The global geometry of the moduli space of curves
Thursday, 1.7.10, 17:00-18:00, Hörsaal II, Albertstr. 23b
The moduli space of curves Mg is the universal parameter\nspace for\nRiemann surfaces of given genus. Its study has been\ninitiated by\nRiemann in 1857 and it has been a long-standing problem to\ndescribe\nthe nature of the moduli space as an algebraic variety. I\nwill survey the\nhistory of the problem starting with Severi's conjecture\nfrom 1915\npredicting that Mg is always unirational, continuing with\nthe work of Harris\nand Mumford spectacularly disproving Severi's conjecture\nand finally\ndiscussing recent results which settle this problem in one\nof the most\ninteresting remaining cases, that of genus 22.\n
Refinement of the Parshin symbol for surfaces
Friday, 2.7.10, 11:15-12:15, Raum 127, Eckerstr. 1
On an algebraic curve there are Tate symbols, which satisfy Weil\nreciprocity law. The analogues in higher dimensions are Parshin\nsymbols, which satisfy Kato-Parshin reciprocity laws. We give a\nrefinement of the Parshin symbol for surfaces, using iterated\nintegrals in the sense of Chen. The product of the refined symbol\nover the cyclic permutations of the functions recovers the Parshin\nsymbol. Also, we construct a logarithmic version of the Parshin\nsymbol. We prove reciprocity laws for both the refined symbol and\nthe logarithmic Parshin symbol.\n\n
Introduction to Vafa-Witten Bounds
Monday, 5.7.10, 16:00-17:00, Raum 404, Eckerstr. 1
Das Curve Diffusion Problem - Homothetische und Translatierende Lösungen
Tuesday, 6.7.10, 16:15-17:15, Raum 404, Eckerstr. 1
Untersuchen wir das Curve Diffusion Problem (ODE 4. Ordnung im R^2) für homothetische und translatierende Abbildungen sowie für spezielle Parametrisierungen, erhalten wir dazu äquivalente skalare ODEs. Im homothetischen Fall zeigen wir globale Existenz der Skalierungsfunktion, im translatierenden Fall zeigen wir globale Existenz Translatierender Curve Diffusion Flows und einige Eigenschaften ihrer Lösungskurven.
About integrability of geodesic flows and isospectrality of Riemannian manifolds
Wednesday, 7.7.10, 14:15-15:15, Raum 404, Eckerstr. 1
We shall explain the work of D. Schueth about the construction of a pair of compact eight-dimensional two-step Riemannian nilmanifolds M, N, which are isospectral and such that M has (Liouville) completely integrable geodesic flow while N has not. We shall see that many of the tools required to prove this can be translated at the Lie algebra level.
Limiting Mixed Hodge Structures
Wednesday, 7.7.10, 14:15-15:15, Raum 127
Blackwell Prediction
Thursday, 8.7.10, 10:15-11:15, Raum 232, Eckerstr. 1
Density models for credit risk
Thursday, 8.7.10, 17:00-18:00, Hörsaal II, Albertstr. 23b
Einige Phänomene im Umfeld der Gross-Zagier-Formel
Friday, 9.7.10, 00:00-01:00, SR 125
Friday, 9.7.10, 14:30-15:30, Hörsaal Rundbau, Albertstr. 21a
Friday, 9.7.10, 17:00-18:00, Innenhof des Physikalischen Instituts
Chens iterierte Integrale und Anwendungen
Monday, 12.7.10, 13:30-14:30, Freiburg
The classifying space of locally filtered vector bundles
Monday, 12.7.10, 16:15-17:15, Raum 427, Eckerstr. 1
Update zu Ricci-flachen vollstaendigen Kaehlermetriken / Ideen zu einem Kaehlerfluss.
Tuesday, 13.7.10, 16:15-17:15, Raum 404, Eckerstr. 1
The Clemens-Schmid sequence
Wednesday, 14.7.10, 14:15-15:15, Raum 127
Minimal submanifolds of higher codimension
Wednesday, 14.7.10, 16:15-17:15, Hörsaal II, Albertstr. 23b
The theory of minimal hypersurfaces has long history and its study is still active in recent years. On the other hand, minimal submanifolds in higher codimension have some different phenomina, as revealed by the fundamental papers by Lawson-Osserman and Harvey-Lawson. In this lecture the main results in Lawson-Osserman problem will be presented.
Thursday, 15.7.10, 17:00-18:00, Hörsaal II, Albertstr. 23b
t.b.a.
Wednesday, 21.7.10, 16:15-17:15, Hörsaal II, Albertstr. 23b
Filtering equations for sufficient statistics in twodimensional disorder problems for exponential families of Lévy processes
Friday, 23.7.10, 11:15-12:15, Raum 404, Eckerstr. 1