To any number eld K and positive integer one can associate a constant which in the case ofK = Q coincides with the classical Hermite constant. Wewill survey some results concerning these constants, and how one can compute some of them for quadratic number elds. Hartwig Bosse (Frankfurt) Non-negative polynomials that are not sums of squares ursday, 11:00 Jaka Cimpric (Ljubljana) A method for c...

We provide a general and consistent formulation for linear subsystem quantum dynamical maps, developed from a minimal set of postulates, primary among which is a relaxation of the usual, restrictive assumption of uncorrelated initial system-bath states. We describe the space of possibilities admitted by this formulation, namely that, far from being limited to only completely positive (CP) maps,...

Let R = ⊕(u,v)∈N2R(u,v) be a standard bigraded algebra over an artinian local ring K = R(0,0). Standard means R is generated over K by a finite number of elements of degree (1, 0) and (0, 1). Since the length l(R(u,v)) of R(u,v) is finite, we can consider l(R(u,v)) as a function in two variables u and v. This function was first studied by van der Waerden [W] and Bhattacharya [B] who proved that...

Given that familiarity is closely associated with positivity, the authors sought evidence for the idea that positivity would increase perceived familiarity. In Experiment 1, smiling and thus positively perceived novel faces were significantly more likely to be incorrectly judged as familiar than novel faces with neutral expressions. In Experiment 2, subliminal association with positive affect (...

We prove general reflection positivity results for both scalar fields and Dirac fields on a Riemannian manifold, and comment on applications to quantum field theory. As another application, we prove the inequality CD ≤ CN between Dirichlet and Neumann covariance operators on a manifold with a reflection.

Based on past contributions by Robert Schrader and Michael Karowski I review the problem of existence of interacting quantum field theory and present recent ideas and results on rigorous constructions. 1 Historical remarks The title of this essay is identical to that of a small conference at the FU-Berlin in honor of Michael Karowski and Robert Schrader at the occasion of their sixtyfifth birth...

We study Deligne’s conjecture on the monodromy weight filtration on the nearby cycles in the mixed characteristic case, and reduce it to the nondegeneracy of certain pairings in the semistable case. We also prove a related conjecture of Rapoport and Zink which uses only the image of the Cech restriction morphism, if Deligne’s conjecture holds for a general hyperplane section. In general we show...