Title: Rational connectedness and parametrization of Galois extensions

Abstract: Given two Galois extensions with group G over the field of rationals Q, is there a Galois extension with group G over the rational function field Q(t) that specializes to both extensions? This and more general rational connectedness questions lie at the heart of the geometry of parametrizing spaces (or versal torsors) for Galois extensions with group G over Q. We shall discuss recent advances in understanding the number of equivalence classes under rational connectedness on such spaces with emphasis on the case of dihedral groups G of 2-power order, where little is known about the rationality of the corresponding parametrizing spaces. 

Joint work with D. Krashen

Zoom: https://huji.zoom.us/j/84202575300?pwd=QXBvNjV0bDBWUmwxVkFIYXpzQ29RQT09