Simple C*-algebras with locally finite decomposition rank

We introduce the notion of locally finite decomposition rank, a structural property shared by many stably finite nuclear C*-algebras. The concept is particularly relevant for Elliott's program to classify nuclear C*-algebras by K-theory data. We study some of its properties and show that a simple unital C*-algebra, which has locally finite decomposition rank, real rank zero and which absorbs the Jiang-Su algebra Z tensorially, has tracial rank zero in the sense of Lin. As a consequence, any such C*-algebra, if it additionally satisfies the Universal Coefficients Theorem, is approximately homogeneous of topological dimension at most 3. Our result in particular confirms the Elliott conjecture for the class of simple unital Z-stable ASH algebras with real rank zero. Moreover, it implies that simple unital Z-stable AH algebras with real rank zero not only have slow dimension growth in the ASH sense, but even in the AH sense.Comment: 30 pages, no figure

AC-Calorimetry at High Pressure and Low Temperature

Recent developments of the AC-calorimetric technique adapted for the needs of high pressure experiments are discussed. A semi-quantitative measurement of the specific heat with a Bridgman-type of pressure cell as well as a diamond anvil cell is possible in the temperature range 0.1 K < T < 10 K. The pressure transmitting medium used to ensure good pressure conditions determines to a great extent via its thermal conductivity the operating frequency and thus the accessible temperature range. Investigations with different pressure transmitting media for T > 1.5 K reveal for solid He a cut-off frequency which is considerably higher than for steatite. Experiments below 1 K and pressures above 10 GPa clearly show that the pressure dependence of the linear temperature coefficient of the specific heat can be measured. It is in qualitative agreement to a related quantity obtained quasi-simultaneously by electrical resistivity measurements on the same sample.Comment: 14 pages, 7 figures. The manuscript with high resoultion figures (pdf-file, about 1Mb) can be downloaded from http://www.cpfs.mpg.de/~wilhelm

Occupational Structure of Yerwa in the 1920s

Yerwa is the last of the Borno capitals. Although established in the first decade of colonial administration, it cannot be compared with the many other towns like Fort Lamy, Jos, Kaduna, Niamey et al. which all developed about the same time. Colonial interference with the development of Yerwa appears restricted, mainly, to insistence upon wider roads than a Borno town otherwise would have featured and resettlement schemes, e.g. Mafoni, Ari Askeri. The following is based on the premise that as the town - despite time and political circumstances of its emergence - is a distinctive Borno town, also occupational diversification and structure are distinctively related to urban Borno culture

Amplitudes, Form Factors and the Dilatation Operator in N=4\mathcal{N}=4 SYM Theory

We study the form factor of a generic gauge-invariant local composite operator in $\mathcal{N}=4$ SYM theory. At tree level and for a minimal number of external on-shell super fields, we find that the form factor precisely yields the spin-chain picture of integrability in the language of scattering amplitudes. Moreover, we compute the cut-constructible part of the one-loop correction to this minimal form factor via generalised unitarity. From its UV divergence, we obtain the complete one-loop dilatation operator of $\mathcal{N}=4$ SYM theory. Thus, we provide a field-theoretic derivation of a relation between the one-loop dilatation operator and the four-point tree-level amplitude which was observed earlier. We also comment on the implications of our findings in the context of integrability.Comment: 39 pages, several figures, feynmp; v2: references added, typos corrected; v3: references added, typos corrected, one explanation improved, matches published versio

Alopecia

Poetry by Laura Wilhelm. Runner-Up in the 2017 Manuscripts Poetry Contest with Alessandra Lynch