Mannigfaltigkeiten mit positiver Schnittkrümmung auf einer offenen dichten Menge
Donnerstag, 1.12.11, 14:00-15:00, HS Weismann-Haus, Albertstr. 21 a
Donnerstag, 1.12.11, 17:00-18:00, Hörsaal II, Albertstr. 23b
frei
Relative version of the Kontsevich-Zagier conjecture on periods.
Freitag, 2.12.11, 10:00-11:00, Raum 404, Eckerstr. 1
We formulate and prove a relative version of the K-Z conjecture on periods. In this relative version, numbers (and rational numbers) will be replaced by Laurent series (and rational functions).
Crepant resolutions of Calabi-Yau orbifolds
Montag, 5.12.11, 16:15-17:15, Raum 404, Eckerstr. 1
A Calabi-Yau orbifold in complex dimension 3 is locally modeled on C^3/G with G a finite subgroup of SL(3,C). When G acts with an isolated fixed point on C^3, a crepant resolution has the structure of an asymptotically locally euclidean (ALE) manifold. Using index theory techniques we derive a geometrical interpretation of the McKay correspondence which relates the geometry of the crepant resolution to the representation theory of the finite group G. This extends a result of Kronheimer and Nakajima to this higher dimensional case.
Higher Order Finite Volume Schemes for the Shallow Water Equations with well-balancing and wetting & drying
Dienstag, 6.12.11, 14:00-15:00, Raum 226, Hermann-Herder-Str. 10
Generalized Witten Genus and Complete Intersections
Dienstag, 6.12.11, 16:15-17:15, Raum 127, Eckerstr. 1
Witten genus is the loop space analogue of the Hirzebruch A-hat genus. On a string manifold, the Witten genus is a modular form and is the equivariant index of the Dirac operator on the free loop space. Hohn and Stolz conjectured that existence of a positive Ricci curvature metric on a string manifold implies the vanishing of the Witten genus. In this talk, we will present vanishing results for generalized Witten genus on complete intersections and describe a possible mod 2 extension of the Hohn-Stolz conjecture. The talk is based on the joint work with Qingtao Chen and Weiping Zhang.
The descriptive set-theoretical complexity of the embeddability relation
Mittwoch, 7.12.11, 16:30-17:30, Raum 404, Eckerstr. 1
Der differenzierbare Sphärensatz
Donnerstag, 8.12.11, 17:00-18:00, Hörsaal II, Albertstr. 23b
Der klassische Sphärensatz von Berger und Klingenberg besagt, dass eine vollständige einfach zusammenhängende Riemannsche Mannigfaltigkeit mit Schnittkrümmung 1<K\bleq 4 homöomorph zur Sphäre ist. Mit Hilfe des Ricci Flusses und Ergebnissen von Hamilton bzw. Böhm, Wilking konnten Brendle und Schoen zeigen, dass unter den genannten Voraussetzungen sogar Diffeomorphie gilt.
Donnerstag, 8.12.11, 17:00-18:00, Hörsaal II, Albertstr. 23b
Negative curves on algebraic surfaces
Freitag, 9.12.11, 10:00-11:00, Raum 404, Eckerstr. 1
It has been a long-standing folklore conjecture going back to Enriques, that on a smooth projective surface over the complex numbers the self-intersection of curves has a lower bound. \n\nIn a joint work with Bauer, Harbourne, Knutsen, Müller-Stach, and Szemberg, we disprove the conjecture with the help of certain Hilbert modular surfaces.
Censoring and truncation: inverse probability weighted estimators of survival
Freitag, 9.12.11, 11:15-12:15, Raum 404, Eckerstr. 1
The hazard has been the basis for non- and semiparametric estimation of survival with (right) censored and (left) truncated data, as reflected in the dominant use of the Kaplan-Meier estimator and the Cox proportional hazards model. We show that the Kaplan-Meier has an equivalent representation as an inverse probability weighted empirical cumulative distribution function (ipw-ecdf), which has an immediate extension to the competing risks setting. The weights in this ipw-ecdf form suggest an estimator of the subdistribution hazard in the situation of competing risks. The resulting nonparametric product-limit estimator is also equivalent to the standard nonparametric estimator for the cause specific cumulative incidence function. Furthermore, by using the proper filtration, a martingale property is derived for the weighted counting process that corresponds to the subdistribution. Using this martingale property, several results and proofs from standard survival analysis are easily extended to the competing risks setting. As an example, we briefly discuss asymptotics in the proportional subdistribution hazards model.
