Jay Yang

Graduate Fellow

Summer 2016:  As for concrete results, the most notable the progress towards the completion of the paper "Random Toric Surfaces and a Threshold for Smoothness". I hope to have it on arxiv within the month, much of this semester has been spent improving this paper in various ways. This includes importantly fixing many of the minor issues that cropped up in close inspection. But as well as edits of that form, I have significantly refined the result that I had a the beginning of the semester. In addition to the actual work of preparing this paper for publication, I gave a talk this semester about the contents of this paper at the Algebraic Geometry Seminar.

In new work, my adviser Daniel Erman and I have also begun work on a project tackling the application of the results of the theory of random graphs to Stanley-Reisner ideals. We are hoping to get results about the expected values of betti table entries. In particular our preliminary work has yielded at least an idea for a proof that the expected values of the first row of the betti table follows a normal curve.

I have also used the time to move my further my studies. In additon to classes, in the past semester, I've learned the basics of tropical geometry, and gave a talk about it in the graduate algebraic geometry seminar.