On residual categories for Grassmannians

We define and discuss some general properties of residual categories of Lefschetz decompositions in triangulated categories. In the case of the derived category of coherent sheaves on the Grassmannian $\text{G}(k,n)$ we conjecture that the residual category associated with Fonarev's Lefschetz exceptional collection is generated by a completely orthogonal exceptional collection. We prove this conjecture for $k = p$, a prime number, modulo completeness of Fonarev's collection (and for $p = 3$ we check this completeness).Comment: Final version. To appear in PLM

On the derived category of the adjoint Grassmannian of type F

We construct a full rectangular Lefschetz collection in the derived category of the adjoint Grassmannian in type $\mathrm{F}_4$. This gives the first example of a full exceptional collection on this variety and also completes the proof of a conjecture due to Alexander Kuznetsov and the author that relates the structure of the derived category of coherent sheaves to the small quantum cohomology in the case of adjoint varieties for non-simply laced groups.Comment: v2: minor improvements throughout the text, introduction made more precise, section 4 reorganised and clarifie

Ownership, access and sequential investment

We extend the property-rights framework to allow for: a separation of the ownership rights of access and veto; and sequential investment. Parties investing first (ex ante) do so before contracting is possible. Parties that invest second (ex post) can contract on (at least some) of their investment costs. Along with this cost-sharing effect, the incentive to invest is affected by a strategic effect generated by sequential investment. Together these effects can overturn some of the predictions of the property-rights literature. For example, the most inclusive ownership structure might not be optimal, even if all investments are complementary.property rights; access; veto; firm organization; sequential investment; holdup

Gromov-Witten correspondences, derived categories, and Frobenius manifolds

In this thesis we consider questions arising in Gromov-Witten theory, quantum cohomology and mirror symmetry. The first two chapters deal with Gromov-Witten theory and derived categories for moduli spaces of stable curves of genus zero with n marked points. In the third chapter we consider Landau-Ginzburg models for odd-dimensional quadrics. In the first chapter we study moduli spaces of stable maps with target being the moduli space of stable curves of genus zero with n marked points, and curve class being a class of a boundary curve. An explicit formula for the respective Gromov-Witten invariants is given. In the second chapter we consider inductive constructions of semi-orthogonal decompositions and exceptional collections in the derived category of moduli spaces moduli spaces of stable curves of genus zero with n marked points based on a nice presentation of these spaces as consecutive blow-ups due to Keel. In the third chapter we give an ad hoc partial compactification of the standard Landau-Ginzburg potential for an odd-dimensional quadric, and study its Gauss-Manin system in the case of three dimensional quadrics. We show that under some hypothesis this Landau-Ginzburg potential would give a Frobenius manifold isomorphic to the quantum cohomology of a three dimensional quadric

Hochschild cohomology of generalised Grassmannians

We compute the Hochschild-Kostant-Rosenberg decomposition of the Hochschild cohomology of generalised Grassmannians, i.e. partial flag varieties associated to maximal parabolic subgroups in a simple algebraic group. We explain how the decomposition is concentrated in global sections for so-called (co)minuscule and (co)adjoint generalised Grassmannians, and we suggest that for (almost) all other cases the same vanishing of the higher cohomology does not hold. Our methods give an explicit partial description of the Gerstenhaber algebra structure for the Hochschild cohomology of cominuscule and adjoint generalised Grassmannians. We also consider the case of adjoint partial flag varieties in type A, which are associated to certain submaximal parabolic subgroups.Comment: 41 pages, 2 appendice

Ownership, access and sequential investment

We extend the property-rights framework to allow for: a separation of the ownership rights of access and veto; and sequential investment. Parties investing first (ex ante) do so before contracting is possible. Parties that invest second (ex post) can contract on (at least some) of their investment costs. Along with this cost-sharing effect, the incentive to invest is affected by a strategic effect generated by sequential investment. Together these effects can overturn some of the predictions of the property-rights literature. For example, the most inclusive ownership structure might not be optimal, even if all investments are complementary

Surface Electrostatics of Lipid Bilayers by EPR of a pH-Sensitive Spin-Labeled Lipid

AbstractMany biophysical processes such as insertion of proteins into membranes and membrane fusion are governed by bilayer electrostatic potential. At the time of this writing, the arsenal of biophysical methods for such measurements is limited to a few techniques. Here we describe a, to our knowledge, new spin-probe electron paramagnetic resonance (EPR) approach for assessing the electrostatic surface potential of lipid bilayers that is based on a recently synthesized EPR probe (IMTSL-PTE) containing a reversibly ionizable nitroxide tag attached to the lipids’ polar headgroup. EPR spectra of the probe directly report on its ionization state and, therefore, on electrostatic potential through changes in nitroxide magnetic parameters and the degree of rotational averaging. Further, the lipid nature of the probe provides its full integration into lipid bilayers. Tethering the nitroxide moiety directly to the lipid polar headgroup defines the location of the measured potential with respect to the lipid bilayer interface. Electrostatic surface potentials measured by EPR of IMTSL-PTE show a remarkable (within ±2%) agreement with the Gouy-Chapman theory for anionic DMPG bilayers in fluid (48°C) phase at low electrolyte concentration (50 mM) and in gel (17°C) phase at 150-mM electrolyte concentration. This agreement begins to diminish for DMPG vesicles in gel phase (17°C) upon varying electrolyte concentration and fluid phase bilayers formed from DMPG/DMPC and POPG/POPC mixtures. Possible reasons for such deviations, as well as the proper choice of an electrostatically neutral reference interface, have been discussed. Described EPR method is expected to be fully applicable to more-complex models of cellular membranes