Logic Seminar
|
Thu, 05/05/2011 17:00 |
Jamshid Derakhshan (Oxford) |
Logic Seminar  |
L3 |
|
This is joint with with Mark Berman, Uri Onn, and Pirita Paajanen.
Let K be a local field with valuation ring O and residue field of size q, and G a Chevalley group. We study counting problems associated with the group G(O). Such counting problems are encoded in certain zeta functions defined as Poincare series in q^{-s}. It turns out that these zeta functions are bounded sums of rational functions and depend only on q for all local fields of sufficiently large residue characteristic. We apply this to zeta functions counting conjugacy classes or dimensions of Hecke modules of interwining operators in congruence quotients of G(O). To prove this we use model-theoretic cell decomposition and quantifier-elimination to get a theorem on the values of 'definable' integrals over local fields as the local field varies. |
|||
|
Thu, 12/05/2011 16:00 |
Daniel Bertrand (Paris) |
Logic Seminar Number Theory Seminar |
L3 |
|
The points in question can be found on any semi-abelian surface over an elliptic curve with complex multiplication. We will show that they provide counter-examples to natural expectations in a variety of fields : Galois representations (following K. Ribet's initial study from the 80's), Lehmer's problem on heights, and more recently, the relative analogue of the Manin-Mumford conjecture. However, they do support Pink's general conjecture on special subvarieties of mixed Shimura varieties.
|
|||
|
Thu, 19/05/2011 17:00 |
Logic Seminar |
L3 | |
|
Thu, 26/05/2011 17:00 |
Enrique Casanovas (Barcelona) |
Logic Seminar |
L3 |
| "We will talk on stability, simplicity, nip, etc of partial types. We will review some known results and we will discuss some open problems." | |||
|
Thu, 02/06/2011 17:00 |
Carlo Toffalori - joint work with Gena Puninski (Florence - Moscow) |
Logic Seminar |
L3 |
| Recent papers by Butler-Campbell-Kovàcs, Rump, Prihoda-Puninski and others introduce over an order O over a Dedekind domain D a notion of "generalized lattice", meaning a D-projective O-module. We define a similar notion over Dedekind-like rings – a class of rings intensively studied by Klingler and Levy. We examine in which cases every generalized lattices is a direct sum of ordinary – i.e., finitely generated – lattices. We also consider other algebraic and model theoretic questions about generalized lattices. | |||
|
Thu, 09/06/2011 16:00 |
David Masser |
Logic Seminar Number Theory Seminar |
L3 |
In the last twelve years there has been much study of what happens when an algebraic curve in  -space is intersected with two multiplicative relations 
for  linearly independent in  . Usually the intersection with the union of all  is at most finite, at least in zero characteristic. In Oxford nearly three years ago I could treat a special curve in positive characteristic. Since then there have been a number of advances, even for additive relations
provided some extra structure of Drinfeld type is supplied. After reviewing the zero characteristic situation, I will describe recent work, some with Dale Brownawell, for and for  with Frobenius Modules and Carlitz Modules. |
|||
|
Thu, 16/06/2011 17:00 |
Rizos Sklinos (Leeds) |
Logic Seminar |
L3 |
|
After Sela and Kharlampovich-Myasnikov independently proved that non abelian free groups share the same common theory model theoretic interest for the subject arose. In this talk I will present a survey of results around this theory starting with basic model theoretic properties mostly coming from the connectedness of the free group (Poizat). Then I will sketch our proof with C.Perin for the homogeneity of non abelian free groups and I will give several applications, the most important being the description of forking independence. In the last part I will discuss a list of open problems, that fit in the context of geometric stability theory, together with some ideas/partial answers to them. |
|||
