Unfortunately things have gotten more busy so I haven’t been writing on the blog. However, I found a new way to prepare talks that I really like: I type out my notes in a way which I hope is readable to someone who has not been to the talk. It is halfway between an expository paper and lecture notes and the advantage is that I have a product which I can share on my webpage (and I find it more useful than slides — I am starting to dislike slides presentations for seminar talks). Anyway, I’ll advertise some of these here (I’ve never actually posted about my own research on this blog, so it’s a first!):
1. I’ve been working with Laurent Gruson and Jerzy Weyman on finding geometric interpretations for orbits in “Vinberg -representations”. I gave a talk on this at Princeton (notes) and Michigan (notes). The Princeton talk is more introductory in nature, and even though there is overlap, the two sets of notes should complement one another (for the record, both talks were approximately 1 hour, 45 minutes).
2. A separate project with Weyman involves trying to understand Koszul homology for certain classes of determinantal-like ideals. The motivation comes from trying to classify minimal free resolutions over quadric hypersurface rings and in trying to understand a certain result of Koike and Terada in combinatorial representation theory. I’m giving a talk on this tomorrow at Michigan (notes).
It’s a bit time-consuming, but I think preparing notes like this can be very useful, especially for projects which haven’t been finished yet (it helps me gain direction). I hope more people try it!