SEMINARI DI O-MINIMALITA'

Around a conjecture of Wilkie

Tipo Seminario: 
Relatore: 
Olivier Le Gal

In order to understand the local behaviour of the maps definable in expansions of the complex field C by holomorphic functions, and since, identifying C with R^2, these functions are locally definable in reducts of the structure R_an generated by all subanalytic sets, Wilkie started a systematic study of the reducts of R_an generated by a collection of restricted holomorphic maps.

Data Seminario: 
Tuesday, May 5, 2015
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:30
Affiliazione: 
Université de Bourgogne, Francia
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

Nuij type pencils of hyperbolic polynomials

Tipo Seminario: 
Relatore: 
Krzysztof Kurdyka

Nuij's theorem states that if a polynomial p(z) with real coefficient is hyperbolic (i.e. has only real roots) then p+sp' is also hyperbolic
for any real number s. We study other perturbations of hyperbolic  polynomials of the form 
                            p_a(z,s): =p(z) +\sum_{k=1}^d a_ks^kp^{(k)}(z).

Data Seminario: 
Wednesday, April 29, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 15:00
Affiliazione: 
Université de Savoie, Francia
Ora Inizio: 
Saturday, January 1, 0000 - 13:30

Improvements in the Pila-Wilkie theorem for curves

Tipo Seminario: 
Relatore: 
Gareth Jones

The Pila-Wilkie theorem gives a bound on the number of rational points of bounded height lying on the transcendental part of a set definable in an o-minimal expansion of the real field. I'll explain the background to the Pila-Wilkie theorem and then discuss the result itself. I'll then go on to mention some instances in which the Pila-Wilkie theorem can be improved. Finally, I'll discuss some diophantine applications.

Data Seminario: 
Wednesday, April 22, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 15:00
Affiliazione: 
University of Manchester, U.K.
Ora Inizio: 
Saturday, January 1, 0000 - 13:30

Tangential Center problem for Darboux Centers

Tipo Seminario: 
Relatore: 
Pavao Mardesic

I will present a joint work with Colin Christopher (U. Plymouth UK). It concerns planar polynomial vector fields.

Data Seminario: 
Tuesday, April 14, 2015
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:30
Affiliazione: 
Université de Bourgogne, Francia
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

Definable henselian valuation rings

Tipo Seminario: 
Relatore: 
Alexander Prestel

A valuation ring O of a field K is called "henselian" if every polynomial in one variable with coefficients from O that has a simple zero in the quotient of O w.r.t. its maximal ideal, has already a zero in K. Such henselian fields are for example  local fields and all generalized power series fields. In all these examples the valuation ring O remains fixed under all field automorphisms from K. The reason for this is that O can be defined by a first order formula in the language of rings.

Data Seminario: 
Tuesday, March 17, 2015
Aula: 
Sala delle Riunioni (Dip. Matematica Applicata)
Ora Fine: 
Saturday, January 1, 0000 - 15:00
Affiliazione: 
Universität Konstanz, Germania
Ora Inizio: 
Saturday, January 1, 0000 - 13:30

Sets with few rational points

Tipo Seminario: 
Relatore: 
Georges Comte

In the spirit of famous papers by Pila & Bombieri and Pila & Wilkie, I will explain how to bound the number
of rational points, with respect to their height, in various kinds of sets, such as algebraic varieties of a given degree,
transcendental sets definable in some o-minimal (or not) structure over the real field, and, after joint work
with R. Cluckers and F. Loeser, also definable sets in non-archimedean contexts.
The talk will consist in a survey of results and I will go into some of the proofs only in order to give the main ideas relating

Data Seminario: 
Thursday, March 12, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:30
Affiliazione: 
Université de Savoie, Francia
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

Lebesgue integration of geometrically interesting classes of functions

Tipo Seminario: 
Relatore: 
Raf Cluckers

Starting from a class of functions called 'subanalytic', and which share many properties with semi-algebraic functions, I will give an overview of results on integration of subanalytic functions, up to their Fourier transforms. I will recall all this material, as well as explain geometric relevance.

Data Seminario: 
Friday, March 13, 2015
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 15:00
Affiliazione: 
Université Lille 1, Francia, e Universiteit Leuven, Belgio
Ora Inizio: 
Saturday, January 1, 0000 - 13:30

Polynomial-Exponential Equations

Tipo Seminario: 
Relatore: 
Ayhan Günaydin

We consider polynomial‐exponential equations over the complex
numbers where
the variables run through the rational numbers. Classically, the integer
solutions of
such equations are considered and there are several finiteness results in the
literature for those solutions. We present a method to reduce the rational
solutions to integer ones and give a description of them using the earlier
results.  As a corollary, we get a finiteness result. If time permits,
we will present

Data Seminario: 
Friday, January 23, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
MSGSU Istanbul, Turchia
Ora Inizio: 
Saturday, January 1, 0000 - 09:30

Real closed rings and o-minimality

Tipo Seminario: 
Relatore: 
Marcus Tressl

Real closed rings are rings that occur frequently in the study of o-minimal fields (such as the real field).
Examples are rings of continuous functions that have algebraic graph, or valuation rings of o-minimal fields.
The talk will give an introduction to the subject from scratch and describe recent work
on algebraic and decidability questions for various real closed rings.

Data Seminario: 
Tuesday, December 16, 2014
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 15:00
Affiliazione: 
University of Manchester
Ora Inizio: 
Saturday, January 1, 0000 - 13:30

Counting points and o-minimality

Tipo Seminario: 
Relatore: 
Margaret Thomas

The results surveyed in this talk are part of a wider, flourishing interaction between diophantine geometry and o-minimality. The central problem is to bound the density of rational and algebraic points on certain subsets of the reals. Beginning with work by Bombieri and Pila in the 1980s, a key breakthrough came from the application of o-minimality to the problem by Pila and Wilkie in 2006. This, in particular thanks to a strategy utilizing their result developed by Pila and Zannier, has found many significant applications to important open problems in number theory.

Data Seminario: 
Friday, November 14, 2014
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:30
Affiliazione: 
University of Konstanz
Ora Inizio: 
Saturday, January 1, 0000 - 10:00
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