"Hilbert Series for Instanton Moduli Spaces" :
The moduli space of instantons of k G instantons on C^2, for a gauge group G is a well studied object, both in physics and in mathematics. An algebraic way to construct the moduli space is well known from the work of ADHM, that is understood in field theory as a Higgs branch of certain N=2 supersymmetric quiver gauge theories, and in string theory as the bound states of branes within branes in the Dp D(p+4) system.
The reduced moduli space of instantons is known to be a singular hyperKahler cone of quaternionic dimension kh-1, with h the dual coxeter number of G. As such it admits many nice features and can be related to the chiral ring of the corresponding quiver gauge theory. This talk will go over the Hilbert series, a rational function that counts operators in the chiral ring, and show how it can be used to understand features of the moduli space of instantons.
The methods in computing the Hilbert series, further allow to get results for cases where G is an exceptional group. In such cases the ADHM construction is not available, and the computation gives information on brane configurations with exceptional gauge groups.