Some combinatorial identities appearing in the calculation of the cohomology of Siegel modular varieties

In the computation of the intersection cohomology of Shimura varieties, or of the $L^2$ cohomology of equal rank locally symmetric spaces, combinatorial identities involving averaged discrete series characters of real reductive groups play a large technical role. These identities can become very complicated and are not always well-understood (see for example the appendix of [8]). We propose a geometric approach to these identities in the case of Siegel modular varieties using the combinatorial properties of the Coxeter complex of the symmetric group. Apart from some introductory remarks about the origin of the identities, our paper is entirely combinatorial and does not require any knowledge of Shimura varieties or of representation theory.Comment: 17 pages, 1 figure; to appear in Algebraic Combinatoric

The Intersection Complex as a Weight Truncation and an Application to Shimura Varieties

The purpose of this talk is to present an (apparently) new way to look at the intersection complex of a singular variety over a finite field, or, more generally, at the intermediate extension functor on pure perverse sheaves, and an application of this to the cohomology of noncompact Shimura varieties.Mathematic

Assessing the two-dimensional behaviour of drystone retaining walls by full-scale experiments and yield design simulation

International audienceDrystone walling is a widespread form of construction that utilises local materials. It has received growing interest over the past few years, owing to the recognition of its rich heritage in the framework of sustainable development. However, the growth of dry masonry has been slowed by the lack of scientific evidence proving its reliability. The authors have previously established a model based on yield design to assess drystone wall stability. This theoretical approach has been supplemented by field experiments on full-scale drystone retaining walls that were backfilled until failure with a cohesionless soil. These field experiments followed a first set of experiments in 2002-2003 in which the walls were loaded using hydrostatic pressure. The aim of these experimental programmes was to achieve better understanding of drystone masonry behaviour under loading, and of its failure mode. The present paper consists of a comparative analysis of these theoretical and experimental results, and provides a richer understanding of drystone retaining wall phenomenology. Further perspectives on this work are presented in the conclusion

Yield design modelling of dry joint retaining structures

International audienceThis study presents an analysis of dry masonry retaining structures based on yield design theory: the structure stability is assessed using rigid block and shear failure mechanisms in the wall and its backfill. An application of this simulation on 2D scale-down brick and wood models is then addressed, showing close agreement between theoretical predictions and experimental results. Finally, the possibility of widespreading the study to periodic dry joint and dry-stone retaining structures is discussed