Münchner Mathematische KalenderKalender mit mathematischen Vorträgen im Raum MünchenMon, 11 Dec 2017 18:40:19 +0100
http://mathcal.ma.tum.de/mc/showtalks?
04.12.2017 14:15 Alexander Szimayer: Rating Under Asymmetric Information
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1073
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1073We analyze how a firm’s reputation and track record affect its rating and cost of debt. We model a setting in which outsiders such as a rating agency and the firm’s creditors continuously update their assessment of the firm’s true state described by its cash flow. They observe the latter only imperfectly due to asymmetric information. Other things equal, the rating agency optimally rates a firm with the same observed cash flow higher, if the historical minimum is sufficiently low. Thus, the rating is not only driven by the most recent information, but history matters. The rating agency refines its unbiased cash flow estimate by ruling out the most overestimated types, leading to an overestimation at default. In response, the firm delays default and lower asset values are available to creditors upon default.
04.12.2017 15:00 Harry Joe: Estimation of tail dependence coefficients and extreme joint tail probabilities
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1105
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1105Let C be a d-dimensional copula. With a random sample from this copula, several methods are introduced for estimation of the upper and lower tail dependence coefficients, as well as extreme joint tail probabilities such as the probability that all variables exceed their 0.99 quantiles and all variables are below their 0.01 quantiles.
The main theory is based on (i) a tail expansion of the distribution D() of maximum or minimum of the random vector on the copula scale and (ii) a tail expansion of an integral of D(). Item (ii) comes from investigating a tail-weighted dependence measure that is related to an estimate of the extremal index for multivariate extreme value data. The estimation methods for extreme joint tail probabilities consist of (a) likelihood-based threshold methods (for observations of appropriate maxima/minima that lie beyond a threshold, or (b) weighted regression
methods. Examples will be used for illustration of the main ideas.
06.12.2017 14:30 Prof. Dr. Gilad Lerman (University of Minnesota): Non-convex Robust Subspace Recovery
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1111
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1111The setting of robust subspace recovery assumes datasets composed of inliers drawn around a low-dimensional subspace and of outliers that do not lie nearby this subspace. The goal is to robustly determine the underlying subspace of such datasets, while having low computational complexity. We present a mathematical analysis of a non-convex energy landscape for robust subspace recovery. We prove that an underlying subspace is the only stationary point and minimizer in a large neighborhood if a generic condition holds for a dataset. We further show that if the generic condition is satisfied, a geodesic gradient descent method over the Grassmannian manifold can exactly recover the underlying subspace with proper initialization. The condition is shown to hold with high probability for a certain model of data. We also discuss guarantees of another nonconvex strategy and open problems in the area.
see http://www.ma.tum.de/Mathematik/FakultaetsKolloquium#AbstractLerman
06.12.2017 16:00 Prof. Dr. Fabrizio Catanese (Universität Bayreuth): The (never ending?) story of Algebraic geometry: history of the origins and modern classification theory
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1113
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1113The history of algebraic geometry starts with Pythagoras' theorem, and even more with the theorem of Pappus (300 A.D.) , which I shall illustrate as a motivating case for the introduction of projective geometry. There was a long lapse of time between Pappus' theorem and Pascal's theorem (1640 ca). Pascal did not prove his theorem, and similarly occurred for the theorem of Bezout in 1750. The appropriate tools were developed only in the 19th century, through use of the projective coordinates (extending the barycentric coordinates of Moebius) and through the theory of resultants. The Bezout theorem allows powerful generalizations of the theorem of Pappus-Pascal, which I will illustrate. But the greatest breakthrough came in the theory of algebraic surfaces: for instance the discovery of the Lines on a cubic surface, due to Cayley, and conceptually understood through the plane model due to Cremona. The latter brought to the development of birational geometry, where essential was the contribution of the Italian school, not only on the projective side (Del Pezzo, Fano), but especially with the birational classification of algebraic surfaces, due to Castelnuovo and Enriques (1895-1914).
