Colloquium abstracts

Cristian Martinez*
Universidad del Norte Barranquilla, Colombia
June 8, 2020

Stability Conditions and Applications:  A couple of decades have passed since Bridgeland introduced the concept of stability condition. Since then geometric stability conditions have become one of the main modern tools used to study properties of vector bundles on projective varieties. From vanishing theorems for the cohomologies of a vector bundle to the Brill-Noether theorem to algorithms to run a Minimal Model Program for moduli spaces of sheaves, stability conditions and their wall-crossing behavior have provided us with new ways to attack classical problems in Algebraic Geometry. However, even though the theory of stability conditions on surfaces is somehow well developed, the existence of geometric stability conditions on an arbitrary variety is still widely open with only a few examples to show for dimensions 3 and higher. In this talk, I will gently introduce the concept of stability condition and present some applications of this theory on surfaces. Then I will talk about conjectures and counterexamples on how a s