Next Event

ALPE took place in Toulouse on the 17-18 of November, 2025.

Programme

List of talks and abstracts.

Titles and abstracts

• Özgür Bayındır Towards the classification of DGAs with polynomial homology ▼
  We study the classification of Z-DGAs with polynomial homology Fp[x], motivated by computations in algebraic K-theory. We prove that there are infinitely many such DGAs for even |x| and that for |x| >=2p-2 any such DGA is formal as a ring spectrum. Combining our results with earlier work of the second author and Tamme, we obtain new (relative) algebraic K-theory computations for rings such as the mixed characteristic coordinate axes Z[x]/px and the group ring Z[C_p^n]. This work is joint with Markus Land.
• Xujia Chen Surgery on Operads ▼
  A "manifold operad" is an operad (O(1), O(2), ...) where each O(n) is a topological manifold with boundary, and such that the decomposables in O(n) form the boundary of O(n) in the expected way. For example, the Fulton-MacPherson operads, which come from the configuration space of points on Euclidean spaces, are manifold operads. We present a general method of constructing examples of manifold operads, by doing surgery. For example, given an arbitrary cobordism C between the sphere and another closed manifold M, together with a free Z/2Z-action on C whose restriction to the sphere is the antipodal map, we can construct a manifold operad O such that O(2)=M. We achieve this through the development of the theory of cobordisms of manifold operads which depends crucially on combinatorial results for posets.This is joint work in preparation with Connor Malin and Paolo Salvatore.
• Ryan Grady Concordance Bicategories ▼
  I will describe joint work with Chris Boehlert in which we modify the tangle category by replacing isotopies by concordances. In dimension one, the resulting category categorifies the classical knot concordance group, including the action of satellite operators.
• Tasos Moulinos Unipotent spectra and duality for syntomic cohomology ▼
  In this talk I will introduce the notion of a unipotent spectrum. This is a stabilized variant of Toën's theory of affine stacks. I will describe some properties inherited by this stable infinity category of "unipotent spectra" and give various examples of such objects. Unipotent spectra give rise to unipotent stable homotopy groups and unipotent homology groups, which are new invariants for schemes, taking values in unipotent group schemes (as opposed to say abelian groups, for ordinary spectra). Due to the vanishing of higher ext groups, the theory simplifies further upon restricting to sites of perfect schemes and one obtains a duality in the spirit of Milne's duality for perfect unipotent groups; I will describe this and explain how syntomic cohomology of characteristic p schemes fits into the picture.
• Adrien Sauvaget Strata of differentials and Witten classes with spin signs. ▼
  I will consider give an overview of certain cohomology classes of moduli spaces of curves, namely: classes of strata of differentials and Witten’s classes. I will explain that these two family of classes admits canonical lifts to the moduli spaces of curves with a spin structure (square root of the co-tangent line), therefore we can refine these classes according to the sign of the spin structure. I will present some open problems, and recent results on the algebraic structure of these refined classes.
• Anna Sopena Pluripotential operadic calculus ▼
  For complex manifolds, there exists a refined notion of weak equivalence related to both Dolbeault and anti-Dolbeault cohomology. This class of weak equivalences naturally defines a stronger formality notion. In particular, satisfying the ddbar-Lemma property does not imply formality in this new sense. The goal of this talk is to introduce a novel operadic framework designed to understand this homotopical situation. Namely, I will present pluripotential A-infinity algebras as well as a homotopy transfer theorem based on this strong notion of weak equivalence.