Introduction to the Yamabe invariant
Montag, 3.5.10, 16:15-17:15, Raum 404, Eckerstr. 1
t.b.a.
Dienstag, 4.5.10, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
t.b.a.
Dienstag, 4.5.10, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
"Introduction to Ricci flow for n>2"
Dienstag, 4.5.10, 16:15-17:15, Raum 404, Eckerstr. 1
Algebraische Geometrie. Reine Mathematik, wo man sie vielleicht nicht vernutet.
Dienstag, 4.5.10, 19:30-20:30, Hörsaal II, Albertstr. 23b
Der Vortrag illustriert anhand anschaulicher Beispiele einige \nhistorische und aktuelle Forschungsprobleme der algebraischen Geometrie und \nnennt praktische Anwendungen der Theorie. Die Anwendungen berühren zum Teil \nThemenkreise, bei denen man nicht sofort an Algebra denken würde. \n
Shimuravarietaeten, Arakelov Geometrie und Kudlas Vermutungen
Mittwoch, 5.5.10, 11:15-12:15, Raum 404, Eckerstr. 1
In dem Vortrag werden anhand eines einfachen Beispiels (der Modulkurve,\nalso dem Parameterraum elliptischer Kurven)\ndie Begriffe der Theorie ganzzahliger, kanonischer Modelle von\nShimuravarietaeten erklaert. Anschliessend\ngebe ich eine kurze Einfuehrung in die Arakelov Theorie\n(man kann diese als Maschinerie sehen, um klassische Hoehen a la Weil\nkonzeptionell zu verstehen)\nund ihre Besonderheiten im Bezug auf die Anwendung auf ganzzahlige Modelle\nder Shimuravarietaten. Dies ermoeglicht Kudlas Vermutungen\nueber Arakelovtheoretische Groessen (Hoehen, arithmetische Volumen)\nsogenannter orthogonaler Shimuravarietaeten\nund gewisser spezieller Zykel auf diesen zu formulieren.\nDiese bringen die entsprechenden Groessen in Zusammenhang mit den\nFourierkoeffizienten gewisser Eisensteinreihen.\nIch erwaehne ebenfalls ein Resultat meiner Dissertation welches Evidenz\nfuer Teile der Vermutungen in hoheren Dimensionen liefert.\nKudlas Vermutungen sind entstanden, um die beruehmten Resultate von Gross,\nZagier und Kohnen konzeptionell zu verstehen,\nwelche u.a. einen Spezialfall der Birch- and Swinnerton-Dyer Vermutung\nimplizieren.
Variation von Hodge-Strukturen
Mittwoch, 5.5.10, 14:15-15:15, Raum 127
Donnerstag, 6.5.10, 17:00-18:00, Hörsaal II, Albertstr. 23b
Estimation of direct effect for survival data using the Aalen additive hazards model
Freitag, 7.5.10, 09:30-10:30, IMBI, Stefan-Meier-Str.26
We are interested in estimating the direct effect of an exposure variable X on a survival outcome T. In case of an intermediate variable K and an unobserved confounder U for the effect of K on T standard regression techniques will render a biased estimate of the direct effect of X on T. This problem may be solved with the inclusion of additional information, L, that removes the effect of U on K. However, if L is also affected by X then standard methods are still not appropriate. Marginal structural models have been suggested to tackle this problem but they need estimation of specific weights that may be quite unstable. To overcome this problem, Goetgeluk et al. (JRSSB, 2009) suggested a so-called G-estimation approach in the case of an un-censored response variable. In this talk I show how to generalize their approach to the setting of survival data. I start out by describing the dynamic path analysis approach and point out that it may give wrong answers in case of an un-measured confounder.
Detecting the Emergence of a Signal in a Noisy Image
Freitag, 7.5.10, 11:15-12:15, Raum 404, Eckerstr. 1
We study sequential change-point detection when observations form a sequence of independent Gaussian random fields, and the change-point is the time at which a signal of known functional form involving a finite number of unknown parameters appears. We first identify a detection procedure of Shiryayev-Roberts type that is asymptotically minimax up to terms that vanish as the false detection rate converges to zero. We then compare approximations to the Shiryayev-Roberts detection procedure with comparatively simple approximations to CUSUM type procedures. Although the CUSUM type procedures are suboptimal, our numerical studies indicate that they compare favorably to the asymptotically optimal procedures.
Differential forms on singular spaces
Freitag, 7.5.10, 11:15-12:15, Raum 127, Eckerstr. 1
Given an algebraic variety X and a resolution of singularities Z of X with exceptional set E it is a natural (old) question whether, or under which additional assumptions, regular differential forms defined on the smooth part of X extend over E to regular differential forms on Z.\n\nAfter discussing examples showing that extension is not possible in general, I will introduce and discuss (log-)canonical singularities and sketch the proof of the following result : extension (with logarithmic poles) holds for varieties with (log-)canonical singularities. \n\nThe talk is based on joint work with Stefan Kebekus, Sándor Kovács, and Thomas Peternell.
Der Twistorraum von Quaternionisch-Kähler Mannigfaltigkeiten und Skalarkrümmung
Montag, 10.5.10, 16:15-17:15, Raum 404, Eckerstr. 1
Eine Abschätzung für die Skalarkrümmung einer Quaternionisch-Kähler Mannigfaltigkeit bei Vergrößerung der Metrik auf Flächen wird im Falle positiver Skalarkrümmung gegeben. Mit Hilfe der Konstruktion des Twistorraums einer Quaternionisch-Kähler Mannigfaltigkeit wird das Problem auf den Kähler Fall zurückgeführt.
