Linear Systems on Metric graphs and Some Applications to Tropical Geometry and Non-Archimedean Geometry

Series: 
Dissertation Defense
Thursday, June 26, 2014 - 11:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
School of Mathematics, Georgia Tech
The work in this dissertation is mainly focused on three subjects which are essentially related to linear systems on metric graphs and its application: (1) rank-determining sets of metric graphs, which can be employed to actually compute the rank function of arbitrary divisors on an arbitrary metric graph, (2) a tropical convexity theory for linear systems on metric graphs, and (3) smoothing of limit linear series of rank one on refined metrized complex (an intermediate object between metric graphs and algebraic curves),