I will especially explain the connections to topology, the genus of a curve, to finally illustrate the \(P_{12}\) theorem which gives the "rough" classification of algebraic surfaces through the 12th plurigenus \(P_{12}\) and the linear genus. Time permitting, I shall talk about later and recent developments (transcendental methods, the fine classification of surfaces, moduli spaces) and open questions.
07.12.2017 16:30 Antti Knowles: Mesoscopic eigenvalue correlations of random matrices.
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1095
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1095Ever since the pioneering works of Wigner, Gaudin, Dyson, and Mehta, the correlations of eigenvalues of large random matrices on short scales have been a central topic in random matrix theory. On the microscopic spectral scale, comparable with the typical eigenvalue spacing, these correlations are now well understood for Wigner matrices thanks to the recent solution of the Wigner-Gaudin-Dyson-Mehta universality conjecture. In this talk I focus on eigenvalue density-density correlations between eigenvalues whose separation is much larger than the microscopic spectral scale; here the correlations are much weaker than on the microscopic scale. I discuss to what extent the Wigner-Gaudin-Dyson-Mehta universality remains valid on such larger scales, for Wigner matrices and random band matrices.
11.12.2017 14:00 Jeff Hogan (The University of Newcastle, Australia): On the search for multidimensional wavelets
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1129
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1129A family of real-valued, regular, compactly supported, orthonormal, multiresolution wavelets on the line was produced by Ingrid Daubechies in 1988. Several of the techniques used by Daubechies, including spectral factorization, are unavailable in higher dimensions. In work with David Franklin (Newcastle) and Matthew Tam (Goettingen) the application of techniques such as iterated projections, the Douglas-Rachford algorithm, and PALM (Proximal Alternating Linearized Minimization) to the construction of (non-tensorial) multidimensional wavelets has been investigated. I'll report on the progress of this project and discuss several extensions we hope to address in future work.
11.12.2017 16:00 Dr. Jan Nagel: Random walk on a barely supercritical branching random walk
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1079
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1079The motivating question for this project is how a random walk behaves on a barely supercritical percolation cluster, that is, an infinite percolation cluster when the percolation probability is close to the critical value. As a more tractable model, we approximate the percolation cluster by the embedding of a Galton-Watson tree into the lattice. When the random walk runs on the tree, the embedded process is a random walk on a branching random walk. Now we can consider a barely supercritical branching process conditioned on survival, with survival probability approaching zero. In this setting the tree structure allows a fine analysis of the random walk and we can prove a scaling limit for the embedded process under a nonstandard scaling. The talk is based on a joint work with Remco van der Hofstad and Tim Hulshof.
11.12.2017 17:30 Dr Daniel Ueltschi (University of Warwick): Random interchange model on the complete graph and the Poisson-Dirichlet distribution
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1125
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1125In 2005, Schramm considered the random interchange model on the complete graph and he proved that the lengths of long cycles have Poisson-Dirichlet distribution PD(1). If one adds the weight 2^{#cycles}, one gets Toth's representation of the quantum Heisenberg model. In this case, we prove (essentially) that long cycles have distribution PD(2). In a related model of random loops, that involves "double bars" as well as "crosses", we prove that long loops have distribution PD(1). Joint work with J. Björnberg and J. Fröhlich.
12.12.2017 14:15 Daniel Cremers (TU München): Combinatorial Solutions to Elastic Shape Matching
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1114
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1114In my presentation, I will focus on four different shape
matching problems, namely the matching between two planar shapes, the
matching between two 3D shapes, the matching between a shape and an
image and the matching between a planar and a 3D shape. In all cases,
I will discuss combinatorial formulations for elastic shape
matching and show how optimal or near-optimal solutions can be
computed using dynamic programming or integer linear programming.
12.12.2017 17:00 Serge Nicaise (Universitè de Valenciennes, France): Regularity of solutions of elliptic problems with Dirac measures as data
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1119
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1119In this talk we study the Laplace equation with Dirac right-hand side.
