Automorphe Formen auf orthogonalen Gruppen
Thursday, 3.5.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Wir geben eine kurze Einführung in die Theorie der automorphen Formen auf orthogonalen Gruppen und beschreiben Anwendungen in der Theorie der unendlich-dimensionalen Lie-Algebren
Kirwan polytopes and representations
Monday, 7.5.12, 16:15-17:15, Raum 404, Eckerstr. 1
Constrained Willmore tori in S^3
Tuesday, 8.5.12, 16:15-17:15, Raum 404, Eckerstr. 1
Canonization of hypersmooth equivalence relations
Wednesday, 9.5.12, 16:30-17:30, Raum 404, Eckerstr. 1
Thursday, 10.5.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Kähler-Einstein metrics with edges
Monday, 14.5.12, 16:15-17:15, Raum 404, Eckerstr. 1
I will discuss the geometric problem of finding KE metrics which are bent along a divisor, and the equivalent analytic problem of solving the associated singular Monge-Ampere equation. There are several interesting applications for these metrics. Furthermore, the classical Aubin-Yau estimates do not work in this setting and a new route to the solvability of this equation must be found. This is joint work with Jeffres and Rubinstein.
Thursday, 17.5.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Kozykel für charakteristische Klassen in der glatten Deligne-Kohomologie
Monday, 21.5.12, 16:15-17:15, Raum 404, Eckerstr. 1
Aufbauend auf den Ergebnissen meines letzten Vortrags werde ich (nach einer kurzen Wiederholung) die Unabhängigkeit von getroffenen Wahlen und die Natürlichkeit der Konstruktion untersuchen.
Numerical Ricci-DeTurck flow
Tuesday, 22.5.12, 16:15-17:15, Raum 404, Eckerstr. 1
We present a numerical method for the computation of\nn-dimensional Ricci-DeTurck flow.\nRicci flow is a geometric flow deforming a time-dependent\nmetric on a Riemannian manifold\nproportional to its Ricci curvature. Ricci-DeTurck flow is\na reparametrization of this flow\nusing the harmonic map flow in order to get a strictly\nparabolic PDE.\nOur numerical method is based on the assumption\nthat the manifold is orientable and differentiably\nembeddable in \bR^{n+1}.\nBy this means, it is possible to do computations in the\nbasis of the ambient space.\nA weak formulation of Ricci-DeTurck flow is derived such\nthat it only contains tangential gradients.\nA spatial discretization of this formulation with finite\nelements on polyhedral hypersurfaces\nand an implicit time discretization lead to an algorithm\nfor computing Ricci-DeTurck flow.\nWe have performed numerical tests for two and three\ndimensional hypersurfaces\nusing piecewise linear finite elements.\nThe generalization to non-orientable hypersurfaces of\nhigher codimensions is still open.\n
On an old question of Lusin concerning countably continuous Borel functions
Wednesday, 23.5.12, 16:30-17:30, Raum 404, Eckerstr. 1
Abstract: A famous question of Lusin asked whether every Borel function is countably continuous, i.e. can be written as a countable union of partial continuous functions (with arbitrary domains). This question can be straightforwardly generalized by replacing continuous functions with functions of a fixed Baire class. Both questions where answered negatively already in the Thirties, but (except for the basic case of countably continuous functions, where the Pawlikowski function provides a somewhat canonical counterexample) the desired functions are usually obtained indirectly using nontrivial Baire category argument, universal functions and diagonalization. The aim of this talk is to present new extremely simple counterexamples, which are in a sense canonical and can be seen as generalizations of the Pawlikowski function. Such examples allow also to fully describe the structure under inclusion of finite level Borel classes of functions. Finally, if time permits we will also present some (partial) positive results showing that functions appearing in certain finite level Borel classes turn out to be always countably continuous in a definable way.
Film uber Juri Manin
Thursday, 24.5.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Interpolation on subspaces
Friday, 25.5.12, 10:00-11:00, Raum 404, Eckerstr. 1
Let P1,...Pr be points in the projective space \bP^n and let m1,...,mr be positive integer. If n=2, then the conjecture of Segre, Harbourne, Gimigliano, Hirschowitz predicts that if the points are general, then the scheme Z=m1P1+...+mrPr either imposes independent conditions on linear systems of curves of degree d, or this system has a non-reduced base curve. For higher n, even the conjectural picture is less clear. On the other hand, a celebrated result of Alexander and Hirschowitz says, that if m1,...,mr are fixed, then the conditions imposed\nby Z on hypersurfaces of degree d are independent, provided d is sufficiently large. There is no reason to restrict imposing conditions only to points. Hartshorne and Hirschowitz studied the postulation problem for a set of general lines in \bP^n. They showed that lines behave as\npoints, i.e. general lines impose independent conditions on\nhypersurfaces. The proof of this result is pretty involved.\nWe study the problem more generally, asking for conditions\nimposed by general configurations of linear subspaces and allowing multiplicities.\n\nThis is work in progress, joint with Brian Harbourne, Marcin Dumnicki, Joaquim Roe and Halszka Tutaj-Gasinska.\n
Bradford Hill Memorial Lecture 2012
Friday, 25.5.12, 11:15-12:15, Raum 404, Eckerstr. 1
Hospital-acquired (nosocomial) infections (NIs) constitute a major medical problem in that they increase patients’ morbidity and mortality. They also lead to an increase of costs due to additional medical care and prolongation of length of hospital stay. Some of these infections are thought to be preventable; identification of patients at high risk is therefore of central importance, as is the assessment of their sequelae. Incidence of nosocomial infections varies according to type, size and other characteristics of hospitals and wards and is usually highest in intensive care units.\n\nThe vast majority of evidence on determinants and consequences of NIs comes from observational studies that besides being prone to various, well-known biases often suffer from inadequate statistical analyses. Two major flaws are prominent in the infection literature: The first is caused by ignoring the temporal dynamics, i. e. that NIs are time-dependent exposures. Implicitly assuming that they are already known at time of admission leads to so-called time-dependent bias and usually to an exaggerated estimate of their consequences. This issue is frequently related to design aspects and sometimes further complicated by delayed study entry that leads to left truncated data. The second flaw is caused by ignoring competing risks so that patients are censored at the time a competing event occurs. Since the cumulative incidence function depends on the hazard of the event of primary interest as well as on the hazard of all competing events ignoring them may lead to a completely misleading assessment.\n\nTo address these issues, we advocate a multistate model where the temporal dynamics as well as competing risks are incorporated, quantities of interest can be estimated and inference can be based on with R packages being available. The model and the resulting strategies for the statistical analysis are explained and illustrated by using data from studies on nosocomial pneumonia in intensive care units and on in-hospital bacteraemia caused by Staphylococcus aureus in a Scottish hospital. Furthermore, we also will explain the key issues made using results from a study on hospital-acquired bacteraemia in African children, a study on meticillin-resistant Staphylococcus aureus colonisation and infection in surgical patients and - outside the realm of NIs - from a popular investigation on the mortality of Oscar nominees.\n\nIn the last part of the presentation we will discuss problems related with defining and estimating the attributable mortality due to NIs. It is shown that this concept can be nicely embedded into the multistate model framework. However, interpretational problems remain since the evidence that can be derived from observational studies is limited. So not only an appropriate statistical treatment of data on nosocomial infections, but also more randomized studies investigating the impact of preventive measures are urgently needed!\n
Thursday, 31.5.12, 17:00-18:00, Hörsaal II, Albertstr. 23b