In the late 90's, S. K. Donaldson and R. P. Thomas
suggested a program on gauge theory in higher dimensions.
In alignment with this program, Thomas introduced
the holomorphic Casson invariant for a smooth projective Calabi-Yau
The holomorphic Casson invariant is a deformation invariant of a smooth
projective Calabi-Yau threefold.
Thomas defined it by constructing algebro-geometrically a virtual moduli
of the moduli space of semi-stable sheaves under some technical assumptions.
This can be viewed as a complex analogy of the Taubes-Casson invariant
defined by C. H. Taubes.
However, it is not achieved as yet to construct the invariant
in a "gauge theoretic", or an analytic way.
In this seminar, we exhibit an analytic approach to this invariant
by using perturbed Hermitian-Einstein equations over a compact Kahler
which we call Donaldson-Thomas equations.
We begin this seminar with some backgrounds on the holomorphic Casson
and the Hermitian-Einstein equations.
Subsequently, we introduce the Donaldson-Thomas equations
and describe local structures of the moduli space of solutions
to the Donaldson-Thomas equations.
Furthermore, we discuss analytic results on solutions to the equations,
aiming at constructing the holomorphic Casson invariant
for compact Kahler threefolds.