On K3 surfaces in physics and geometry
Freitag, 9.12.11, 14:00-15:00, Hörsaal 1, Physik Hochhaus, Hermann-Herder-Straße 3
Matrix models, enumerative geometry and integrability
Montag, 12.12.11, 16:15-17:15, Raum 404, Eckerstr. 1
Some of generating functions in enumerative geometry are known to be related to matrix integrals and \nclassical integrable hierarchies of KP/Toda type. In recent years it become clear that the partition functions of the \nthis still not completely described set of models posses other nice properties such \nas cut-and-join-type representations, random partition descriptions and Virasoro-type constraints. \nI will explain some of the aforementioned properties and relations between them for three important models, namely Hermitian matrix model,\nKontsevich-Witten tau-function and generating function of Hurwitz numbers.
Osserman natural tangent bundles on surfaces
Dienstag, 13.12.11, 16:15-17:15, Raum 127, Eckerstr. 1
Let (M,g) be a riemannian surface and \(G\) a\ng-natural nondegenerate\nmetric on its tangent bundle TM. We compute explicitly the\nspectrum of some Jacobi operators on (TM , G) and give\nnecessary and sufficient conditions for\n(TM , G) to be a 4-dimensional Osserman manifold.\n\n
A Gandy Theorem for Abstract Structures and Applications to First-Order Definability
Mittwoch, 14.12.11, 16:30-17:30, Raum 404, Eckerstr. 1
Donnerstag, 15.12.11, 17:00-18:00, Hörsaal II, Albertstr. 23b
Varietäten mit trivialer kanonischer Klasse: Faserungen und Blätterungen
Freitag, 16.12.11, 10:00-11:00, Raum 404, Eckerstr. 1
Die Struktur kompakter Kähler-Mannigfaltigkeiten X, die eine nirgends verschwindende holomorphe Differentialform vom Grad p=dim X besitzen, wird durch den fundamentalen Zerlegungssatz von Beauville und Bogomolov beschrieben: jedes solche X hat eine endliche Überlagerung, die in ein Produkt von Tori, Calabi-Yau-Mannigfaltigkeiten und Hyperkähler-Mannigfaltigkeiten zerfällt. \n\nIn meinem Vortrag werde ich mich mit zwei Problemstellungen befassen, die in Zusammenhang zu diesem klassischen Resultat stehen. Zum einen werde ich erste Schritte in Richtung eines Zerlegungssatzes für singuläre Varietäten mit trivialem kanonischen Bündel diskutieren. Diese treten auf natürliche Weise im Rahmen der Klassifikationstheorie für höher-dimensionale algebraische Varietäten auf. Zum anderen werde ich Ergebnisse über die feinere Struktur von Hyperkähler-Mannigfaltigkeiten vorstellen, die Auskunft darüber geben, wann eine solche Mannigfaltigkeit eine Abbildung auf einen Raum kleinerer Dimension zulässt.
Vorstellungsvortrag
Freitag, 16.12.11, 10:00-11:00, Raum 404, Eckerstr. 1
Rigidity of complete Riemannian cylinders without conjugate points
Montag, 19.12.11, 16:15-17:15, Raum 404, Eckerstr. 1
On the transversality problem for the Cauchy-Riemann operator in symplectic geometry
Dienstag, 20.12.11, 16:15-17:15, Raum 127, Eckerstr. 1
Holomorphic curves are the most valuable tools to study the global properties of symplectic manifolds and also play a prominent role in string theory. In order to define algebraic invariants, one has to show that the moduli space of holomorphic curves carries a smooth structure of dimension equal to the Fredholm index of a nonlinear Cauchy-Riemann operator. Assuming that this nonlinear Cauchy-Riemann operator, viewed as a section in a Banach space bundle over a Banach manifold of maps, meets the zero section transversally, the desired result would follow from an infinite-dimensional bundle version of the implicit function theorem. In this talk I will show that multiply-covered holomorphic curves are the reason why transversality does not hold in general. Apart from giving hints at the new infinite-dimensional differential geometry of polyfolds, which were built in order to approach this problem in full generality, I will show how to achieve transversality in interesting special cases and finally illustrate a geometrical application to questions about stable hypersurfaces in symplectic manifolds.
Theorien ohne die Baumeigenschaft 2. Art
Mittwoch, 21.12.11, 16:30-17:30, Raum 404, Eckerstr. 1
Determinants and algebraic K-theory
Donnerstag, 22.12.11, 17:00-18:00, Hörsaal II, Albertstr. 23b
Algebraic K-theory captures arithmetic properties of rings. The\nfirst algebraic K-group of a commutative ring is closely related to the\nunits of the ring via a suitable determinant map. For brave new rings (aka\nstructured ring spectra) such determinant maps do not exist in general:\nFor the algebraic K-theory of the sphere spectrum Waldhausen showed that\nsuch a map cannot exist and work of Ausoni-Dundas-Rognes proves a negative\nresult for complex connective K-theory. I will motivate why we would like\nto have (suitable versions of) determinants and sketch some work in\nprogress joint with John Rognes on that question.
Donnerstag, 29.12.11, 17:00-18:00, Hörsaal II, Albertstr. 23b