Motivations of Ulrich bundles naturally came from linear algebra and commutative algebra. Thanks to
Eisenbud and Schreyer, such an algebraic notion dives into the geometric world, and become a key object
to observe the cone of cohomology tables and Cayley-Chow forms. They asked whether every projective
variety supports an Ulrich bundle, which is still wildly open even for smooth surfaces. In the very recent
years, Ulrich bundles have received a lot of attention, and many constructions of rank 2 Ulrich bundles
on surfaces are studied as well. In this talk, we review various motivations of Ulrich bundles and ideas for
the construction of rank 2 Ulrich bundles on surfaces.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/158