Barcelona · 2–3 November 2026

The next ALPE takes place in Barcelona on Monday 2 and Tuesday 3 November 2026. Talks take place in room IC, ground floor. Venue information.

The conference dinner is planned for Monday 2 November at 20:00. Restaurant details will follow.

Programme

Talks are 55 minutes long, with time for questions at the end.

Speakers & abstracts

• Margarida MeloTropicalizing the Moduli Space of Trigonal CurvesAbstract

  In recent years, it has become clear that many well-behaved algebro-geometric moduli spaces can be "tropicalized" via modular maps, allowing one to study properties of the original spaces through their tropical counterparts. A first step in this process is often to give a tropical interpretation of the combinatorial data used in the compactification. When such a relationship exists, the tropical modular interpretation can be used to investigate geometric properties of the original moduli space.

  This approach has been particularly successful for the moduli space of curves and its Deligne–Mumford compactification by stable curves, and has subsequently been extended to many other moduli spaces, including those of abelian varieties, universal Jacobians, admissible covers, spin curves, and hyperelliptic curves. In many of these cases, understanding the combinatorial structure of the corresponding tropical moduli spaces has led to important insights into the geometry of the original spaces.

  In this talk, I will present joint ongoing work with Angelina Zheng on this interplay in the case of trigonal curves. The geometry of trigonal curves is expected to reveal interesting topological properties of the moduli space of curves. However, as I will explain, tropical trigonal curves exhibit subtle combinatorial features that make the problem particularly rich and interesting.

• Leopold ZollerMassey products on Kähler manifoldsAbstract

  By a famous result of Deligne-Griffiths-Morgan-Sullivan, compact Kähler manifolds are formal in the sense of rational homotopy theory and in particular all Massey products vanish. However, the bidifferential graded algebra structure on the complex valued differential forms gives rise to refined notions of quasi-isomorphism and formality, so-called strong formality, which is obstructed by so-called ABC-Massey products. We study these Massey products and show that they do not necessarily vanish on Kähler manifolds. In particular Kähler manifolds are not necessarily strongly formal. On the other hand we prove that toric manifolds are always strongly formal.

• Marcy RobertsonModular operads and Galois symmetries of surfacesAbstract

  The mapping class groups of compact oriented surfaces with boundary are linked by homomorphisms induced by gluing boundary components. These groups and gluing maps can be modelled by a modular operad of groupoids, whose automorphisms describe symmetries compatible with gluing across all genera. After profinite completion, this construction gives an operadic model for the Teichmüller tower.

  I will describe a presentation theorem for this operad, with generators and relations in genera zero and one, giving an operadic form of Grothendieck's two-level principle. Using work of Nakamura and Schneps, we apply this presentation to construct an action of their subgroup of the profinite Grothendieck–Teichmüller group on the completed surface operad, and hence a faithful action of the absolute Galois group of the rationals.

  The required operadic language will be introduced geometrically, with no prior familiarity assumed. This is joint work with Luciana Basualdo Bonatto.

• Oscar Cosserat Deformation theory and numerical analysis in Poisson geometryAbstract

  There is an analogy between deformation theory and time-discretisation of ODEs, where the time step of the numerical method plays the role of a deformation parameter. In this talk, I will explain how these two points of view interact. The main part of the talk will be devoted to explaining how to construct numerical methods in Hamiltonian mechanics by deforming Lagrangian submanifolds. As a perspective, I will mention the other direction of this analogy, namely: how to get back insights in deformation theory through those constructions.

• Alejandro CabreraAbout differentiation and van Est isomorphism for higher Lie groupoidsAbstract

  This talks reports on recent work with Matias del Hoyo. We first present a direct, geometric approach to differentiation of simplicial manifolds into higher Lie algebroids. The key result states that differentiation is generated by modding out higher order Taylor expansion terms with respect to a grading which incorporates the geometry of intersecting degeneracy loci. In particular, from this viewpoint, graded commutativity at the infinitesimal level is an emergent feature. We also observe that this approach gives rise to a (strict) van Est map which differentiates cochains and we prove a generalization of van Est isomorphism theorem in cohomology. Finally, we comment on the relation to other approaches, the underlying algebraic construction and applications.

• Filippo VivianiOn the classification of compactified universal JacobiansAbstract

  We classify all the modular compactifications of the universal Jacobian over the moduli stack of pointed smooth curves (joint work with M. Fava and N. Pagani). We then discuss which ones are relatively projective.