Please join us welcoming Ph. D student Jose Medel for this week's graduate student seminar.  

Our Graduate Student Seminar gives students the ability to showcase interesting results that they have found in their research. Presenters are typically graduate students in mathemathematics, but can also be undergraduates, students in other disiplines, and faculty as well. 

Presentations should be able to be understood by undergraduate students in mathematics or related disipline. 

Title: Holomorphic line bundles and blowing up singularities in K3 surfaces

Abstract: For this talk, I’ll introduce holomorphic line bundles over complex surfaces. I’ll also introduce basic invariants algebraic geometers use to calculate holomorphic line bundles. After some definitions and basic examples, I’ll give a little proof of a special case of the famous hairy ball theorem. That is, all vector fields over S^2 have at least 2 zeros up to multiplicity. Lastly, after a few more definitions, I’ll conclude the talk with resolution of singularities of K3 surfaces and calculations of their Cohomology groups.