On Wednesday, we reminded ourselves of the whole story of N=2 gauge theory with the SU(2) gauge symmetry - i.e. Seiberg-Witten I - under the leadership of Kirill Saraikin. This nice application of the holomorphy of the prepotential; the known conditions on the allowed behavior around singularities; a known expansion around infinity may be used to reconstruct the low-energy physics exactly. We discussed how much it is known for sure that there are three singularities on the moduli space - of course, the Dijkgraaf-Vafa constructions give us the whole result, including the fact that there are three singularities.
On Thursday, Christopher Beasley who is gonna be at Harvard explained his interesting work with Edward Witten about the non-Abelian localization of Chern-Simons theory. The partition sum was evaluated for a very special subclass of three-dimensional manifolds, the so-called Seifert manifolds, which may be visualized as a U(1) bundle over the genus g Riemann surfaces. Why is it non-Abelian? For their conjecture to work, one must find a group H that acts on the configuration space, and in their case, it is a non-Abelian group.
On Friday, Tasneem Zehra Husain was talking about the SUGRA solutions for M5-branes wrapped on the cycles of various manifolds. She spent some time with introduction - supergravity equations of motion, the conditions for preserved supersymmetry - and the main task is to find out some generally satisfied conditions that hold for the manifolds even after you take the back-reaction into account. The main condition of this sort says that the Hodge dual of the calibration form is closed - i.e. the calibration form is co-closed.