Departamento de Matemáticas UAM

Seminario de Álgebra Conmutativa, Geometría Algebraica y Aritmética

Lunes 3 de diciembre de 2018 a las 11:30h en el aula 420 del módulo 17

Conferenciante Angus J. Macintyre (Queen Mary University of London)

Titulo: Analogues for exponential fields of algebraic-geometric notions

Abstract. Tarski raised in the 1930's some logical questions about the real exponential field. Answers to these questions did not come till the 1990's in the work of Wilkie and Wilkie-Macintyre (based on work of Hovanski, and insights of Schanuel). Wilkie's work initiated numerous very important uses of the notion of o-minimality.
Work of Zilber about twenty years ago initiated serious study of the complex exponential, from a logical point of view concerning exponential algebraic sets. More dramatically, it revealed the existence of other exponential fields (the Zilber fields) with highly structured notions of exponential dependence and exponential dimension (including a general Steinitz theory). It was conjectured by Zilber that the complex exponential field is a Zilber field. This would imply Schanuel's Conjecture and a very deep Hilbert Nullstellensatz for exponential-algebraic sets.
I will discuss the analysis, algebra and model theory that has gone in to establishing a rich theory of exponential dimension.