Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces

For the derived category of bounded complexes of sheaves on a smooth projective surface, Bridgeland and Arcara-Bertram constructed Bridgeland stability conditions $(Z_m, \mathcal P_m)$ parametrized by $m \in (0, +\infty)$. In this paper, we show that the set of mini-walls in $(0, +\infty)$ of a fixed numerical type is locally finite. In addition, we strengthen a result of Bayer by proving that the moduli of polynomial Bridgeland semistable objects of a fixed numerical type coincides with the moduli of $(Z_m, \mathcal P_m)$-semistable objects whenever $m$ is larger than a universal constant depending only on the numerical type. We further identify the moduli of polynomial Bridgeland semistable objects with the Gieseker/Simpson moduli spaces and the Uhlenbeck compactification spaces.Comment: 26 page

On blowup formulae for the S-duality conjecture of Vafa and Witten

This is the first part of two papers. In this part, we prove the blowup formulae for virtual Hodge polynomials of Gieseker moduli spaces of rank-2 stable sheaves and Uhlenbeck compactification spaces over algebraic surfaces. In particular, we verify the blowup formulae for the S-duality conjecture of Vafa-Witten, i.e. the blowup formulae for the Euler numbers of instanton moduli spaces over algebraic surfaces.Comment: 24 page

Detecting peroxiredoxin hyperoxidation by one-dimensional isoelectric focusing

The activity of typical 2-cys peroxiredoxin (Prxs) can be regulated by hyperoxidation with a consequent loss of redox activity. Here we developed a simple assay to monitor the level of hyperoxidation of different typical 2-cys prxs simultaneously. This assay only requires standard equipment and can compare different samples on the same gel. It requires much less time than conventional 2D gels and gives more information than Western blotting with an antibody specific for hyperoxidized peroxiredoxin. This method could also be used to monitor protein modification with a charge difference such as phosphorylation