I am no longer at the University of Bergen.
My areas of research are algebraic topology and homotopy theory. Specific interests include colocalization and localization in algebraic topology, homological algebra and various structures on triangulated categories (such as stratification).
In more detail, I am interested in colocalization and localization in triangulated categories that come from topology, such as the derived category of cochains on a topological space or those that come up in stable homotopy. I have named colocalization before localization not only because I am more interested in it than in localization, but also because in many cases it is actually better behaved than certain types of localization. This good behavior is probably one reason why local-cohomology has been so successful in commutative algebra.
Stratification for triangulated categories is a machinery developed by Benson, Iyengar and Krause to classify certain subcategories of a given triangulated category. Colocalization and localization are integral to stratification. I am also interested in deeper structures which cannot always be detected by stratification. Such a structure exists in the derived categories of complete intersections rings. It is an idea due to Benson and Greenlees to look for such structure in derived categories of cochains on spaces. It turns out that derived categories of cochains on elliptic spaces have this structure, as well as other spaces. One way to access such structure is by using the Hochschild cohomology of the algebra in question, which explains my interest in this theory.
Publications and preprints
- D. J. Benson, J. P. C. Greenlees, S. Shamir, Complete intersections and mod p cochains, accepted to Algebraic & Geometric Topology. arXiv:1104.4244 [math.AT]
- S. Shamir, Stratifying derived categories of cochains on certain spaces, Mathematische Zeitschrift. doi: 10.1007/s00209-011-0960-1
- S. Shamir, A spectral sequence for the Hochschild cohomology of a coconnective dga, accepted to Mathematica Scandinavica. arXiv:1011.0600 [math.KT]
- S. Shamir, A colocalization spectral sequence. arXiv:0910.5251 [math.AT]
- J. P. C. Greenlees, K. Hess, S. Shamir, Complete intersections in rational homotopy theory, accepted to the Journal of Pure and Applied Algebra. arXiv:0906.3247 [math.AT]
- S. Shamir, Colocalization functors in derived categories and torsion theories, Homology, Homotopy and Applications, Vol. 13 (2011), No. 1, pp.75-88. doi:10.4310/HHA.2011.v13.n1.a3
- S. Shamir, Cellular approximations and the Eilenberg-Moore spectral sequence, Algebraic & Geometric Topology 9 (2009) 1309-1340. doi:10.2140/agt.2009.9.1309
- S. Shamir, O. Kupferman, E. Shamir, Branching-depth hierarchies, Electronic Notes in Theoretical Computer Science 39(1) (2000). doi:10.1016/S1571-0661(05)82504-6
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Copyright Barbara Loester