iTHEMS Math Seminar by Dr. Yalong Cao on August 6, 2021

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