Wochenplan des Fachbereichs Mathematik und Informatik
Oberseminar Differentialgeometrie: Boris Vertman, Oldenburg, Vortrag: Stability of the Ricci de Turck flow on singular spaces
am Montag, 28.05.2018 16:15 im Raum SR4
Abstract. We discuss stability of the Ricci de Turck flow near Ricci-flat metrics with isolated conical singularities. More precisely, we construct a Ricci de Turck flow which starts sufficiently close to a Ricci-flat metric with isolated conical singularities and converges to a singular Ricci-flat metric under an assumption of integrability, linear and tangential stability. We provide a characterization of conical singularities satisfying tangential stability and discuss examples where the integrability condition is satisfied.
Prof. Dr. Arnd Scheel(University of Minnesota) CENOS Kolloquium-Pattern selection through directional quenching
am Dienstag, 29.05.2018 16:30 im Raum 222 Institute for Applied Physics
Interfaces or boundaries affect the formation of crystalline phases in sometimes quite dramatic ways. We are interested in examples where such interfaces arise through directional quenching and separate a striped phase from a uniform, non-crystalline state. Examples range from the alignment of convection roles in Benard convection to the robust patterning through presomites in limb formation, or the formation of helicoidal precipitates in recurrent precipitation. It turns out that growing the crystalline region leads to the selection of crystallographic parameters near the interface. We describe results for model problems such as Allen-Cahn, Cahn-Hilliard, and Swift-Hohenberg equations that quantify crystalline strain for small and large speeds and predict alignment parallel, perpendicular, or at oblique angles to the growth interface.
Oberseminar Differentialgeometrie: Anand Dessai, Fribourg, Vortrag: Moduli space of metrics of nonnegative sectional/positive Ricci curvature on homotopy real projective spaces
am Montag, 04.06.2018 16:15 im Raum SR4
We show that the moduli space of metrics of nonnegative sectional curvature on a smooth closed manifold homotopy equivalent to RP^5 has infinitely many connected components. The proof involves Brieskorn spheres, the nonnegatively curved metrics constructed by Grove-Ziller and computations of eta invariants. We also discuss corresponding results in higher dimensions for the moduli space of metrics of positive Ricci curvature.