Gorenstein homological algebra and universal coefficient theorems

We study criteria for a ring—or more generally, for a small category—to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones. Among the universal coefficient theorems covered by our methods we find, besides all the classic examples, several exotic examples arising from the KK-theory of C*-algebras and also Neeman’s Brown–Adams representability theorem for compactly generated categories

Rokhlin Dimension for Flows

This research was supported by GIF Grant 1137/2011, SFB 878 Groups, Geometry and Actions and ERC Grant No. 267079. Part of the research was conducted at the Fields institute during the 2014 thematic program on abstract harmonic analysis, Banach and operator algebras, and at the Mittag–Leffler institute during the 2016 program on Classification of Operator Algebras: Complexity, Rigidity, and Dynamics.Peer reviewedPostprin

Cartan subalgebras and the UCT problem, II

We show that outer approximately represenbtable actions of a finite cyclic group on UCT Kirchberg algebras satisfy a certain quasi-freeness type property if the corresponding crossed products satisfy the UCT and absorb a suitable UHF algebra tensorially. More concretely, we prove that for such an action there exists an inverse semigroup of homogeneous partial isometries that generates the ambient C*-algebra and whose idempotent semilattice generates a Cartan subalgebra. We prove a similar result for actions of finite cyclic groups with the Rokhlin property on UCT Kirchberg algebras absorbing a suitable UHF algebra. These results rely on a new construction of Cartan subalgebras in certain inductive limits of Cartan pairs. We also provide a characterisation of the UCT problem in terms of finite order automorphisms, Cartan subalgebras and inverse semigroups of partial isometries of the Cuntz algebra $\mathcal{O}_2$. This generalizes earlier work of the authors.Comment: minor revisions; final version, accepted for publication in Math. Ann.; 26 page

Thermal diffusivity, effusivity and conductivity of CdMnTe mixed crystals

Cd1-xMnxTe mixed crystals belong to a class of materials called ‘‘semimagnetic semiconductor’’ or diluted magnetic semiconductor (DMS) with addition of magnetic ions like Mn2+ implemented into crystal structure. The crystals under investigation were grown from the melt by the high pressure high temperature modified Bridgman method in the range of composition 0 < x < 0.7. Thermal properties of these compounds have been investigated by means of photopyroelectric (PPE) calorimetry in both, back and front detection configuration. The values of the thermal diffusivity and effusivity were derived from experimental data. Thermal conductivity of the specimens was calculated from the simple theoretical dependencies between thermal parameters. The influence of Mn concentration on thermal properties of Cd1-xMnxTe crystals have been presented and discussed

Locomotion modulates specific functional cell types in the mouse visual thalamus

The visual system is composed of diverse cell types that encode distinct aspects of the visual scene and may form separate processing channels. Here we present further evidence for that hypothesis whereby functional cell groups in the dorsal lateral geniculate nucleus (dLGN) are differentially modulated during behavior. Using simultaneous multi-electrode recordings in dLGN and primary visual cortex (V1) of behaving mice, we characterized the impact of locomotor activity on response amplitude, variability, correlation and spatiotemporal tuning. Locomotion strongly impacts the amplitudes of dLGN and V1 responses but the effects on variability and correlations are relatively minor. With regards to tunings, locomotion enhances dLGN responses to high temporal frequencies, preferentially affecting ON transient cells and neurons with nonlinear responses to high spatial frequencies. Channel specific modulations may serve to highlight particular visual inputs during active behaviors

Photopyroelectric spectroscopy and calorimetry

In this tutorial, we present an overview of the development of the photopyroelectric (PPE) technique, from its beginnings in 1984, through to the present day. The tutorial is organized in five sections, exploring both theoretical and experimental aspects of PPE detection, as well as some important spectroscopic and calorimetric applications. In the “Introduction” section we present the fundamental basics of photothermal phenomena and the state-of-the-art of the photopyroelectric technique. In the “Theoretical aspects” section we describe some specific cases of experimental interest, with examples in both back and front detection configurations. Several mathematical expressions for the PPE signal in specific detection modes (combined back-front configurations and PPE-IRT methods) are also deduced. The “Instrumentation and experiment” section contains two sub-sections. The first describes several examples of set-ups used for both room temperature and temperature-controlled experiments. The second sub-section is dedicated to the configuration of detection cells and to the various sensor/sample assemblies that are currently used in spectroscopic and calorimetric experiments for both liquid and solid samples. The “Applications” section is in fact a collection of experimental results dedicated to the thermal characterization of a wide range of solid and liquid samples. At the end of this section we present some examples that have been selected to convey that the PPE technique is not only useful in the investigation of optical and thermal properties of a variety of condensed matter samples, but also to study physical and chemical processes such as molecular associations, food adulteration or phase transitions. In “Concluding remarks” we summarize the advantages of this technique in spectroscopic and calorimetric applications