Decreased activity of inducible nitric oxide synthase type 2 and modulation of the expression of glutathione S-transferase alpha, bcl-2, and metallothioneins during the differentiation of CaCo-2 cells.

Reactive oxygen species modulate the cell growth of a wide variety of mammalian cells. To determine whether oxidative metabolism is altered during the differentiation process, we studied the expression of pro- and antioxidant proteins in proliferating and differentiated CaCo-2 cells, a human colon adenocarcinoma cell line. Nitric oxide synthase type 2 (iNOS) produces nitric oxide (NO). Depending on its rate of synthesis, NO may either promote cellular and DNA damage or reduce the ability of other free radicals to induce cell injury. Using Western and Northern blot analysis and arginine conversion assay, we demonstrate that the expression of iNOS decreases when cells undergo differentiation. This biological event entails a diminished production of NO metabolites and correlates with the loss of activation of soluble guanylate cyclase activity. In differentiated cells, a 2-fold down-regulation of the nuclear factor kappa B activity was observed, suggesting that nuclear factor kappa B could be one of the iNOS gene regulatory factors in the CaCo-2 model. In parallel, we studied the expression of other antioxidant proteins including glutathione S-transferase alpha (GST alpha), bcl-2, and the metallothioneins (MTs). We show that the protein levels of GST alpha and MT increase during the differentiation of CaCo-2 cells, whereas bcl-2 levels decrease. Our investigation indicates that the expression of iNOS, GST alpha, bcl-2, and MT is associated with the enterocytic differentiation. The shift in the expression of specific antioxidant genes during CaCo-2 cell differentiation may occur to avoid alterations in the cell redox potential

Tree modules and counting polynomials

We give a formula for counting tree modules for the quiver S_g with g loops and one vertex in terms of tree modules on its universal cover. This formula, along with work of Helleloid and Rodriguez-Villegas, is used to show that the number of d-dimensional tree modules for S_g is polynomial in g with the same degree and leading coefficient as the counting polynomial A_{S_g}(d, q) for absolutely indecomposables over F_q, evaluated at q=1.Comment: 11 pages, comments welcomed, v2: improvements in exposition and some details added to last sectio

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

Poisson-de Rham homology of hypertoric varieties and nilpotent cones

We prove a conjecture of Etingof and the second author for hypertoric varieties, that the Poisson-de Rham homology of a unimodular hypertoric cone is isomorphic to the de Rham cohomology of its hypertoric resolution. More generally, we prove that this conjecture holds for an arbitrary conical variety admitting a symplectic resolution if and only if it holds in degree zero for all normal slices to symplectic leaves. The Poisson-de Rham homology of a Poisson cone inherits a second grading. In the hypertoric case, we compute the resulting 2-variable Poisson-de Rham-Poincare polynomial, and prove that it is equal to a specialization of an enrichment of the Tutte polynomial of a matroid that was introduced by Denham. We also compute this polynomial for S3-varieties of type A in terms of Kostka polynomials, modulo a previous conjecture of the first author, and we give a conjectural answer for nilpotent cones in arbitrary type, which we prove in rank less than or equal to 2.Comment: 25 page

The hypertoric intersection cohomology ring

We present a functorial computation of the equivariant intersection cohomology of a hypertoric variety, and endow it with a natural ring structure. When the hyperplane arrangement associated with the hypertoric variety is unimodular, we show that this ring structure is induced by a ring structure on the equivariant intersection cohomology sheaf in the equivariant derived category. The computation is given in terms of a localization functor which takes equivariant sheaves on a sufficiently nice stratified space to sheaves on a poset.Comment: Significant revisions in Section 5, with several corrected proof

Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds

We present a proof of the mirror conjecture of Aganagic-Vafa [arXiv:hep-th/0012041] and Aganagic-Klemm-Vafa [arXiv:hep-th/0105045] on disk enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary framing. In particular, we recover previous results on the conjecture for (i) an inner brane at zero framing in the total space of the canonical line bundle of the projective plane (Graber-Zaslow [arXiv:hep-th/0109075]), (ii) an outer brane at arbitrary framing in the resolved conifold (Zhou [arXiv:1001.0447]), and (iii) an outer brane at zero framing in the total space of the canonical line bundle of the projective plane (Brini [arXiv:1102.0281, Section 5.3]).Comment: 39 pages, 11 figure

Small representations of finite classical groups

Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of representations of the group. In particular, the representations of small dimensions tend to contribute the largest terms to these sums, so a systematic knowledge of these small representations could lead to proofs of important conjectures which are currently out of reach. Despite the classification by Lusztig of the irreducible representations of finite groups of Lie type, it seems that this aspect remains obscure. In this note we develop a language which seems to be adequate for the description of the "small" representations of finite classical groups and puts in the forefront the notion of rank of a representation. We describe a method, the "eta correspondence", to construct small representations, and we conjecture that our construction is exhaustive. We also give a strong estimate on the dimension of small representations in terms of their rank. For the sake of clarity, in this note we describe in detail only the case of the finite symplectic groups.Comment: 18 pages, 9 figures, accepted for publications in the proceedings of the conference on the occasion of Roger Howe's 70th birthday (1-5 June 2015, Yale University, New Haven, CT

SYZ mirror symmetry for hypertoric varieties

We construct a Lagrangian torus fibration on a smooth hypertoric variety and a corresponding SYZ mirror variety using $T$-duality and generating functions of open Gromov-Witten invariants. The variety is singular in general. We construct a resolution using the wall and chamber structure of the SYZ base.Comment: v_2: 31 pages, 5 figures, minor revision. To appear in Communications in Mathematical Physic

Gauge Theory, Mirror Symmetry, and the Geometric Langlands Program

I provide an introduction to the recent work on the Montonen-Olive duality of N = 4 super-Yang-Mills theory and the Geometric Langlands Program