We prove regularity results in a scale of weighted Sobolev spaces, the
weight being the distance to the support of the right-hand side. Model
situations in dimension three are treated by using Fourier, Laplace or
Mellin technique that reduces the problem to a Helmholtz problem in
two dimensions. Hence the key point stays on estimates for the
solution of the Helmholtz problem in standard or weighted Sobolev
spaces which are uniform with respect to the parameter.
14.12.2017 15:45 Angkana Rueland (MPI Leipzig): Microstructures in Shape Memory Alloys: Rigidity vs Flexibility
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1062
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1062Shape-memory materials undergo a first order, diffusionless phase transformation, in which symmetry is lost. Mathematically, they are often modelled by non-convex, multi-well energies within the framework of the calculus of variations. Minimizers of these energies are often subject to a fascinating dichotomy: While solutions with high regularity are often quite rigid, solutions with low regularity are in many cases very flexible. I will discuss this in the context of the cubic-to-orthorhombic phase transformation, where this dichotomy already arises for the geometrically linearized theory of elasticity.
Further, I will present first results which quantify this dichotomy.
This is based on joint work with C. Zillinger and B. Zwicknagl.
14.12.2017 16:30 Stefan Schreieder: Das Rationalitätsproblem für quadrische Bündel (Antrittsvorlesung)
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1096
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1096Ein klassisches Problem der algebraischen Geometrie beschäftigt sich mit der Frage, welche algebraischen Varietäten rational sind. Es werden kurz die Geschichte dieses Problems sowie einige der wichtigsten Ergebnisse erklärt. Dann wird der Fall von quadrischen Bündeln über rationalen Basen betrachtet und es werden neue Ergebnisse über die Irrationalität solcher Varietäten vorgestellt.
14.12.2017 17:15 Augusto Gerolin (University of Jyväskylä / Finland): Multi-marginal Optimal Transport
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1063
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1063In this talk, we give an overview on theoretical aspects of Optimal Transport for finitely many marginals. The main problem we discuss is to understand when a Monge-Kantorovich minimizer is of Monge-type in this multi-marginal setting. In particular, we highlight the challenging case of repulsive cost functions, which are important for Density Functional Theory.
18.12.2017 14:00 Andreas Langer (Universität Stuttgart): Automated parameter selection for non-smooth image reconstruction problems
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1130
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1130In image reconstruction one often minimizes a non-smooth functional consisting of one or two data- fidelity terms, a regularization term, and parameters, which balance the aforementioned terms. The proper choice of the parameters is delicate. In fact, badly chosen weights either may not only remove noise but also details in images, or retain noise in homogeneous regions. Hence a good reconstruction may be obtained by choosing the parameters such that a good compromise of the aforementioned effects are made.
We revisit the disrcepancy principle and demonstrate how it can be used for finding parameters in functionals consisting of one and two data terms. However, since images consist of multiple objects of different scales, it is expected that spatially varying weights would give better reconstructions than a scalar parameter. In this vein we adapte our proposed algorithm for computing distributed weights. We study the convergence behaviour of the proposed algorithms and present several numerical experiments for image reconstruction.
18.12.2017 15:00 Christian Bick (University of Oxford, UK): Oscillator Networks: Collective Dynamics through Generalized Interactions
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1128
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1128The function of many real-world systems that consist of interacting oscillatory units depends on their collective dynamics such as synchronization. The Kuramoto model, which has been widely used to study collective dynamics in oscillator networks, assumes that interactions between oscillators is determined by the sine of the differences between pairs of oscillator phases. We show that more general interactions between identical phase oscillators allow for a range of collective effects, ranging from chaotic fluctuations to dynamics of localized frequency synchrony patterns.
18.12.2017 16:30 Dr. Caio Teodoro De Magalhaes Alves (Universität Leipzig) : TBA
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1110
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1110TBA
21.12.2017 16:30 Dirk Hundertmark: Eine kurze Geschichte schwach gebundener Zustände in der Quantenmechanik.
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1097
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1097Quantenmechanik in einer und zwei Dimensionen ist vollkommen anders als in höherer Dimension. Warum ist dies so, und wie ist das mit der berühmten Cwikel-Lieb-Rosenblum-Schranke verbunden?