Forgetful maps between Deligne-Mostow ball quotients

We study forgetful maps between Deligne-Mostow moduli spaces of weighted points on P^1, and classify the forgetful maps that extend to a map of orbifolds between the stable completions. The cases where this happens include the Livn\'e fibrations and the Mostow/Toledo maps between complex hyperbolic surfaces. They also include a retraction of a 3-dimensional ball quotient onto one of its 1-dimensional totally geodesic complex submanifolds

Moduli Spaces for D-branes at the Tip of a Cone

For physicists: We show that the quiver gauge theory derived from a Calabi-Yau cone via an exceptional collection of line bundles on the base has the original cone as a component of its classical moduli space. For mathematicians: We use data from the derived category of sheaves on a Fano surface to construct a quiver, and show that its moduli space of representations has a component which is isomorphic to the anticanonical cone over the surface.Comment: 8 page

Equivariant volumes of non-compact quotients and instanton counting

Motivated by Nekrasov's instanton counting, we discuss a method for calculating equivariant volumes of non-compact quotients in symplectic and hyper-K\"ahler geometry by means of the Jeffrey-Kirwan residue-formula of non-abelian localization. In order to overcome the non-compactness, we use varying symplectic cuts to reduce the problem to a compact setting, and study what happens in the limit that recovers the original problem. We implement this method for the ADHM construction of the moduli spaces of framed Yang-Mills instantons on $\R^{4}$ and rederive the formulas for the equivariant volumes obtained earlier by Nekrasov-Shadchin, expressing these volumes as iterated residues of a single rational function.Comment: 34 pages, 2 figures; minor typos corrected, to appear in Comm. Math. Phy

Semitoric integrable systems on symplectic 4-manifolds

Let M be a symplectic 4-manifold. A semitoric integrable system on M is a pair of real-valued smooth functions J, H on M for which J generates a Hamiltonian S^1-action and the Poisson brackets {J,H} vanish. We shall introduce new global symplectic invariants for these systems; some of these invariants encode topological or geometric aspects, while others encode analytical information about the singularities and how they stand with respect to the system. Our goal is to prove that a semitoric system is completely determined by the invariants we introduce

Exercise blood-drop metabolic profiling links metabolism with perceived exertion

BACKGROUND: Assessing detailed metabolism in exercising persons minute-to-minute has not been possible. We developed a “drop-of-blood” platform to fulfill that need. Our study aimed not only to demonstrate the utility of our methodology, but also to give insights into unknown mechanisms and new directions. METHODS: We developed a platform, based on gas chromatography and mass spectrometry, to assess metabolism from a blood-drop. We first observed a single volunteer who ran 13 km in 60 min. We particularly monitored relative perceived exertion (RPE). We observed that 2,3-bisphosphoglycerate peaked at RPE in this subject. We next expanded these findings to women and men volunteers who performed an RPE-based exercise protocol to RPE at Fi O 2 20.9% or Fi O 2 14.5% in random order. RESULTS: At 6 km, our subject reached his maximum relative perceived exertion (RPE); however, he continued running, felt better, and finished his run. Lactate levels had stably increased by 2 km, ketoacids increased gradually until the run’s end, while the hypoxia marker, 2,3 bisphosphoglycerate, peaked at maximum relative perceived exertion. In our normal volunteers, the changes in lactate, pyruvate, ß hydroxybutyrate and a hydroxybutyrate were not identical, but similar to our model proband runner. CONCLUSION: Glucose availability was not the limiting factor, as glucose availability increased towards exercise end in highly exerted subjects. Instead, the tricarboxylic acid?oxphos pathway, lactate clearance, and thus and the oxidative capacity appeared to be the defining elements in confronting maximal exertion. These ideas must be tested further in more definitive studies. Our preliminary work suggests that our single-drop methodology could be of great utility in studying exercise physiology

Gauging the Poisson sigma model

We show how to carry out the gauging of the Poisson sigma model in an AKSZ inspired formulation by coupling it to the a generalization of the Weil model worked out in ref. arXiv:0706.1289 [hep-th]. We call the resulting gauged field theory, Poisson--Weil sigma model. We study the BV cohomology of the model and show its relation to Hamiltonian basic and equivariant Poisson cohomology. As an application, we carry out the gauge fixing of the pure Weil model and of the Poisson--Weil model. In the first case, we obtain the 2--dimensional version of Donaldson--Witten topological gauge theory, describing the moduli space of flat connections on a closed surface. In the second case, we recover the gauged A topological sigma model worked out by Baptista describing the moduli space of solutions of the so--called vortex equations.Comment: 49 pages, no figures. Typos corrected. Presentation improve

The cohomology of quotients in symplectic and algebraic geometry

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