Logic Seminar
|
Thu, 14/10/2010 17:00 |
Dr Koenigsmann (Oxford) |
Logic Seminar  |
L3 |
|
Thu, 21/10/2010 17:00 |
Wilfrid Hodges |
Logic Seminar |
L3 |
| In 1974 Haim Gaifman conjectured that if a first-order theory T is relatively categorical over T(P) (the theory of the elements satisfying P), then every model of T(P) expands to one of T. The conjecture has long been known to be true in some special cases, but nothing general is known. I prove it in the case of abelian groups with distinguished subgroups. This is some way outside the previously known cases, but the proof depends so heavily on the Kaplansky-Mackey proof of Ulm's theorem that the jury is out on its generality. | |||
|
Thu, 28/10/2010 17:00 |
Raf Cluckers (Leuven) |
Logic Seminar |
L3 |
| Motivic exponential integrals are an abstract version of p-adic exponential integrals for big p. The latter in itself is a flexible tool to describe (families of) finite expontial sums. In this talk we will only need the more concrete view of "uniform in p p-adic integrals" instead of the abstract view on motivic integrals. With F. Loeser, we obtained a first transfer principle for these integrals, which allows one to change the characteristic of the local field when one studies equalities of integrals, which appeared in Ann. of Math (2010). This transfer principle in particular applies to the Fundamental Lemma of the Langlands program (see arxiv). In work in progress with Halupczok and Gordon, we obtain a second transfer principle which allows one to change the characteristic of the local field when one studies integrability conditions of motivic exponential functions. This in particular solves an open problem about the local integrability of Harish-Chandra characters in (large enough) positive characteristic. | |||
|
Thu, 04/11/2010 17:00 |
Andrew Brooke-Taylor (Bristol) |
Logic Seminar |
L3 |
| Vopenka's Principle is a very strong large cardinal axiom which can be used to extend ZFC set theory. It was used quite recently to resolve an important open question in algebraic topology: assuming Vopenka's Principle, localisation functors exist for all generalised cohomology theories. After describing the axiom and sketching this application, I will talk about some recent results showing that Vopenka's Principle is relatively consistent with a wide range of other statements known to be independent of ZFC. The proof is by showing that forcing over a universe satisfying Vopenka's Principle will frequently give an extension universe also satisfying Vopenka's Principle. | |||
|
Thu, 18/11/2010 17:00 |
Marcus Tressl (Manchester) |
Logic Seminar |
L3 |
|
Thu, 25/11/2010 17:00 |
John Truss (Leeds) |
Logic Seminar |
L3 |
|
Thu, 02/12/2010 17:00 |
Salma Kuhlmann (Konstanz) |
Logic Seminar |
L3 |
Consider the valued field  of generalised series, with real coefficients and
monomials in a totally ordered multiplicative group  . In a series of papers,
we investigated how to endow this formal algebraic object with the analogous
of classical analytic structures, such as exponential and logarithmic maps,
derivation, integration and di fference operators. In this talk, we shall discuss
series derivations and series logarithms on (that is, derivations that
commute with in finite sums and satisfy an in finite version of Leibniz rule, and
logarithms that commute with infi nite products of monomials), and investigate
compatibility conditions between the logarithm and the derivation, i.e. when
the logarithmic derivative is the derivative of the logarithm. |
|||
