Angus McAndrew is speaking in the Algebra Seminar this week. We will go out for lunch after the talk. When: Friday 5 May, 12-1pm Where: Carslaw 173 Title: A descent theorem for K3 surfaces Abstract: Descent problems have fascinated mathematicians since ancient times. A modern descent question asks for the field of definition of a given algebraic variety, i.e. whether there is a criterion for when it can be descended from a field to a smaller one. A theorem of Grothendieck gives an answer to this question in the case of abelian varieties and transcendental field extensions. We will discuss a general conjecture inspired by this, and prove it in the case of K3 surfaces, under some hypotheses. The proof uses Madapusi-Pera’s work on the Kuga-Satake construction.