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Durham University

Research & business

Research lectures, seminars and events

The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but  wish to enquire about attending one of the events please contact the organiser or host department.


 

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Events for 12 January 2021

Daniele Turchetti: Schottky spaces and moduli of curves over Z

1:00pm, Zoom

Schottky uniformization is the description of an analytic curve as the quotient of an open dense subset of the projective line by the action of a Schottky group. All Riemann surfaces can be uniformized in this way, as well as some p-adic curves, called Mumford curves. In this talk, I will present a construction of universal Mumford curves: analytic spaces that parametrize both archimedean and non-archimedean uniformizable curves of a fixed genus. This result relies on the existence of suitable moduli spaces for marked Schottky groups, that can be built using the theory of Berkovich spaces over rings of integers of number fields developed by Poineau.

After introducing Berkovich analytic geometry from the beginning, I will describe universal Mumford curves and explain how these can be used as a framework to study arithmetic-geometric objects such as the Tate curve and Teichmüller modular forms. This is based on joint work with Jérôme Poineau.

Contact herbert.gangl@durham.ac.uk, jack.g.shotton@durham.ac.uk for more information about this event.