Forthcoming events in this series
11:00
11:00
"Definability of Derivations in the Reducts of Differentially Closed Fields".
11:00
Not having rational roots is diophantine."
Abstract
"We give a diophantine criterion for a polynomial with rational coefficients not to have any
rational zero, i.e. an existential formula in terms of the coefficients expressing this property. This can be seen as a kind of restricted
model-completeness for Q and answers a question of Koenigsmann."
11:00
11:00
'On the model theory of representations of rings of integers'
Abstract
following the joint paper with L.Shaheen http://people.maths.ox.ac.uk/zilber/wLb.pdf
11:00
11:00
Algebraic spaces and Zariski geometries.
Abstract
I will explain how algebraic spaces can be presented as Zariski geometries and prove some classical facts about algebraic spaces using the theory of Zariski geometries.
11:00
11:00
11:00
``Multiplicative relations among singular moduli''
Abstract
I will report on some joint work with Jacob Tsimerman
concerning multiplicative relations among singular moduli.
Our results rely on the ``Ax-Schanuel'' theorem for the j-function
recently proved by us, which I will describe.
11:00
11:00
'Model-completeness for Henselian valued fields with finite ramification'
Abstract
This is joint work with Angus Macintyre. We prove a general model-completeness theorem for Henselian valued fields
stating that a Henselian valued field of characteristic zero with value group a Z-group and with finite ramification is model-complete in the language of rings provided that its residue field is model-complete. We apply this to extensions of p-adic fields showing that any finite or infinite extension of p-adics with finite ramification is model-complete in the language of rings.
11:00
11:00
"The first-order theory of G_Q".
Abstract
Motivated by an open conjecture in anabelian geometry, we investigate which arithmetic properties of the rationals are encoded in the absolute Galois group G_Q. We give a model-theoretic framework for studying absolute Galois groups and discuss in what respect orderings and valuations of the field are known to their first-order theory. Some questions regarding local-global principles and the transfer to elementary extensions of Q are raised.
11:00
Matrix multiplication is determined by orthogonality and trace.
Abstract
Everything measurable about a quantum system, as modelled by a noncommutative operator algebra, is captured by its commutative subalgebras. We briefly survey this programme, and zoom in one specific incarnation: any bilinear associative function on the set of n-by-n matrices over a field of characteristic not two, that makes the same vectors orthogonal as ordinary matrix multiplication and gives the same trace as ordinary matrix multiplication, must in fact be ordinary matrix multiplication (or its opposite). Model-theoretic questions about the hypotheses and scope of this theorem are raised.
11:00
'Chevalley's Theorem and quantifier elimination for ACF in a scheme-theoretic setting'
11:00
Axiomatizing Q by "G_Q + ε"
Abstract
we discuss various conjectures about the absolute Galois group G_Q of the field Q of rational numbers and to what extent it encodes the elementary theory of Q.