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Full-Text Articles in Algebraic Geometry
Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna Tymoczko
Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna Tymoczko
Department of Math & Statistics Faculty Publications
Springer varieties are studied because their cohomology carries a natural action of the symmetric group Sn and their top-dimensional cohomology is irreducible. In his work on tangle invariants, Khovanov constructed a family of Springer varieties Xn as subvarieties of the product of spheres (S2)n. We show that if Xn is embedded antipodally in (S2)n then the natural Sn-action on (S2)n induces an Sn-representation on the image of H*(Xn). This representation is the Springer representation. Our construction admits an elementary (and geometrically …
The Bar-Natan Skein Module Of The Solid Torus And The Homology Of (N,N) Springer Varieties, Heather M. Russell
The Bar-Natan Skein Module Of The Solid Torus And The Homology Of (N,N) Springer Varieties, Heather M. Russell
Department of Math & Statistics Faculty Publications
This paper establishes an isomorphism between the Bar-Natan skein module of the solid torus with a particular boundary curve system and the homology of the (n, n) Springer variety. The results build on Khovanov's work with crossingless matchings and the cohomology of the (n, n) Springer variety. We also give a formula for comultiplication in the Bar-Natan skein module for this specific three-manifold and boundary curve system.
Determining Error Bars In Measurements Of Ultrashort Laser Pulses, Ziyang Wang, Erik Zeek, Rick Trebino, Paul Kvam
Determining Error Bars In Measurements Of Ultrashort Laser Pulses, Ziyang Wang, Erik Zeek, Rick Trebino, Paul Kvam
Department of Math & Statistics Faculty Publications
We present a simple and automatic method for determining the uncertainty in the retrieved intensity and phase versus time (and frequency) due to noise in a frequency-resolved optical-gating trace, independent of noise source. It uses the ‘‘bootstrap’’ statistical method and also yields an automated method for phase blanking (omitting the phase when the intensity is too low to determine it).