Next Event

The next ALPE will take place in Montpellier on the 23-24 of March, 2026. For information about the venue, check the location tab.

More information will appear soon.

Programme

List of talks and abstracts.

Talks are 55 minutes long with some time for questions at the end. Talks will take place at IMAG, in room 430 on Monday and in room 109 on Tuesday.

Titles and abstracts

• Chenjing Bu Semiorthogonal decompositions for stacks ▼
  I will explain a joint work in progress with Tudor Pădurariu and Yukinobu Toda on a construction of semiorthogonal decompositions on derived categories of coherent sheaves on algebraic stacks, based on the framework of component lattices developed in my previous work with collaborators. This can be seen as a categorification of Donaldson–Thomas theory, and in particular, of a decomposition theorem in cohomology obtained in an earlier joint work. I will also discuss its applications to categorification of quantum groups and to the Dolbeault geometric Langlands conjecture.
• Julien Grivaux Derived intersections via regular derived critical loci ▼
  If X and Y are closed subschemes of an ambiant scheme Z, the study of the derived intersections of X and Y has been widely investigated by a number of authors, starting with the work of Serre where X and Y have complementary dimensions but intersect along a possibly non-reduced zero-dimensional scheme. In the case of a clean intersection, meaning that the scheme-theoretic intersection T of X and Y is smooth, the derived intersection does not always live on T, although it is locally isomorphic to the total space of a shifted vector bundle over T. This problem is one of the main reason behind some technical difficulties in Grothendieck's famous Borel-Serre 1958 paper. In this talk, we will present a toy model to study these objects, which consist of the nicest possible derived critical loci among the ones having a nontrivial derived structure. It turns out that this model is rather powerful. On one hand, it encompasses many features of derived intersections in a fairly explicit way. On the other hand, it gives an angle of attack to study explicitly projective derived intersections. This is joined work with Tristan Bozec.
• Francesca Pratali Localization of ∞-operads ▼
  Operads are combinatorial gadgets encoding categories of algebras. In modern homotopy theory, where categories are replaced by infinity-categories, operads are replaced by their homotopy-coherent version, infinity-operads. A natural way infinity-operads arise is through the process of (derived) localization, the process of freely inverting a class of morphisms in a homotopy-coherent way. In this talk, we shall see that every infinity-operad arises as a localization of a discrete one, and that this establishes an equivalence of homotopy theories. These results generalize analogue ones for infinity-categories proven by Joyal and Stevenson, resp. Barwick and Kan. We will see that essential to prove such results is the dendroidal formalism for infinity-operads, based on a certain category of trees and its combinatorics. If time permits, I will also highlight some open questions. Part of this work is joint with K. Arakawa and V. Carmona.
• Anja Svraka Additivity of constructible factorization algebras ▼
  Factorization algebras, introduced by Costello and Gwilliam, encode the structure of observables in perturbative quantum field theory and capture concepts such as the operator product and correlation functions. Beyond this, their local structures encompass familiar algebraic objects including associative and A_{\infty}-algebras, vertex algebras, bimodules, and E_n-algebras. Examples of the latter include (possibly braided) tensor categories and n-fold loop spaces. In many situations of interest, particularly in the presence of defects or boundaries, it is natural to consider constructible factorization algebras. Examples are given by factorization homology. In this talk, I will present recent joint work with Victor Carmona proving an additivity theorem for constructible factorization algebras on manifolds with corners, resolving a conjecture of Ginot. These results address the behavior of factorization algebras under products of spaces and are an important step in a more general additivity result for conical manifolds. Furthermore, results of this kind provide an essential step towards comparing the models for higher Morita categories developed by Scheimbauer and Haugseng, two widely used frameworks in the study of dualizability and topological field theories.
• Nikola Tomic AKSZ theories from shifted Poisson structures and shifted coisotropic reduction ▼
  The AKSZ procedure is a construction of field theories described by Alexandrov–Kontsevich–Schwarz–Zaboronsky. Given a 2-dimensional manifold M, they construct a geometrical object 𝓕_T(M) corresponding to fields on M with a symplectic target T. Such field theory is obtained as a mapping space Map(M,T) and is called a σ-model. This construction has a natural interpretation in shifted symplectic geometry, where the mapping space will have the structure of a derived stack and T will be a derived stack with an n-shifted symplectic form. In their seminal paper, Pantev–Toën–Vaquié–Vezzosi showed that for any compact oriented manifold M of dimension d, it is possible to endow the mapping stack Map(M,T) with a (n-d)-shifted symplectic form. This process has been extended into an extended TFT taking values in shifted Lagrangian correspondences by Calaque–Haugseng–Scheimbauer. Given a shifted symplectic structure, it is natural to study quantization of it, but the correct theory were quantization takes place is the theory of shifted Poisson structures. Shifted Poisson derived stacks are more general that shifted symplectic derived stacks and then harder to study. Such object is expected to satisfies the same properties than shifted symplectic ones. In particular, there should be a way to construct (n-d)-shifted Poisson structures on Map(M,T), given an n-shifted Poisson structure on T. In this talk, I will explain how my recent structure result on shifted Poisson structures gives such a construction. I will also explain how fuctoriality of such a construction is expected to behave and sketch a construction of this functor. In the process, I will explain how we extract a construction of shifted coisotropic reductions, a shifted analog of classical coisotropic reductions. If time permits, I will try to discuss expected results for quantizations of such theories.
• Sofian Tur-Dorvault The motivic fundamental groupoid at tangential basepoints ▼
  If U is a smooth scheme over a subfield of the field of complex numbers, it is known from the work of Pierre Deligne and Alexander Goncharov that the prounipotent completion of the fundamental group of U^an based at any point has a motivic incarnation. More precisely, its coordinate ring arises as the degree-zero homology of the Betti realization of a Hopf algebra object in Voevodsky's triangulated category of motives. More generally, he conjectured a similar property for the fundamental group based at a "point at infinity", i.e. the datum of a point x on a smooth compactification of U with normal crossings boundary, together with the datum of a tangent vector at x, normal to the boundary. While Deligne and Goncharov proved this conjecture in the case of the projective line minus three points, the general case remained still open. In this talk, I will explain how logarithmic geometry, together with the notion of virtual morphisms between log schemes, allows one to construct the motivic fundamental group in full generality and to compute its realizations.