external perturbations. We explore a formal gradient-flow or entropy structure of these equations and an interplay between the entropy density and the stochastic terms in order to investigate properties of the solution.
This talk is based on a joint work with G. Dhariwal, F.Huber, A.Jüngel (Vienna University of Technology) and Christian Kuehn (Technical University of Munich).
Symmetries of discrete structures
Though perhaps not true in high dimensions our experience in small
dimension shows that beautiful objects do have symmetries.
Symmetries are my guide to construct extremal codes and lattices.
The notion of extremality stems from a very fruitful connection between codes and invariant theory of finite groups and its analogous relation between lattices and modular forms.
Invariant theory allows to upper bound the error correcting properties of codes in certain families. Codes achieving this upper bound are called extremal. In 1973 Neil Sloane published a short note asking whether there is an extremal code of length 72. Since then many mathematicians search for such a code, developing new tools to narrow down the structure of its symmetry group. We now know that, if such a code exists, then it has at most 5 symmetries.
The methods for studying this question involve explicit and constructive
applications of well known classical theorems in algebra and group theory,
like Burnside's orbit counting theorem and quadratic reciprocity,
as well as basic representation theoretic methods and tools from the theory of quadratic forms.
Similar methods have been recently developed to study extremal lattices
admitting certain symmetries.
In my talk I will survey the results obtained on extremal codes and lattices
and give some nice examples of the use of symmetries to reduce the search space.
University of Potsdam
Are locality and renormalisation reconcilable?
Sylvie Paycha, University of Potsdam, on leave from the University
According to the principle of locality in physics, events taking place
at different locations should behave independently, a feature expected
to be reflected in the measurements. The latter are compared with
theoretic predictions which use renormalisation techniques in order to
deal with divergences from which one wants to derive finite quantities.
The purpose of this talk is to confront locality and renormalisation.
We shall present a multivariate approach to renormalisation which
encodes locality as an underlying algebraic principle. It can be
applied to various situations involving renormalisation, such as
divergent multizeta functions and their generalisations, namely
discrete sums on cones and discrete sums associated with trees.
This talk is based on joint work with P. Clavier, L. Guo and B. Zhang
Max Planck Institute for Mathematics in the Sciences
Computational Algebraic Analysis
The language of D-modules permits an investigation of linear differential equations by algebraic methods. In this talk, I want to give an insight into computational aspects of the theory.
Otto von Guericke University Magdeburg
Tangent cones of Schubert varieties in Type A
One way to define Type A Schubert varieties is as matrix varieties, that is as a subset of SLn satisfying some extra conditions.
The geometry of this variety is tightly connected to the combinatorics of the symmetric group Sn on n letters. Moreover to each element w in S_n there exists one such variety X_w.
In this talk I will explain a new approach to a characterization which Schubert varietes X_w and X_v for different w,v in S_n share the same tangent cone at the identity.
This is joint work with Stephane Gaussent (Saint Etienne).
No prior knowledge of Schubert varieties will be assumed.
Ewa B. Weinmüller
Numerical Treatment of Implicit Singular BVPs in ODEs
Technical University of Berlin
Variational models for pattern formation in materials
The formation of patterns or microstructures in materials can often be understood as the result of a competition between different energy contributions, for example an elastic bulk energy and a (higher order) surface energy. Among many others, typical examples include microstrcuctures in shape-memory alloys, shape formation in elastically strained thin crystalline films, and the formation of rafts in biomembranes. In this talk, I shall discuss some recent analytical results on the associated variational problems, which typically involve vectorial, non-convex nonlinear functionals.
- Francesca Arici, Radboud University Nijmegen
- Tatjana Eisner, Leipzig University
- Barbara Gentz, University of Bielefeld
- Angkana Rüland, MPI for Mathematics in the Sciences
- Rebecca Waldecker, Martin-Luther-University Halle-Wittenberg
- Milena Wrobel, Carl von Ossietzky Universität Oldenburg
Administrative ContactValeria Hünniger
MPI for Mathematics in the Sciences
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