Mapping class groups of K3 surfaces from a Thurstonian viewpoint, I: the smooth Mordell-Weil group
Mapping class groups of K3 surfaces from a Thurstonian viewpoint, I: the smooth Mordell-Weil group
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In many ways the state of our understanding of homeomorphisms of 4-manifolds at the end of 2023 is essentially that of our understanding of homeomorphisms of 2-manifolds in 1973, before Thurston changed everything. In two talks I will report on some first steps in a project (joint with Eduard Looijenga) whose ultimate goal is to address this. I will focus on the case of K3 surfaces.听 One appealing aspect of this topic is the surprising variety of concepts that naturally arise, including : the theory infinite reflection groups; Hodge theory; the theory of integral quadratic forms; 听period mappings; families of elliptic curves; 听and much more. 听
In this first talk I'll start with the big picture, and then explain how an idea from number theory can be used to understand mapping class groups of K3 surfaces.听
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