Past Event

ALPE took place in Barcelona on the 21-22 of May, 2025.

Programme

List of talks and abstracts.

Titles and abstracts

• Julie Bergner - University of Virginia Combinatorial examples of 2-Segal sets and their Hall algebras ▼
  The notion of a 2-Segal set encodes an algebraic structure that is similar to that of a category, but for which composition need not exist or be unique, yet is still associative. The fact that such structures give rise to Hall algebras, generalizing constructions in representation theory and algebraic geometry, is one of the primary motivations for studying them. In this talk, we look at 2-Segal sets that arise from trees and graphs and their associated Hall algebras. These examples are discrete versions of the analogous 2-Segal spaces of trees and graphs developed by G\'alvez-Carrillo, Kock, and Tonks, and provide a way to explore various general constructions quite explicitly. Much of this work is joint with Borghi, Dey, G\'alvez-Carrillo, and Hoekstra Mendoza.
• Francesca Carocci - Università di Roma II-Roma Tor Vergata Correlated Gromov-Witten invariants ▼
  In this talk we introduce a geometric refinement of Gromov-Witten invariants for P1-bundles relative to the natural fiberwise boundary structure. We call these refined invariants correlated Gromov-Witten invariants. We will introduce the correlated invariants, discuss their properties and provide some computations in the case of P1-bundles over an elliptic curve. Such invariants are expected to play a role in the degeneration formula for reduced Gromov-Witten invariants for abelian and K3 surfaces. This is a joint work with Thomas Blomme.
• Natàlia Castellana - Universitat Autònoma de Barcelona Descent and stratification in equivariant homotopy theory ▼
  In this talk I will report on joint work with T. Barthel, D. Heard, N. Naumann, L. Pol and B. Sanders. The object of study are localizing, smashing and thick ideals in nice stable infinity categories with emphasis in equivariant stable homotopy cateogries. The goal is to investigate to what extend one can descend such classifications along commutative algebras.
• Jiaqi Fu - Université Toulouse III Paul Sabatier p-th power maps of higher Lie algebras ▼
  In characteristic p, the p-th power of a derivation is again a derivation. This operation, known as the p-restriction, plays a crucial role in the ``algebraic integration'' of Lie algebras developed by Ekedahl, offering a geometric interpretation on Jacobson’s purely inseparable Galois theory of exponential 1. Analogous operations exist for various notions of higher Lie algebras in characteristic p. We will introduce a (conjectural) list of homotopy operations and their relations on these higher Lie algebras over Z/2Z, and discuss potential applications to derived deformation theory.
• Marco Gualtieri - University of Toronto and ICREA @ UPC Higher structures in generalized complex geometry ▼
  I will review the occurrence of groupoids, double groupoids, and Lie 2-groupoids as well as shifted symplectic structures in the study of generalized complex and Kahler geometry.
• Joost Nuiten - Université Toulouse III Paul Sabatier The infinitesimal tangle hypothesis ▼
  The tangle hypothesis is a variant of the cobordism hypothesis that considers cobordisms embedded in some finite-dimensional Euclidean space (together with framings). Such tangles of codimension k can be organized into an E_k-monoidal d-category, where d is the maximal dimension of the tangles. The tangle hypothesis then asserts that this category of tangles is the free E_k-monoidal d-category with duals generated by a single object. In this talk, based on joint work in progress with Yonatan Harpaz, I will describe an infinitesimal version of the tangle hypothesis: Instead of showing that the E_k-monoidal category of tangles is freely generated by an object, we show that its cotangent complex is free of rank 1. This provides support for the tangle hypothesis (of which it is a direct consequence), but can also be used to reduce the tangle hypothesis to a statement at the level of E_k-monoidal (d+1, d)-categories by means of obstruction theory.
• Gabriele Rembado - Universities of Montpellier and Maryland Deformations & quantizations of moduli spaces of wild meromorphic connections ▼
  Fuchsian systems on the Riemann sphere have a natural Poisson space of parameters. Their admissible (= isomonodromic) deformations lead to a certain nonautonomous integrable Hamiltonian system, whose quantization is tantamount to the Knizhnik--Zamolodchikov connection in conformal field theory. In this talk we will aim at a review of part of this story, and then present extensions involving linear systems of ODEs with irregular singularities. It is joint work with D. Calaque, G. Felder, R. Wentwort & M. Chaffe, L. Topley, D. Yamakawa & P. Boalch, J. Douçot, M. Tamiozzo.
• Pim Spelier - Utrecht Universiteit Log Donaldson-Thomas invariants of Calabi-Yau 4-folds ▼
  Donaldson-Thomas invariants of a variety X are enumerative invariants counting subschemes of X. For X a Calabi-Yau 3-fold, one possible way to compute these due to Ranganthan and Maulik is by degenerating X, and computing the logarithmic Donaldson-Thomas invariants of the pieces. In this talk, I will explain this story for 3-folds, and present work on how to extend this to counting points in a Calabi-Yau 4-fold.