We will discuss new ideas and techniques for producing positive Dehn twist factorizations of surface mapping classes (joint work with Mustafa Korkmaz), which yield novel constructions of interesting symplectic and smooth 4-manifolds, such as small symplectic Calabi-Yau surfaces and exotic rational surfaces, via Lefschetz fibrations and pencils.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/6656