We plan to investigate topics revolving around the combinatorial aspects of algebraic geometry. We plan to work on topics that have emerged from our previous collaborations and seek to capitalize on our expertise in complementary aspects of the project. We also plan to inform each other of various topics of mutual interest that we have learned recently. We foresee three research articles in the cutting edge of combinatorial algebraic geometry as an outcome. We also plan to deliver lectures based on the work carried out during the meeting. We also plan to visit our colleagues in the Marseille area following our research in pairs.
We propose to work on three topics: Tutte polynomials and free resolutions (Spencer Backman and Madhusudan Manjunath), Geometric and Algebraic Structures in Smoothing Limit Linear Series (Ye Luo and Madhusudan Manjunath) and Castelunuovo’s Lemma for Graphs (Spencer Backman and Ye Luo). The first topic seeks to systematically study homological approach to Tutte expansions. The second topic is motivated by certain spaces of trees that arise in the smoothings of limit linear series of rank one on metrized complexes of algebraic curves. The third topic is motivated by an analogue on graphs of a lemma of Castelunuovo about linear series on algebraic curves.