Forthcoming Seminars › Seminar Series

Logic Seminar

Thu, 26/04/2012
17:00 		Angus Macintyre (QMUL) Logic Seminar Add to calendar L3
Connecting Schanuel's Conjecture to Shapiro's Conjecture
Shapiro's Conjecture says that two classical exponential polynomials over the complexes can have infinitely many common zeros only for algebraic reasons. I will explain the history of this, the connection to Schanuel's Conjecture, and sketch a proof for the complexes using Schanuel, as well as an unconditional proof for Zilber's fields.
Thu, 10/05/2012
17:00 		Jamshid Derakhshan Logic Seminar Add to calendar L3
Uniformly defining valuation rings in Henselian valued fields with finite and pseudo-finite residue field
This is joint work with Raf Cluckers, Eva Leenknegt, and Angus Macintyre.We give a first-order definition, in the ring language, of the ring of p-adic integers inside the field p-adic numbers which works uniformly for all p and for valuation rings of all finite field extensions and of all local fields of positive characteristic p, and in many other Henselian valued fields as well. The formula canbe taken existential-universal in the ring language. Furthermore, we show the negative result that in the language of rings there does not exist a uniform definition by an existential formula and neither by a universal formula. For any fixed general p-adic field we give an existential formula in the ring language which defines the valuation ring. We also state some connections to some open problems.
Thu, 17/05/2012
17:00 		*Cancelled* Logic Seminar Add to calendar L3
To Be Announced
Thu, 24/05/2012
17:00 		Pierre Simon (Ecole Normale Superiore) Logic Seminar Add to calendar L3
S-independence in NIP theories
I will explain how to define a notion of stable-independence in NIP theories, which is an attempt to capture the "stable part" of types.
Thu, 31/05/2012
16:00 		Jochen Koenigsmann (Oxford) Logic Seminar Add to calendar
Number Theory Seminar Add to calendar 		L3
Fields with the absolute Galois group of $ \mathbb{Q} $.
Thu, 07/06/2012
16:00 		Jakob Stix (Heidelberg) (Heidelberg) Logic Seminar Add to calendar
Number Theory Seminar Add to calendar 		L3
On the section conjecture in anabelian geometry
The section conjecture of Grothendieck's anabelian geometry speculates about a description of the set of rational points of a hyperbolic curve over a number field entirely in terms of profinite groups and Galois theory. In the talk we will discuss local to global aspects of the conjecture, and what can be achieved when sections with additional group theoretic properties are considered.
Thu, 14/06/2012
17:00 		Özlem Beyarslan (Bogazici) Logic Seminar Add to calendar L3
Algebraic closure in pseudofinite fields
A pseudofinite field is a perfect pseudo-algebraically closed (PAC) field which has $ \hat{\mathbb{Z}} $ as absolute Galois group. Pseudofinite fields exists and they can be realised as ultraproducts of finite fields. A group $ G $ is geometrically represented in a theory $ T $ if there are modles $ M_0\prec M $ of $ T $, substructures $ A,B $ of $ M $, $ B\subset acl(A) $, such that $ M_0\le A\le B\le M $ and $ Aut(B/A) $ is isomorphic to $ G $. Let $ T $ be a complete theory of pseudofinite fields. We show that, geometric representation of a group whose order is divisibly by $ p $ in $ T $ heavily depends on the presence of $ p^n $'th roots of unity in models of $ T $. As a consequence of this, we show that, for almost all completions of the theory of pseudofinite fields, over a substructure $ A $, algebraic closure agrees with definable closure, if $ A $ contains the relative algebraic closure of the prime field. This is joint work with Ehud Hrushovski.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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