K-orbit closures on G/B as universal degeneracy loci for flagged vector bundles with symmetric or skew-symmetric bilinear form

We use equivariant localization and divided difference operators to determine formulas for the torus-equivariant fundamental cohomology classes of $K$-orbit closures on the flag variety $G/B$, where G = GL(n,\C), and where $K$ is one of the symmetric subgroups O(n,\C) or Sp(n,\C). We realize these orbit closures as universal degeneracy loci for a vector bundle over a variety equipped with a single flag of subbundles and a nondegenerate symmetric or skew-symmetric bilinear form taking values in the trivial bundle. We describe how our equivariant formulas can be interpreted as giving formulas for the classes of such loci in terms of the Chern classes of the various bundles.Comment: Minor revisions and corrections suggested by referees. Final version, to appear in Transformation Group

Equivariant pretheories and invariants of torsors

In the present paper we introduce and study the notion of an equivariant pretheory: basic examples include equivariant Chow groups, equivariant K-theory and equivariant algebraic cobordism. To extend this set of examples we define an equivariant (co)homology theory with coefficients in a Rost cycle module and provide a version of Merkurjev's (equivariant K-theory) spectral sequence for such a theory. As an application we generalize the theorem of Karpenko-Merkurjev on G-torsors and rational cycles; to every G-torsor E and a G-equivariant pretheory we associate a graded ring which serves as an invariant of E. In the case of Chow groups this ring encodes the information concerning the motivic J-invariant of E and in the case of Grothendieck's K_0 -- indexes of the respective Tits algebras.Comment: 23 pages; this is an essentially extended version of the previous preprint: the construction of an equivariant cycle (co)homology and the spectral sequence (generalizing the long exact localization sequence) are adde

Syzygies in equivariant cohomology for non-abelian Lie groups

We extend the work of Allday-Franz-Puppe on syzygies in equivariant cohomology from tori to arbitrary compact connected Lie groups G. In particular, we show that for a compact orientable G-manifold X the analogue of the Chang-Skjelbred sequence is exact if and only if the equivariant cohomology of X is reflexive, if and only if the equivariant Poincare pairing for X is perfect. Along the way we establish that the equivariant cohomology modules arising from the orbit filtration of X are Cohen-Macaulay. We allow singular spaces and introduce a Cartan model for their equivariant cohomology. We also develop a criterion for the finiteness of the number of infinitesimal orbit types of a G-manifold.Comment: 28 pages; minor change

Tilt Texture Domains on a Membrane and Chirality induced Budding

We study the equilibrium conformations of a lipid domain on a planar fluid membrane where the domain is decorated by a vector field representing the tilt of the stiff fatty acid chains of the lipid molecules, while the surrounding membrane is fluid and structureless. The inclusion of chirality in the bulk of the domain induces a novel budding of the membrane, which preempts the budding induced by a decrease in interfacial tension.Comment: 5 pages, 3 figure

An extremal effective survey about extremal effective cycles in moduli spaces of curves

We survey recent developments and open problems about extremal effective divisors and higher codimension cycles in moduli spaces of curves.Comment: Submitted to the Proceedings of the Abel Symposium 2017. Comments are welcom

GALEX J201337.6+092801: The lowest gravity subdwarf B pulsator

We present the recent discovery of a new subdwarf B variable (sdBV), with an exceptionally low surface gravity. Our spectroscopy of J20136+0928 places it at Teff = 32100 +/- 500, log(g) = 5.15 +/- 0.10, and log(He/H) = -2.8 +/- 0.1. With a magnitude of B = 12.0, it is the second brightest V361 Hya star ever found. Photometry from three different observatories reveals a temporal spectrum with eleven clearly detected periods in the range 376 to 566 s, and at least five more close to our detection limit. These periods are unusually long for the V361 Hya class of short-period sdBV pulsators, but not unreasonable for p- and g-modes close to the radial fundamental, given its low surface gravity. Of the ~50 short period sdB pulsators known to date, only a single one has been found to have comparable spectroscopic parameters to J20136+0928. This is the enigmatic high-amplitude pulsator V338 Ser, and we conclude that J20136+0928 is the second example of this rare subclass of sdB pulsators located well above the canonical extreme horizontal branch in the HR diagram.Comment: 5 pages, accepted for publication in ApJ Letter

On Non-Abelian Symplectic Cutting

We discuss symplectic cutting for Hamiltonian actions of non-Abelian compact groups. By using a degeneration based on the Vinberg monoid we give, in good cases, a global quotient description of a surgery construction introduced by Woodward and Meinrenken, and show it can be interpreted in algebro-geometric terms. A key ingredient is the `universal cut' of the cotangent bundle of the group itself, which is identified with a moduli space of framed bundles on chains of projective lines recently introduced by the authors.Comment: Various edits made, to appear in Transformation Groups. 28 pages, 8 figure

Curvature-coupling dependence of membrane protein diffusion coefficients

We consider the lateral diffusion of a protein interacting with the curvature of the membrane. The interaction energy is minimized if the particle is at a membrane position with a certain curvature that agrees with the spontaneous curvature of the particle. We employ stochastic simulations that take into account both the thermal fluctuations of the membrane and the diffusive behavior of the particle. In this study we neglect the influence of the particle on the membrane dynamics, thus the membrane dynamics agrees with that of a freely fluctuating membrane. Overall, we find that this curvature-coupling substantially enhances the diffusion coefficient. We compare the ratio of the projected or measured diffusion coefficient and the free intramembrane diffusion coefficient, which is a parameter of the simulations, with analytical results that rely on several approximations. We find that the simulations always lead to a somewhat smaller diffusion coefficient than our analytical approach. A detailed study of the correlations of the forces acting on the particle indicates that the diffusing inclusion tries to follow favorable positions on the membrane, such that forces along the trajectory are on average smaller than they would be for random particle positions.Comment: 16 pages, 8 figure

Complete intersections: Moduli, Torelli, and good reduction

We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conjecture, as proved for curves and abelian varieties by Faltings. For example, we prove an analogue of the Shafarevich conjecture for cubic and quartic threefolds and intersections of two quadrics.Comment: 37 pages. Typo's fixed. Expanded Section 2.