In the first hour, I will describe the standard trisection of CP^2 and how to put complex curves in CP^2 into bridge position with respect to this trisection. Time permitting, I will also present trisections of projective surfaces obtained as a branched covers over these curves. In the second hour, I will describe how to compute the homology and intersection form from a trisection diagram.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/TopologySeminar