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Workshop on singularities : semigroups, topology and valuations (28th - 31th October 2019) at Complutense University of Madrid.

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Courses by : Marco D’Anna (Catania Univ.) Good semigroups and value semigroups of plane curve singularities Julio Moyano (Univ. Jaume I) Poincaré series associated with plane curve singularities Patrick Popescu-Pampu (Univ. Lille I) A tropical and logarithmic study of Milnor fibers. The summary of these courses are indicated below. There will be some additional talks among those proposed by the participants (see the webpage). There is the possibility to apply for some financial support to attend the conference (see the webpage). Deadline to propose a talk or apply for finantial support : 15th September Please register on the webpage in order to facilitate the logistics of the conference. The organizers are : Patricio Almirón Cuadros, Pedro Daniel González Pérez, Alejandro Melle Hernández

Summaries of the courses

"Good semigroups and value semigroups of curve singularities". This mini course will consist of four sessions with the following structure : - Value semigroups of algebroid curves. Basic properties. Good semigroups. Analogies and differences with respect to the case of algebroid branches and numerical semigroups. - Computation of lengths. Conductor and degree of singularity. Genus of a good semigroup. Symmetric and almost symmetric good semigroups. - Multiplicity sequences and multiplicity tree. Arf rings and semigroups. Complement of a good ideal. Apéry set. Embedding dimension. Type. -Algorithmic characterization of value semigroups of a plane algebroid curve with two branches.

"Poincaré series associated with plane curve singularities"

In this mini-course we will introduce the Poincaré series associated to a plane curve singularity, developing the ideas of Campillo, Delgado and Kiyek (1994), and Campillo, Delgado and Gusein-Zade (in a series of papers from 1997 to 2007), and including some tecniques of motivic nature.

"A tropical and logarithmic study of Milnor fibers"

I will explain in this course how to combine tools from tropical and logarithmic geometry in order to explore the structure of Milnor fibers of smoothings of isolated singularities of complex analytic spaces. As an ilustration of the general technique, I will explain a proof of the so-called "Milnor fiber conjecture" of Neumann and Wahl, which expresses iteratively the Milnor fibers of certain complex surface singularities in terms of the Milnor fibers of simpler singularities. This course may be seen as a simultaneous introduction to the intimately related tropical and logarithmic geometries. t will be based on a joint work with Maria Angelica Cueto and Dmitry Stepanov.Vista previa del archivo adjunto cartel_workshop_singularities.pdf