"Manifolds with positive curvature operators are space forms" Teil I:
Dienstag, 11.5.10, 16:15-17:15, Raum 404, Eckerstr. 1
Klassifizierende Räume für Hodge-Strukturen
Mittwoch, 12.5.10, 14:15-15:15, Raum 127
Donnerstag, 13.5.10, 17:00-18:00, Hörsaal II, Albertstr. 23b
Donnerstag, 13.5.10, 17:00-18:00, Hörsaal II, Albertstr. 23b
Microstructure of a double auction market
Montag, 17.5.10, 10:15-11:15, FRIAS House, Albertstr. 19, lecture hall
Remarks about the curvatures of regular curves in euclidean spaces
Montag, 17.5.10, 16:15-17:15, Raum 404, Eckerstr. 1
Correlation and hierarchies in finacial markets
Dienstag, 18.5.10, 10:15-11:15, FRIAS House, Albertstr. 19, lecture hall
Electrolit flows in porous media.
Dienstag, 18.5.10, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
"Manifolds with positive curvature operators are space forms" Teil II:
Dienstag, 18.5.10, 16:15-17:15, Raum 404, Eckerstr. 1
Stochastische Paradoxien als didaktische Provokation
Dienstag, 18.5.10, 19:30-20:30, Hörsaal II, Albertstr. 23b
Paradoxien sind Stolpersteine unseres natürlichen Denkens. Im Mathematikunterricht können Sie insbesondere auf dem Gebiet der Stochastik als Provokationen und Denkanlässe zur kognitiven Aktivierung, Bearbeitung und Klärung dienen und deutlich machen, dass Mathematik ein Gebiet der formalen Abenteuer und nicht resultatorientierter Algorithmik ist.
Beispiele für Hodge-Strukturen
Mittwoch, 19.5.10, 14:15-15:15, Raum 127
Investment proviles of classes of investors
Mittwoch, 19.5.10, 16:15-17:15, FRIAS House, Albertstr. 19, lecture hall
Geometrische singuläre Störungstheorie
Donnerstag, 20.5.10, 17:00-18:00, Hörsaal II, Albertstr. 23b
Free monomial resolutions
Freitag, 21.5.10, 11:15-12:15, Raum 127, Eckerstr. 1
The main goal of the talk consist of the combinatorial construction of the\nfree resolutions for the algebraic objects that are defined in terms of\ngenerators and relations.\nFor the case of associative algebras the procedure looks as follows\n(first due to Anick):\nYou start from the algebra \(A\), First one should find the algebra \(\hat{A}\)\nof the same size but with monomial relations (this can be done using the\ntheory of Grobner bases), second one construct the free resolution of\n\(\hat{A}\) using the combinatorics of words. Now to get the resolution of\n\(A\) it is enough to deform the differential in the latter monomial\nresolution of \(\hat{A}\).\nI will show what can and what can not be done in more general settings, for\nexample for operads.\nAs a conclusion (If I have time) I will show how one can compute the\nhomology of the operad of Batalin-Vilkoviski algebras.
From genomes to phenotypes - statistical applications in transcriptomics, high-throughput RNAi and microscopy image based phenotyping
Freitag, 21.5.10, 11:15-12:15, Raum 404, Eckerstr. 1
How do variations in the genomes of individuals shape their phenotypes?\nRecent technological progress in high-throughput sequencing, genetic tools and automated microscopy imaging enable powerful experiments to address this question and place exciting challenges for data analysis and modelling.\n\nThe talk will have two sections:\nFirst, I will report a statistical error model for high throughput nucleotide sequencing data. This technology provides quantitative readouts in assays for RNA expression (RNA-Seq) and protein-DNA binding (ChIP-Seq). Statistical inference of differential signal in these data needs to take into account their natural variability throughout the dynamic range. When the number of replicates is small, error modeling is needed to achieve statistical power. We propose an error model that uses the negative binomial distribution, with variance and mean linked by local regression, to model the null distribution of the count data. The method controls type-I error and provides good detection power. A free open-source R/Biondonductor software package, “DESeq”, is available.\n\nSecond, I will describe some aspects of the statistical modelling of large-scale RNAi experiments, where the response of cellular populations to the RNAi perturbations is monitored by live-cell microscopy. The data are analysed by automated image analysis, fitting of dynamic models of cell cycle progression, extraction of multivariate phenotypes, and definition of a multivariate phenotypic landscape.
Symmetry and Regularity of Solutions for Nonlinear Integral and PDE Systems
Freitag, 21.5.10, 16:15-17:15, Hörsaal II, Albertstr. 23b
abstract\n
Krümmungseigenschaften von Perioden-Gebieten I
Mittwoch, 26.5.10, 14:15-15:15, Raum 127
Donnerstag, 27.5.10, 17:00-18:00, Hörsaal II, Albertstr. 23b
Donnerstag, 27.5.10, 17:00-18:00, Hörsaal II, Albertstr. 23b
Curvature Operators On Quaternion Kähler Manifolds
Montag, 31.5.10, 16:00-17:00, Raum 404, Eckerstr. 1