13 December 2017, Imperial College London
Lunch: from noon in Huxley 747
Talks: from 1pm in Huxley 130
– travel information
SEEMOD is South and East of England Model Theory network, connecting the University of East Anglia, Oxford University, Queen Mary University of London and Imperial College London.
Speakers
Laura Capuano (Oxford)
Ehud Hrushovski (Oxford)
Silvain Rideau (UC Berkeley)
Ivan Tomasic (QMUL)
Registration and Funding
We ask the participants to register by emailing Charlotte Kestner by 05/12, because lunch will be provided.
Some money is available, particularly for PhD students, for travel expenses and to cover additional caring costs (e.g. childcare). Please contact Charlotte Kestner CC Jonathan Kirby in advance if you wish to claim expenses.
Abstracts
Capuano. Unlikely intersections in families of abelian varieties
What makes an intersection likely or unlikely? A simple dimension count shows that
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What makes an intersection likely or unlikely? A simple dimension count shows that two varieties of dimension r and s are non "likely" to intersect if r is less than codim s, unless there are some special geometrical relations among them. A series of conjectures due to Bombieri-Masser-Zannier, Zilber and Pink rely on this philosophy. In this talk I will present some results in the special case of curves in families of abelian varieties. The proof of this theorem uses a method introduced by Pila and Zannier and combines results coming from o-minimality with some Diophantine ingredients. This is a joint work with F. Barroero.
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Hrushovski. Galois groups, imaginaries and definable measures. Abstract.
Rideau. Groups and fields definable in algebraically closed valued fields (joint with Ehud Hrushovski).
Our goal will be to give a structure theory for groups interpretable in algebraically closed valued fields
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Our goal will be to give a structure theory for groups interpretable in algebraically closed valued fields and to decompose them in terms of groups internal to the value group, groups internal to the residue field and group
schemes over the valuation ring. Groups that contain a stably dominated type which is invariant under the action of the group play an very important role in this structure theory. For example, we can show that all Abelian groups are extensions of groups internal to the value group by groups that are unions of groups with an invariant stably dominated type. We can also relate stably dominated groups to groups schemes over the valuation ring. Finally wewill use those results to show that any field interpretable in an algebraically closed field is either the valued fields itself or its residue field.
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Tomasic. Cohomology of difference algebraic groups.
We develop methods of homological algebra in the difference setting by enriching our usual view
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We develop methods of homological algebra in the difference setting by enriching our usual view of difference algebra. We proceed to study rational cohomology of difference algebraic groups. Some of our calculations may be of independent interest in group theory since we can treat twisted groups of Lie type as difference algebraic groups.
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