The unifying theme of this book is the interplay among noncommutative geometry, physics,
and number theory. The two main objects of investigation are spaces where both the …

Abstract Lectures at the 1998 Les Houches Summer School: Topological Aspects of Low
Dimensional Systems. These lectures contain an introduction to various aspects of Chern …

We derive general expressions for the Kähler form of the L2-metric in terms of standard 2-
forms on vortex moduli spaces. In the case of abelian vortices in gauged linear sigma …

A bstract We investigate the correspondence between two dimensional topological gauge
theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This …

We propose a novel and simple method to compute the partition function of statistical
mechanics of local and semi-local BPS vortices in the Abelian–Higgs model and its non …

The Abelian Higgs model on a compact Riemann surface Σ of genus g is considered. We
show that for g> 1 the Bogomolny equations for multi-vortices at critical coupling can be …

We consider the Yang-Mills instanton equations on the four-dimensional manifold S 2× Σ,
where Σ is a compact Riemann surface of genus g> 1 or its covering space H 2= SU (1, 1)/U …

The quantization of the reduced first-order dynamics of the nonrelativistic model for Chern–
Simons vortices introduced by Manton is studied on a sphere of given radius. We perform …

Abstract We consider U (n+ 1) Yang–Mills instantons on the space Σ× S 2, where Σ is a
compact Riemann surface of genus g. Using an SU (2)-equivariant dimensional reduction …

We evaluate volume of moduli space of BPS vortices on a compact genus h Riemann
surface Σh by using topological field theory and localization technique developed by Moore …