These talks are informal discussion in the area of Superstring Theory. Formal talks are part of the Strings Seminar series above.
Using techniques originating in a certain
approach to Clifford bundles known as "geometric algebra", I discuss
a geometric reformulation of constrained generalized Killing spinor equations
which proves to be particularly effective in the study and classification of
supersymmetric flux compactifications of string and M-theory. As an
application, I discuss the most general N=2 compactifications of M-theory to
three dimensions, which were never studied in full generality before. I also
In an anisotropic limit of the weakly-coupled, 2+1-dimensional non-Abelian
gauge theories are equivalent to a collection of integrable
1+1-dimensional quantum field theories. This fact makes it possible to
understand confinement near this limit. Using exact form factors, it is
possible to study the theory away from the extreme anisotropic limit. The
string tension between fundamental color sources is found. Adjoint sources
are not confined. Some ideas concerning the isotropic case and the
generalization to 3+1 dimensions will be discussed.
After reviewing the cosmological constant/dark energy problem(s), I will present a dynamical mechanism wheiren a gap forms turning the unstable perturbative gravitational vacuum into a non-perturbative vacuum. Similar to the BCS theory this mechanism reflects the formation of Cooper-pairs which can cancel the would be large cosmological constant. Furthermore, when this mechanism is forumlated in the Ashtekar-Sen variables the cosmological constant problem bears close semblance to the strong CP problem in QCD. Open issues with this approach will also be addresssed.