Marta Aldasoro will defend his thesis on Tuesday, June 9th

The defence will take place at Aula 1.A1, Faculty of Science and Technology (EHU - Leioa) at 16:30

Marta Aldasoro Rosales completed her Bachelor’s degree in Mathematics at the University of the Basque Country (2015–2019) and subsequently obtained a Master’s degree in Advanced Mathematics from the Complutense University of Madrid (2019–2020).

In January 2021, she began her PhD under the supervision of Javier Fernández de Bobadilla in the Mathematical Physics group, within the STAG area at BCAM. Since September of this academic year, she has been at the University of Zaragoza on a Teaching and Research Fellow contract, working alongside Jorge Martín Morales.

Her thesis, titled “Deformations of μ–constant Surface Singularities and the A’Campo Space in Logarithmic Geometry” is supervised by Prof. Javier Fernández de Bobadilla (BCAM & Ikerbasque). It is scheduled to be defended on June 9th, 2026, at Aula 1.A1, Faculty of Science and Technology (EHU - Leioa) at 16:30 p.m. 

On behalf of all members of BCAM, we would like to wish her all the best for the future, both professionally and personally.

Abstract

We summarize the main results of this thesis.

For the first result, we work with a 1-parameter family σ : X →∆ of isolated hypersurface singularities of fibre dimension 2. We show that if the Milnor number is constant, then any semistable model, obtained from σ after a sufficiently large base change must satisfy nontrivial restrictions. These restrictions are in terms of the dual complex, Hodge structure and numerical invariants of the central fibre. To achieve this, we make use of the Steenbrink spectral sequence degenerating to the cohomology of a generic fibre of the resolution, endowed with the limit mixed Hodge structure.

In the second part of the thesis, we extend the classical A’Campo space to the setting of fine log analytic spaces. We associate the A’Campo space to a fine log analytic space, whose ghost sheaf is quasi-constructible with respect to a finite trivializing stratification, and show that this construction is compatible with exact and vertical morphisms that admit coverings by good charts. More precisely, we obtain a functor from a suitable category of fine log analytic spaces to the category of topological manifolds with boundary and continuous maps.

Furthermore, under a natural transversality condition on the associated sharp cone, the local A’Campo space of a fine monoid carries a smooth structure obtained by pulling back the free-monoid model of Fernández de Bobadilla and Pełka, and this smooth structure is compatible with the topological structure introduced here.