Rigid rational curves in positive characteristic
Friday, 1.2.19, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
Rational curves are central to higher-dimensional algebraic geometry. If a rational curve “moves” on a variety, then the variety is uniruled and in characteristic zero, this implies that the variety has negative Kodaira dimension. Over fields of positive characteristic, varieties can be inseparably uniruled without having negative Kodaira dimension. However, I will show in my talk that in the case that a rational curve moves on a surface of non-negative Kodaira dimension, then this rational curve must be “very singular”. In higher dimensions, there is a similar result that is more complicated to state. I will also give examples that show the results are optimal. This is joint work with Kazuhiro Ito and Tetsushi Ito.
Eigenvalues of a perturbed anharmonic oscillator
Monday, 4.2.19, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
In this talk, we will discuss the spectral properties of the perturbation of the generalized anharmonic oscillator. We consider a piecewise Hölder continuous perturbation, and investigate how the Hölder constant might affect\non the eigenvalues. More precisely, we derive the first several terms in the asymptotic expansion for the eigenvalues.
Eigenvalues of a perturbed anharmonic oscillator
Monday, 4.2.19, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
In this talk, we will discuss the spectral properties of the perturbation of the generalized anharmonic oscillator. We consider a piecewise Hölder continuous perturbation, and investigate how the Hölder constant might affect\non the eigenvalues. More precisely, we derive the first several terms in the asymptotic expansion for the eigenvalues.
Effective theories for heterogeneous multilayers
Tuesday, 5.2.19, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We will report on recent advances in deriving effective theories for thin sheets consisting of multiple layers with (slightly) mismatching equilibria in various energy regimes. Moreover, we will investigate optimal energy configurations and identify a critical energy scaling for their generic shape.\n
Nicht-äquationale Theorien
Wednesday, 6.2.19, 16:30-17:30, Raum 404, Ernst-Zermelo-Str. 1
Eine Theorie ist äquational, falls jede Formel\nboolsche Kombination von Gleichungen ist. Eine Formel ist eine Gleichung, falls die Familie endlicher Durschnitte ihrer Instanzen die Absteigenden-Ketten-Bedingung erfüllt. Jede äquationale Theorie ist stabil, aber Sela und Müller-Sklinos zeigten, dass die nicht-abelsche freie Gruppe nicht äquational ist. Jedoch gibt es bisher wenige\nBeispiele stabiler Theorien, welche nicht äquational sind.\n\nIn einer Zusammenarbeit mit Martin Ziegler produzieren wir sämtliche neuen nicht-äquationalen stabilen Theorien, welche auf den von Hrushovski und Sour konstruierten gefärbten Pseudoraum basiert sind.\n
Thursday, 7.2.19, 17:00-18:00, Hörsaal II, Albertstr. 23b
Existence and Uniqueness of Recursive Equilibria with Aggregate and Idiosyncratic Risk
Friday, 8.2.19, 12:00-13:00, Raum 404, Ernst-Zermelo-Str. 1
In this paper, I study the existence and uniqueness of recursive equilibria in production economies with aggregate risk. The economy features a continuum of agents who, in addition to aggregate risk, face idiosyncratic shocks and borrowing constraints. In particular, I establish existence for the Aiyagari-Bewley growth model à la Krusell and Smith (1998). In contrast to the existing literature, I do not rely on compactness to establish a fixed point. I instead exploit the monotonicity property of the equilibrium model and rely on arguments from convex analysis. Furthermore, this methodology gives rise to a uniqueness result for the Aiyagari-Bewley economy which is not restricted to a risk aversion parameter smaller equal one.