Carlos Florentino

The topology of moduli spaces of free group representations

For any complex affine reductive group G and a fixed choice of maximal compact subgroup K, we show that the G-character variety of a free group strongly deformation retracts to the corresponding K-character space, which is a real semi-algebraic set. Combining this with constructive invariant theory and classical topological methods, we show that the

Singularities of free group character varieties

{{\rm SLm}(3, mathbb {C})}

Schottky uniformization and vector bundles over Riemann surfaces

-character variety of a rank 2 free group is homotopic to an 8 sphere and the

Simultaneous similarity and triangularization of sets of 2 by 2 matrices

{{\rm SLm}(2, mathbb {C})}

STABILITY OF AFFINE G-VARIETIES AND IRREDUCIBILITY IN REDUCTIVE GROUPS

-character variety of a rank 3 free group is homotopic to a 6 sphere.

Character Varieties and the Moduli of Quiver Representations

Abstract We extend the coherent state transform (CST) of Hall to the context of the moduli spaces of semistable holomorphic vector bundles with fixed determinant over elliptic curves. We show that by applying the CST to appropriate distributions, we obtain the space of level k , rank n and genus one non-abelian theta functions with the unitarity of the CST transform being preserved. Furthermore, the shift in the level k → k + n appears in a natural way in this finite-dimensional framework.