I was just at Bar Ilan University for Louis Rowen’s great birthday conference. Included among my fellow speakers were Danny Krashen and Alexander Merkurjev. They told me about something I should have seen long ago: versal torsors. Among other things, versal torsors give a way to produce universal bounds on symbol lengths for central division algebras with bounded index. This blew my mind. Let me show you how it works.More...
Our May AIM workhop on Algebraic Vision was an absolutely fascinating experience. I will eventually write more about things that I learned there, but what I will write about first is of the most interesting from a sociological perspective. It sheds some light on the culture gap between computer vision and pure mathematics.More...
Martin Olsson and I have a new paper about derived Torelli theorems for K3 surfaces. It is a piece of our gradual attempt to recast Torelli theorems in terms of a combination of the derived category and the Chow theory. While we previously showed a very coarse kind of Torelli statement – a certain kind of derived equivalence that respects a filtration on Chow theory implies the existence of an isomorphism – we are now able to show that there is an isomorphism that acts on the cohomology in the same way as the derived equivalence. (There is a slight subtlety involving the filtration-perserving condition, but this is precisely analogous to the condition in the Torelli theorem about preserving ample classes.) Our original proof ultimately used analysis, but the new one is purely algebraic.More...
teaching, grading, analysis
I’m thinking about grading again, as I have to do every quarter. My grading scale is usually not set in stone – I say that exams will have weights that float in some range – and I usually try to look at the data and tweak the weights so that things are fair.
None of this has ever sat right with me. Every professor and lecturer sets his or her own grading scale and we make no effort to harmonize them. Are we hurting the students? What if Professor X and Lecturer Y use scale s, but I’ve been using scale t and this makes my best students fail while propping up my weaker students? (That seems like an absurd edge case, but how can be we sure we aren’t doing something like this?)
I decided to investigate.More...
My online section of Math 126 (our third quarter of calculus) has begun again! If you are taking it, you will find our lecture site here. There is a backing Canvas site (available to UW students only). A few things will be different this quarter:More...
This is my new website, built on Jekyll (which is a static site and blog generator that is markdown-friendly, among other things). This version of the site should stay more up-to-date than my last site. It will also have a mildly blog-like aspect, but I’m not sure how often I’ll actually write anything.More...
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