Stephen McKean (BYU)
Title: Inverse curve problems for del Pezzo surfaces
Abstract: The inverse Galois problem for del Pezzo surfaces asks, over a given field, which groups arise as the automorphism group of a del Pezzo surface over k. Over infinite fields, this problem is still open for del Pezzos of degree at most 4. I will talk about joint work with Enis Kaya, Sam Streeter, and Happy Uppal, in which we solve a weaker problem: which counts of lines and conic bundles occur on del Pezzo surfaces over k? Our solution is valid for any finite, separably closed, local, Hilbertian, or real closed field, and we conjecture that it should hold for arbitrary fields. Time permitting, I will discuss a few cases of the inverse Galois problem for del Pezzo surfaces that we solve en route to the inverse curve problem.
Location: UQAM PK-5675