Forthcoming Seminars › Seminar Series

Logic Seminar

Thu, 16/10/2008
17:00 		Kobi Peterzil (Haifa) Logic Seminar Add to calendar L3
Definably compact, connected groups are elementarily equivalent to compact real Lie groups
(joint work with E. Hrushovski and A. Pillay) If G is a definably compact, connected group definable in an o-minimal structure then, as is known, G/Z(G) is semisimple (no infinite normal abelian subgroup). We show, that in every o-minimal expansion of an ordered group: If G is a definably connected central extension of a semisimple group then it is bi-intepretable, over parameters, with the two-sorted structure (G/Z(G), Z(G)). Many corollaries follow for definably connected, definably compact G. Here are two: 1. (G,.) is elementarily equivalent to a compact, connected real Lie group of the same dimension. 2. G can be written as an almost direct product of Z(G) and [G,G], and this last group is definable as well (note that in general [G,G] is a countable union of definable sets, thus not necessarily definable).
Thu, 23/10/2008
11:00 		Gareth Jones (Manchester) Logic Seminar Add to calendar SR1
Model completeness results for certain Pfaffian structures
I show that the expansion of the real field by a total Pfaffian chain is model complete in a language with symbols for the functions in the chain, the exponential and all real constants. In particular, the expansion of the reals by all total Pfaffian functions is model complete.
Thu, 23/10/2008
17:00 		Dan Segal (Oxford) Logic Seminar Add to calendar L3
Finite and Infinite in Group Theory
Thu, 30/10/2008
17:00 		Jochen Koenigsmann (Oxford) Logic Seminar Add to calendar L3
Defining Z in Q
I will present a universal definition of the integers in the field of rational numbers, building on work discussed by Bjorn Poonen in his seminar last term. I will also give, via model theory, a geometric criterion for the non-diophantineness of Z in Q.
Thu, 13/11/2008
17:00 		Bob Coecke (Oxford Comlab) Logic Seminar Add to calendar L3
Models of quantum phenomena
[This is a joint seminar with OASIS] A formulation of quantum mechanics in terms of symmetric monoidal categories provides a logical foundation as well as a purely diagrammatic calculus for it. This approach was initiated in 2004 in a joint paper with Samson Abramsky (Ox). An important role is played by certain Frobenius comonoids, abstract bases in short, which provide an abstract account both on classical data and on quantum superposition. Dusko Pavlovic (Ox), Jamie Vicary (Ox) and I showed that these abstract bases are indeed in 1-1 correspondence with bases in the category of Hilbert spaces, linear maps, and the tensor product. There is a close relation between these abstract bases and linear logic. Joint work with Ross Duncan (Ox) shows how incompatible abstract basis interact; the resulting structures provide a both logical and diagrammatic account which is sufficiently expressive to describe any state and operation of "standard" quantum theory, and solve standard problems in a non-standard manner, either by diagrammatic rewrite or by automation. But are there interesting non-standard models too, and what do these teach us? In this talk we will survey the above discussed approach, present some non-standard models, and discuss in how they provide new insights in quantum non-locality, which arguably caused the most striking paradigm shift of any discovery in physics during the previous century. The latter is joint work with Bill Edwards (Ox) and Rob Spekkens (Perimeter Institute).
Thu, 20/11/2008
17:00 		Ayhan Gunaydin (Oxford) Logic Seminar Add to calendar L3
Dependent Pairs
I will prove that certain pairs of ordered structures are dependent. There are basically two cases depending on whether the smaller structure is dense or discrete. I will discuss the proofs of two quite general theorems which construe the dividing line between these cases. Among examples are dense pairs of o-minimal structures in the first case, and tame pairs of o-minimal structures in the latter. This is joint work with P. Hieronymi.
Thu, 27/11/2008
16:00 		David Masser (Basel) Logic Seminar Add to calendar
Number Theory Seminar Add to calendar 		L3
Linear equations over multiplicative groups in positive characteristic, sums of recurrences, and ergodic mixing
Solving completely $ x+y-z=1 $ in unknowns taken from the group generated by a variable $ t $ with $ 1-t $ over a finite field is not so easy as might be expected. We present a generalization to arbitrary linear varieties and finitely generated groups (keywords effective Mordell-Lang). We also mention applications to (a) solving equations like $ u_n+v_m+w_l+f_k=0 $ in $ n,m,l,k $ for given recurrences $ u,v,w,f $; and to (b) finding the smallest order of non-mixing of a given algebraic $ {\bf Z}^s $-action. This is joint work with Harm Derksen.
Thu, 04/12/2008
17:00 		Martin Ziegler (Freiburg) Logic Seminar Add to calendar L3
Separably closed fields and equational theories
Fri, 05/12/2008
14:00 		Angus Macintyre (Queen Mary) Logic Seminar Add to calendar
Seminar cancelled

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

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