1. CJM Online first
 Abuaf, Roland; Boralevi, Ada

Orthogonal Bundles and SkewHamiltonian Matrices
Using properties of skewHamiltonian matrices and classic
connectedness results, we prove that the moduli space
$M_{ort}^0(r,n)$ of stable rank $r$ orthogonal vector bundles
on $\mathbb{P}^2$, with Chern classes $(c_1,c_2)=(0,n)$, and trivial
splitting on the general line, is smooth irreducible of
dimension $(r2)n\binom{r}{2}$ for $r=n$ and $n \ge 4$, and
$r=n1$ and $n\ge 8$. We speculate that the result holds in
greater generality.
Keywords:orthogonal vector bundles, moduli spaces, skewHamiltonian matrices Categories:14J60, 15B99 

2. CJM 2014 (vol 66 pp. 961)
 Baird, Thomas

Moduli Spaces of Vector Bundles over a Real Curve: $\mathbb Z/2$Betti Numbers
Moduli spaces of real bundles over a real curve arise naturally
as Lagrangian submanifolds of the moduli space of semistable
bundles over a complex curve. In this paper, we adapt the methods
of AtiyahBott's ``YangMills over a Riemann Surface'' to compute
$\mathbb Z/2$Betti numbers of these spaces.
Keywords:cohomology of moduli spaces, holomorphic vector bundles Categories:32L05, 14P25 

3. CJM 2007 (vol 59 pp. 845)
 Schaffhauser, Florent

Representations of the Fundamental Group of an $L$Punctured Sphere Generated by Products of Lagrangian Involutions
In this paper, we characterize unitary representations of $\pi:=\piS$ whose
generators $u_1, \dots, u_l$ (lying in conjugacy classes fixed initially)
can be decomposed as products of two Lagrangian involutions
$u_j=\s_j\s_{j+1}$ with $\s_{l+1}=\s_1$. Our main result is that such
representations are exactly the elements of the fixedpoint set of an
antisymplectic involution defined on the moduli space
$\Mod:=\Hom_{\mathcal C}(\pi,U(n))/U(n)$. Consequently, as this fixedpoint set is
nonempty, it is a Lagrangian submanifold of $\Mod$. To prove this, we use
the quasiHamiltonian description of the symplectic structure of $\Mod$ and
give conditions on an involution defined on a quasiHamiltonian $U$space
$(M, \w, \mu\from M \to U)$ for it to induce an antisymplectic involution on
the reduced space $M/\!/U := \mu^{1}(\{1\})/U$.
Keywords:momentum maps, moduli spaces, Lagrangian submanifolds, antisymplectic involutions, quasiHamiltonian Categories:53D20, 53D30 
