Deutsche Gedächtnismeisterschaften
Freitag, 7.10.16, 08:30-09:30, Ausgeschilderte Räume in der Eckerstraße 1
Das Mathematische Institut ist am 7. und 8.10.2016 der Gastgeber der deutschen Gedächtnismeisterschaft, der MEMO MASTERS 2016, des Wettbewerbs um das beste Gedächtnis Deutschlands.\n\nFür weitere Informationen, besuchen Sie bitte die verlinkte Homepage der Veranstaltung.
Deutsche Gedächtnismeisterschaften
Samstag, 8.10.16, 08:30-09:30, Ausgeschilderte Räume in der Eckerstraße 1
Das Mathematische Institut ist am 7. und 8.10.2016 der Gastgeber der deutschen Gedächtnismeisterschaft, der MEMO MASTERS 2016, des Wettbewerbs um das beste Gedächtnis Deutschlands.\n\nFür weitere Informationen, besuchen Sie bitte die verlinkte Homepage der Veranstaltung.
Replicating Portfolio Approach to Capital Calculation
Donnerstag, 13.10.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
The replicating portfolio (RP) approach to the calculation of capital for life insurance portfolios is an industry standard. The RP is obtained from projecting the terminal loss of discounted asset liability cash flows on a set of factors generated by a family of financial instruments that can be efficiently simulated. We provide the mathematical foundations and a novel dynamic and path-dependent RP approach for real-world and risk-neutral sampling. We show that the RP approach yields asymptotically consistent capital estimators. We illustrate the tractability of the RP approach by two numerical examples.
Singular weight products on lattices with small discriminant
Freitag, 14.10.16, 13:00-14:00, SR 226, Hermann-Herder-Str. 10
Modular forms are complex valued functions on the upper half plane that\ntransform nicely under the action of some subgroup of\nSL(2,Z), like f((az+b)/(cz+d))) = (cz+d)^k f(z), if a, b, c, d are the coefficients of a matrix, and satisfy\ncertain holomorphy conditions. Here the integer k is called the weight of f. Replacing the codomain by the group algebra of a\ndiscriminant form (a finite abelian group endowed with a quadratic\nform), one obtains vector valued modular forms. These are required to\ninteract with SL(2,Z) via a representation\ndetermined by the respective quadratic form. Borcherds's singular theta\ncorrespondence maps such vector valued modular forms to so-called\nautomorphic products. The latter are meromorphic functions on certain\ncomplex manifolds which also show an interesting transformation\nbehaviour and can be assigned a weight. They have product expansions\nwhich seem to coincide with denominator identities of\ninfinite-dimensional Lie algebras if the weight is singular,\ni.e. minimal in some sense.\n\nThe talk will first give a minimalist introduction to lattices, which\ninduce discriminant forms, and to modular forms. The aim is to present\nthe concept of modular forms for the Weil representation and an\nalgorithm to search for holomorphic automorphic products of singular\nweight, at least in somehow small cases.
Programmdiskussion
Montag, 17.10.16, 16:15-17:15, Raum 404, Eckerstr. 1
Singularities of energy minimizing harmonic mappings from the ball to the sphere
Dienstag, 18.10.16, 16:15-17:15, Raum 404, Eckerstr. 1
Minimizing harmonic maps (i.e. minimizers of the Dirichlet integral) with prescribed boundary conditions from the ball to the sphere may have singularities. For some boundary data it is known that all minimizers of the energy have singularities and the energy is strictly smaller than the infimum of the energy among the continuous extensions (the so called Lavrentiev gap phenomenon occurs). We prove that the Lavrentiev gap phenomenon for harmonic maps into spheres holds on a dense set of zero degree boundary data. This is joint work with P. Strzelecki.
Donnerstag, 20.10.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Competing risks: estimation based on the subdistribution hazard
Freitag, 21.10.16, 09:30-10:30, SR 126 (Raumänderung !)
Contrary to the cause-specific hazard, the subdistribution hazard uniquely determines the cumulative incidence for that cause. Its estimate forms the basis for a nonparametric product-limit type estimate of the cause-specific cumulative incidence. We derive a version using inverse probability weights to correct for right censored and left truncated data that is algebraically equivalent to the classical Aalen-Johansen estimator. Fine and Gray formulated a regression model that assumes proportionality of effects on the subdistribution hazard. When estimating the subdistribution hazard, individuals that experience a competing event remain in the risk set. Therefore, it has been debated whether it is possible to include a time-varying covariable, especially when it is internal: we don't know its value after an individual has died. In the classical survival setting with a single event type, the changing value of a covariable can be represented by creating pseudo-individuals. Each row represents a period during which the value remains constant. The start of this interval can be seen as a form of late entry; it has been called internal left truncation. We can take two different approaches when estimating the subdistribution hazard with time-varying covariables. If we interpret these rows as coming from different pseudo-individuals, we use weights to correct for the late entry. In the other approach, we consider the rows as continuing follow-up form the same individuals and therefore no such weights are used. Using a simple example of a dichotomous time-varying covariable, we contrast the interpretation of the estimates as obtained via both approaches.
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Freitag, 21.10.16, 10:15-11:15, Raum 404, Eckerstr. 1
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The Einstein-Maxwell Equations in Complex Geometry
Montag, 24.10.16, 16:15-17:15, Raum 404, Eckerstr. 1
Originating in physics, LeBrun recently discovered that solutions to the (Euclidean)\nEinstein-Maxwell equations are deeply related to conformally Kähler geometry, at\nleast when an integrable complex structure on space-time is given.\n\nAfter introducing generalizations to higher dimensions of Einstein-Maxwell metrics,\nwe shall discuss their existence from the viewpoint of geometric invariant theory and\nmoment maps. We will also consider the situation when the almost complex structure\nis not integrable.
Sharp-interface limit for the Navier-Stokes-Korteweg equations
Dienstag, 25.10.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Sectional and intermediate Ricci curvature bounds via optimal transport
Dienstag, 25.10.16, 16:15-17:15, Raum 404, Eckerstr. 1
In this talk we present an optimal transport characterization of lower sectional curvature bounds for smooth Riemannian manifolds. More generally, we characterize lower bounds for the p-Ricci tensor in terms of convexity of the relative Reny entropy on Wasserstein space with respect to the p-dimensional Hausdorff measure. The p-Ricci tensor corresponds to taking the trace of the Riemannian curvature tensor on p-dimensional planes. This is a joint work with Andrea Mondino.
Karos, Orakel und ein Typenübergehungssatz
Mittwoch, 26.10.16, 16:30-17:30, Raum 404, Eckerstr. 1
Donnerstag, 27.10.16, 17:00-18:00, Hörsaal II, Albertstr. 23b