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Journals and Conferences
This paper is an introduction to the use of perverse sheaves with positive characteristic coefficients in modular representation theory. In the first part, we survey results relating singularities in finite and affine Schubert varieties and nilpotent cones to modular representations of reductive groups and their Weyl groups. The second part is a brief… (More)
TID and SEE data was taken to qualify and evaluate IC devices for radiation susceptibility in the natural space environment. A summary of the test data is presented and discussed
An important step in the calculation of the triply graded link theory of Khovanov and Rozansky is the determination of the Hochschild homology of Soergel bimodules for SL(n). We present a geometric model for this Hochschild homology for any simple group G, as equivariant intersection homology of B × Borbit closures in G. We show that, in type A these orbit… (More)
We study intersection cohomology complexes on flag varieties with coefficients in a field of positive characteristic and present a combinatorial procedure (based on the W -graph of the Coxeter group) which determines their characters in many cases on low rank flag varieties. Our procedure works uniformly in almost all characteristics (p > 5 is always… (More)
Single event effect (SEE) testing was performed on the Samsung and Spansion 4 Gb NAND flash devices. Testing was performed up to LET = 41 MeV cm2/mg. The parts were characterized for a variety of SEE. Testing and analysis showed that MBU became more prevalent at higher LET values.
The aim of this paper is two-fold. First, we give a fully geometric description of the HOMFLYPT homology of Khovanov-Rozansky. Our method is to construct this invariant in terms of the cohomology of various sheaves on certain algebraic groups, in the same spirit as the authors’ previous work on Soergel bimodules. All the differentials and gradings which… (More)
Single event effects (SEE) and total ionizing dose (TID) data taken for existing and potential space products is presented. The data was collected to evaluate these devices for radiation effects in space environments.
Given a stratified variety X with strata satisfying a cohomological parity-vanishing condition, we define and show the uniqueness of “parity sheaves”, which are objects in the constructible derived category of sheaves with coefficients in an arbitrary field or complete discrete valuation ring. If X admits a resolution also satisfying a parity condition,… (More)
or perhaps with the face of our mother or father. We quickly learn to identify the axis of symmetry and know intuitively that an object is symmetric if it “the same” on both sides of this axis. In mathematics symmetry is abundant and takes many forms. Symmetry like that of the butterfly or a face is referred to as reflexive symmetry. Any line in the plane… (More)
In this note, we give show how the equivariant derived category of Bernstein and Lunts can be extended to a purely algebraic setting, without the use of the theory of stacks. In particular, we show that it is possible to use the yoga of weights in the equivariant derived category, as one would in the usual derived category of a scheme over a finite field.