Past Advanced Class Logic

7 March 2017
11:00
Laura Capuano
Abstract


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 < 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. I will speak about a joint work with F. Barroero (Basel) in this framework in the special case of a curve in a family of elliptic curves. The proof is based on Pila-Zannier method, combining diophantine ingredients with a refinement of a theorem of Pila and Wilkie about counting rational points in sets definable in o-minimal structures.
   Everyone welcome!
 

  • Advanced Class Logic
2 February 2017
11:00
Nicholas Wentzlaff-Eggebert
Abstract


Abstract: We will consider a model theoretic approach to Gelfand-Naimark duality, from the point of view of (generalized) Zariski structures. In particular we will show quantifier elimination for compact Hausdorff spaces in the natural Zariski language. Moreover we may see a slightly unusual construction and tweak to the language, which improves stability properties of the structures.
 

  • Advanced Class Logic
19 January 2017
11:00
Ugur Efem
Abstract


In this talk I will present some answers to the question when every specialisation from a \kappa-saturated extension of 
a Zariski structure is \kappa-universal? I will show that for algebraically closed fields, all specialisations from a \kappa-
saturated extension is \kappa-universal. More importantly, I will consider this question for finite and infinite covers of
Zariski structures. In these cases I will present a counterexample to show that there are covers of Zariski structures 
which have specialisations from a \kappa-saturated extension that are not \kappa-universal. I will present some natural 
conditions on the fibres under which all specialisations from a \kappa-saturated extension of a cover is \kappa-universal. 
I will explain how this work points towards a prospective Ladder Theorem for Specialisations and explain difficulties and 
further works that needs to be considered.
 

  • Advanced Class Logic
16 June 2016
11:00
to
15:45
Andres Villaveces
Abstract
Abstract: finding a "non-commutative limit" of the j-invariant (to real numbers, in a way that captures reasonably well the connection with extensions of number fields) has prompted several approaches (Manin-Marcolli, Castaño-Gendron). I will describe one of these approaches in a brief way, and I will make some connections to the model theory of sheaves.
  • Advanced Class Logic

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