The Coupled Seiberg-Witten Equations, vortices, and Moduli spaces of stable pairs

We introduce coupled Seiberg-Witten equations, and we prove, using a generalized vortex equation, that, for Kaehler surfaces, the moduli space of solutions of these equations can be identified with a moduli space of holomorphic stable pairs. In the rank 1 case, one recovers Witten's result identifying the space of irreducible monopoles with a moduli space of divisors. As application, we give a short proof of the fact that a rational surface cannot be diffeomorphic to a minimal surface of general type.Comment: late

dDOR Is an EcR Coactivator that Forms a Feed-Forward Loop Connecting Insulin and Ecdysone Signaling

SummaryBackgroundMammalian DOR was discovered as a gene whose expression is misregulated in muscle of Zucker diabetic rats. Because no DOR loss-of-function mammalian models are available, we analyze here the in vivo function of DOR by studying flies mutant for Drosophila DOR (dDOR).ResultsWe show that dDOR is a novel coactivator of ecdysone receptor (EcR) that is needed during metamorphosis. dDOR binds EcR and is required for maximal EcR transcriptional activity. In the absence of dDOR, flies display a number of ecdysone loss-of-function phenotypes such as impaired spiracle eversion, impaired salivary gland degradation, and pupal lethality. Furthermore, dDOR knockout flies are lean. We find that dDOR expression is inhibited by insulin signaling via FOXO.ConclusionThis work uncovers dDOR as a novel EcR coactivator. It also establishes a mutual antagonistic relationship between ecdysone and insulin signaling in the fly fat body. Furthermore, because ecdysone signaling inhibits insulin signaling in the fat body, this also uncovers a feed-forward mechanism whereby ecdysone potentiates its own signaling via dDOR

Akt Phosphorylates Both Tsc1 and Tsc2 in Drosophila, but Neither Phosphorylation Is Required for Normal Animal Growth

Akt, an essential component of the insulin pathway, is a potent inducer of tissue growth. One of Akt's phosphorylation targets is Tsc2, an inhibitor of the anabolic kinase TOR. This could account for part of Akt's growth promoting activity. Although phosphorylation of Tsc2 by Akt does occur in vivo, and under certain circumstances can lead to reduced Tsc2 activity, the functional significance of this event is unclear since flies lacking Akt phosphorylation sites on Tsc2 are viable and normal in size and growth rate. Since Drosophila Tsc1, the obligate partner of Tsc2, has an Akt phosphorylation motif that is not conserved in mammals, we investigate here whether Akt redundantly phosphorylates the Tsc complex on Tsc1 and Tsc2. We provide evidence that Akt phosphorylates Tsc1 at Ser533. We show that flies lacking Akt phosphorylation sites on Tsc1 alone, or on both Tsc1 and Tsc2 concurrently, are viable and normal in size. This shows that phosphorylation of the Tsc1/2 complex by Akt is not required for Akt to activate TORC1 and to promote tissue growth in Drosophila

Drosophila Melted Modulates FOXO and TOR Activity

SummaryThe insulin/PI3K signaling pathway controls both tissue growth and metabolism. Here, we identify Melted as a new modulator of this pathway in Drosophila. Melted interacts with both Tsc1 and FOXO and can recruit these proteins to the cell membrane. We provide evidence that in the melted mutant, TOR activity is reduced and FOXO is activated. The melted mutant condition mimics the effects of nutrient deprivation in a normal animal, producing an animal with 40% less fat than normal

The structure of 2D semi-simple field theories

I classify all cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of kappa-classes and by an extension datum to the Deligne-Mumford boundary. Their effect on the Gromov-Witten potential is described by Givental's Fock space formulae. This leads to the reconstruction of Gromov-Witten invariants from the quantum cup-product at a single semi-simple point and from the first Chern class, confirming Givental's higher-genus reconstruction conjecture. The proof uses the Mumford conjecture proved by Madsen and Weiss.Comment: Small errors corrected in v3. Agrees with published versio

THADA regulates the organismal balance between energy storage and heat production

Human susceptibility to obesity is mainly genetic, yet the underlying evolutionary drivers causing variation from person to person are not clear. One theory rationalizes that populations that have adapted to warmer climates have reduced their metabolic rates, thereby increasing their propensity to store energy. We uncover here the function of a gene that supports this theory. THADA is one of the genes most strongly selected during evolution as humans settled in different climates. We report here that THADA knockout flies are obese, hyperphagic, have reduced energy production, and are sensitive to the cold. THADA binds the sarco/ER Ca2+ ATPase (SERCA) and acts on it as an uncoupler. Reducing SERCA activity in THADA mutant flies rescues their obesity, pinpointing SERCA as a key effector of THADA function. In sum, this identifies THADA as a regulator of the balance between energy consumption and energy storage, which was selected during human evolution

Abelian Yang-Mills theory on Real tori and Theta divisors of Klein surfaces

The purpose of this paper is to compute determinant index bundles of certain families of Real Dirac type operators on Klein surfaces as elements in the corresponding Grothendieck group of Real line bundles in the sense of Atiyah. On a Klein surface these determinant index bundles have a natural holomorphic description as theta line bundles. In particular we compute the first Stiefel-Whitney classes of the corresponding fixed point bundles on the real part of the Picard torus. The computation of these classes is important, because they control to a large extent the orientability of certain moduli spaces in Real gauge theory and Real algebraic geometry.Comment: LaTeX, 44 pages, to appear in Comm. Math. Phy

Formality theorems for Hochschild chains in the Lie algebroid setting

In this paper we prove Lie algebroid versions of Tsygan's formality conjecture for Hochschild chains both in the smooth and holomorphic settings. In the holomorphic setting our result implies a version of Tsygan's formality conjecture for Hochschild chains of the structure sheaf of any complex manifold and in the smooth setting this result allows us to describe quantum traces for an arbitrary Poisson Lie algebroid. The proofs are based on the use of Kontsevich's quasi-isomorphism for Hochschild cochains of R[[y_1,...,y_d]], Shoikhet's quasi-isomorphism for Hochschild chains of R[[y_1,...,y_d]], and Fedosov's resolutions of the natural analogues of Hochschild (co)chain complexes associated with a Lie algebroid.Comment: 40 pages, no figure

Reducible Connections in Massless Topological QCD and 4-manifolds

A role of reducible connections in Non-Abelian Seiberg-Witten invariants is analyzed with massless Topological QCD where monopole is extended to non-Abelian groups version. By giving small external fields, we found that vacuum expectation value can be separated into a part from Donaldson theory, a part from Abelian Monopole theory and a part from non-Abelian monopole theory. As a by-product, we find identities of U(1) topological invariants. In our proof, the duality relation and Higgs mechanism are not necessary.Comment: 23 pages, Latex, Some mistakes and typographical errors are revised in it. Especially, results written in section 4 are change

Logarithmic Moduli Spaces for Surfaces of Class VII

In this paper we describe logarithmic moduli spaces of pairs (S,D) consisting of minimal surfaces S of class VII with positive second Betti number b_2 together with reduced divisors D of b_2 rational curves. The special case of Enoki surfaces has already been considered by Dloussky and Kohler. We use normal forms for the action of the fundamental group of the complement of D and for the associated holomorphic contraction germ from (C^2,0) to (C^2,0).Comment: Minor correction of the dimension of the moduli spac