These two talks will be suggestive of what my thesis defense will be like, whenever that is. Similar to Eloisa's talk, the first talk will give a selective review of the (linear) containment problem for symbolic powers of ideals in equicharacteristic rings, with a view towards Harbourne's conjecture in the geometric setting and two published results in the non-regular setting. I'll then summarize key results of my thesis in user-friendly forms, along with a recent improvement for tensor products of finitely-generated domains over algebraically closed fields, based on talking with Mel and Karen in the fall. The second talk will sketch select ideas going into this general "multinomial" containment result, along with suggesting initial applications for "tensor power" domains.

I expect to give at least one "comical" example of using these results in tandem, possibly involving the perfect number 28. Speaker(s): Robert Walker (University of Michigan)