The final Math Seminar of this semester was held on August 9th. This time, we invited our new colleague Dr. Yalong Cao as a speaker.
First, he gave an overview of the celebrated Yang-MIlls theory in real dimensions 3 and 4.
Next, it was explained that one can complexify the above Yang-Mills theory on Calabi-Yau 3 and 4-folds.
The point is that in algebro-geometric setting, moduli spaces of Yang-Mills connections admit nice compactifications.
Finally, he explained the connection between the above story and the enumerative geometry, specifically on counting (stable) coherent sheaves and complex ASD connections on Calabi-Yau 4-folds. He and his collaborators proposed a conjectural sheaf-theoretic interpretation of Klemm-Pandharipande’s BPS invariants of CY 4-folds defined using Gromov-Witten theory.

Reported by Hiroyasu Miyazaki