Joseph Bernstein

Bio: Joseph Bernstein is an academic researcher from Ariel University. The author has contributed to research in topics: Failure rate & Automorphic form. The author has an hindex of 32, co-authored 185 publications receiving 4453 citations. Previous affiliations of Joseph Bernstein include California Institute of Technology & Tel Aviv University.

Equivariant Sheaves and Functors

Abstract: Derived category D G (X) and functors.- DG-modules and equivariant cohomology.- Equivariant cohomology of toric varieties.

P-invariant distributions on GL(N) and the classification of unitary representations of GL(N) (Non-archimedean case)

Abstract: P-invariant pairings 0.1o Let F be a non-archimedean local field, G = GL(n,F), and p c G the subgroup of all matrices with the last ~ow equal to (0,0,...,0,1). Many results about representations o? G were obtained by studying their restrictions to P (.see [GK], [BZI], [BZ2], [ZI]). In this paper we prove the following important technical result x~,hich clarifies the relations between representations of G and their restrictions to P.

Compact Modeling of MOSFET Wearout Mechanisms for Circuit-Reliability Simulation

Abstract: The integration density of state-of-the-art electronic systems is limited by the reliability of the manufactured integrated circuits at a desired circuit density. Design rules, operating voltages, frequencies, and temperatures are precisely chosen to ensure correct product functional operation over its intended lifetime. Thus, in order to obtain the overall performance and functionality bounded by various design and manufacturing constraints, the integrated circuit reliability must be modeled and analyzed at the very beginning of design stages. This paper reviews some of the most important intrinsic wearout mechanisms of MOSFETs (including hot-carrier injection, time-dependent dielectric breakdown, and negative bias temperature instability) and introduces new accelerated-lifetime and SPICE compact models of these wearout mechanisms. Based on these circuit-aging models, a new SPICE reliability simulation approach is proposed and demonstrated with a simplified SRAM design on a commercial 90-nm technology to help designers understand device-failure behaviors, predict circuit reliability, and improve product robustness.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Representation theory and complex geometry

Abstract: Preface.- Chapter 0. Introduction.- Chapter 1. Symplectic Geometry.- Chapter 2. Mosaic.- Chapter 3. Complex Semisimple Groups.- Chapter 4. Springer Theory.- Chapter 5. Equivariant K-Theory.- Chapter 6. Flag Varieties, K-Theory, and Harmonic Polynomials.- Chapter 7. Hecke Algebras and K-Theory.- Chapter 8. Representations of Convolution Algebras.- Bibliography.

Koszul Duality Patterns in Representation Theory

Abstract: The aim of this paper is to work out a concrete example as well as to provide the general pattern of applications of Koszul duality to repre- sentation theory. The paper consists of three parts relatively independent of each other. The first part gives a reasonably selfcontained introduction to Koszul rings and Koszul duality. Koszul rings are certain Z-graded rings with particularly nice homological properties which involve a kind of duality. Thus, to a Koszul ring one associates naturally the dual Koszul ring. The second part is devoted to an application to representation theory of semisimple Lie algebras. We show License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use KOSZUL DUALITY PATTERNS 527 that the block of the Bernstein-Gelfand-Gelfand category O that corresponds to any fixed central character is governed by the Koszul ring. Moreover, the dual of that ring governs a certain subcategory of the category O again. This generalizes the selfduality theorem conjectured by Beilinson and Ginsburg in 1986 and proved by Soergel in 1990. In the third part we study certain cate- gories of mixed perverse sheaves on a variety stratified by affine linear spaces. We provide a general criterion for such a category to be governed by a Koszul ring. In the flag variety case this reduces to the setup of part two. In the more general case of affine flag manifolds and affine Grassmannians the criterion should yield interesting results about representations of quantum groups and affine Lie algebras. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 E-mail address: sasha@math.mit.edu Department of Mathematics, The University of Chicago, Chicago, Illinois 60637 E-mail address: ginzburg@math.uchicago.edu Max-Planck-Institut fur Mathematik, Gottfried-Claren-Strase 26, D-53 Bonn 3, Germany Current address: Mathematisches Institut, Universitat Freiburg, Albertstrase 23b, D-79104 Freiburg, Germany E-mail address: soergel@sun1.mathematik.uni-freiburg.de License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use

Condition Monitoring for Device Reliability in Power Electronic Converters: A Review

Abstract: Condition monitoring (CM) has already been proven to be a cost effective means of enhancing reliability and improving customer service in power equipment, such as transformers and rotating electrical machinery. CM for power semiconductor devices in power electronic converters is at a more embryonic stage; however, as progress is made in understanding semiconductor device failure modes, appropriate sensor technologies, and signal processing techniques, this situation will rapidly improve. This technical review is carried out with the aim of describing the current state of the art in CM research for power electronics. Reliability models for power electronics, including dominant failure mechanisms of devices are described first. This is followed by a description of recently proposed CM techniques. The benefits and limitations of these techniques are then discussed. It is intended that this review will provide the basis for future developments in power electronics CM.

Equivariant cohomology, Koszul duality, and the localization theorem

Abstract: (1.1) This paper concerns three aspects of the action of a compact group K on a space X . The ®rst is concrete and the others are rather abstract. (1) Equivariantly formal spaces. These have the property that their cohomology may be computed from the structure of the zero and one dimensional orbits of the action of a maximal torus in K. (2) Koszul duality. This enables one to translate facts about equivariant cohomology into facts about its ordinary cohomology, and back. (3) Equivariant derived category. Many of the results in this paper apply not only to equivariant cohomology, but also to equivariant intersection cohomology. The equivariant derived category provides a framework in both of these may be considered simultaneously, as examples of ``equivariant sheaves''. We treat singular spaces on an equal footing with nonsingular ones. Along the way, we give a description of equivariant homology and equivariant intersection homology in terms of equivariant geometric cycles. Most of the themes in this paper have been considered by other authors in some context. In Sect. 1.7 we sketch the precursors that we know about. For most of the constructions in this paper, we consider an action of a compact connected Lie group K on a space X , however for the purposes of the introduction we will take K ˆ …S1† to be a torus. Invent. math. 131, 25±83 (1998)