Motives for some PAC fields
Assigning motives to definable sets over pseudo-finite fields;
generalization to other PAC fields with pro-cyclic Galois group;
maps between Grothendieck ring of different such theories
5 pages of notes (2007)
Definable sets in pseudo-finite fields
Invariants for pseudo-finite fields obtained by counting over finite fields
(in particular: dimension and measure); in a fixed pseudo-finite field and
for the theory of all pseudo-finite fields; maps between different Grothendieck rings
and generalization to theories where counting is not possible.
22 slides (2008)
Trees of varieties over ℤ_{p}
Assigning trees to subsets of ℤ_{p}^{n};
conjecture on the (combinatorial) structure of these trees; associated Poincaré series;
some examples where the conjecture holds
16 slides (2008)
Approximate Subgroups / Isometries in valued fields
1. an introductory talk to a result by Breuillard-Green-Tao classified subsets of groups
2. a geometric approach to the rationality of Poincaré series
summaries of two talks; 2 pages (2013)