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Title: From simple groups to symmetries of surfaces Speaker: Rachel Skipper, University of Utah Time: 3:00pm–4:00pm Place: CMC 130 Sponsor:
We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.
Title: Drinfeld Modules, Modular Varieties, and Their Applications in Number Theory Speaker: Mihran Papikian, Penn State Time: 3:00pm–4:00pm Place: CMC 130 Sponsor: G. Micheli
Drinfeld modules provide a remarkable analogue of elliptic curves in the setting of function fields. Introduced by Vladimir Drinfeld in the 1970s, they have since become central objects in number theory. The theory of Drinfeld modules mirror many aspects of the classical theory elliptic curves and modular curves, yet reveal new arithmetic phenomena unique to the function field setting. This talk will provide an overview of these ideas and describe several applications, including analogues of reciprocity laws. The presentation will be accessible to a general mathematical audience.