Sean Monahan, Department of Pure Mathematics, University of Waterloo
"Approximating rational points on horospherical varieties"
I will discuss a recent paper that I wrote with Matt Satriano, the title of which is conveniently the title of this talk (arXiv 2308.11847). David McKinnon has a conjecture known as the “curve of best approximation (COBA)” conjecture, which says that among the sequences which approximate a given rational point on a projective variety, the ones that do their job the best must lie on a rational curve inside the variety. To probe this conjecture, Matt and I explored the case where the variety is horospherical so that we could use the tractable combinatorial theory which these varieties possess. Unfortunately, the stars did not align since this talk will not take place in MC 5417, which is roughly the centre point between the offices of Matt, David, and myself.
QNC 1502