Abstracts

Talks

• Janina Bernardy: A homotopy momentum map for the gauge symmetry of Chern-Simons theory
  
  In Chern-Simons theory, Noether's theorem does not give rise to an equivariant momentum map for the gauge symmetry. However, we will show that the map from infinitesimal gauge transformations to Noether currents can be extended to a homotopy momentum map, that is, a morphism of L_∞-algebras from the Lie algebra of infinitesimal gauge transformations to the L_∞-algebra of Hamiltonian forms. This homotopy momentum map relates to classical constructions by Freed as well as to the homotopy momentum map on the moduli space of flat connections considered by Callies, Frégier, Rogers, and Zambon. This is joint work with Christian Blohmann and Michele Lorenzi.
• Pedro Carvalho: Homological reduction of Courant algebroids
  
  We present a homological model for Courant reduction that extends the classical homological formulation of hamiltonian reduction for symplectic and Poisson structures (Kostant–Sternberg, Stasheff) to the context of Courant algebroids. In particular, we show that the underlying algebraic structure of such a model is that of a dg Courant–Dorfman algebra. Our construction is based on the graded symplectic approach to Courant reduction and the BFV–BRST formalism. As examples, we consider the cases of trivially and general extended actions, whose corresponding models can be shown to give rise to natural differential graded versions of exact Courant algebroids. This is joint work with H. Bursztyn (IMPA).
• Mauricio Correa: On localisation theory on Deligne-Mumford complex superstacks
  
  In this talk we will present an intrinsic localisation theorem for odd holomorphic vector fields on Deligne–Mumford complex superstacks. The theorem yields a global localisation formula in the stacky super setting, together with its specialisation to the case of isolated residual gerbes. We will also briefly describe a toroidal equivariant refinement, formulated in terms of toroidal supergroups and Harish–Chandra superpairs, leading to a super-ABBV-type statement. If time permits, we will conclude with some remarks on possible applications to a super Gromov–Witten theory and to the geometry of supermoduli spaces. This is joint work with Simone Noja.
• Miquel Cueca: Reduction at critical values
  
  In this talk I will show how several reduction procedures at critical values (including: classical Hamiltonian reduction, group valued moment maps, Poisson Lie group valued moment maps and Mikami-Weinstein for proper symplectic groupoids) can be model with a 0-shifted symplectic groupoid in derived manifolds. This is joint work with F. Dorsch, R. Sjamaar and C. Zhu.
• Antonio del Donno: Braided differential calculi and noncommutative Cartan geometries
  
  This works consists of a first attempt at describing the affine model of Cartan geometry in a noncommutative setting. We study first order differential calculi in braided monoidal categories, with a focus on braided bialgebras and Hopf algebras. We introduce a braided analogue of the classical notion of first order differential calculus, and establish a braided version of Woronowicz’s classification theorem for (bi)covariant differential calculi over Hopf algebras. Specialising to the case where B is a braided Hopf algebra in the category of Yetter–Drinfeld modules over a Hopf algebra H, we consider the Radford–Majid biproduct B # H, which defines a canonical Hopf–Galois extension of B. In this setting, we show that smash-product calculi on B # H form a natural and highly structured class of differential calculi compatible with the extension. In particular, we prove that the Maurer–Cartan form splits into a principal connection and a soldering form, and that the coinvariant 1-forms on the total space decompose accordingly. Furthermore, we show that our model naturally admit a notion of frame resolution.
• Filippo Fila Robattino: The Reduced Dirac Structure of General Relativity on Manifolds with Corners
  
  Classical field theories on stratified manifolds present several geometric and algebraic structures. In particular, the space of fields on the boundary is endowed with a symplectic structure, while — in the main examples of field theories — to the (appropriate) space of corner fields one can associate a Dirac structure. In this talk, I will analyze the case of 4D gravity in the Palatini-Cartan formalism, showing how the resulting Dirac corner structure can be obtained as the graph of a Poisson structure. This is a joint work with Alberto Cattaneo and Manuel Tecchiolli, exploiting the general construction due to Bonechi, Canepa, Cattaneo and Schiavina.
• Rita Fioresi: Supergeometric Quantization
  
  In a celebrated 1984 paper Gelfand and Zeleviskii proposed the notion of model, parametrizing irreducible unitary representations of a simple Lie group G. Later on, Gelfand models were inspiring the theory of geometric quantization, where representations of G are realized in the space of sections of unitary line bundles on a suitable symplectic quotient of G. We generalize this construction to the supergeometric setting and provide a criterion for the realization of highest weight super representations, based on the super moment map. This is a joint work with M.-K. Chuah.
• Michael Heins: Convergent Twist Deformations
  
  We discuss a functorial framework for the convergence of Drinfeld's Universal Deformation Formula on spaces of analytic vectors. In our setting, g is always a finite-dimensional Lie algebra with universal envelope U(g). Algebraically, the principal idea is then that a Drinfeld twist induces formal deformations of any algebra our Lie algebra g acts on by derivations. Equipping the representation space with a locally convex topology, we overcome the formal character of this deformation, i.e. pass from a formal deformation parameter h to a complex value of h. This is achieved by matching an equicontinuity condition on the action of the components of the twist with the order of analytic vectors of the representation. Finally, we demonstrate the effectiveness of our theory by applying it to the explicit Drinfeld twists constructed by Giaquinto and Zhang. This is joint work with Chiara Esposito and Stefan Waldmann.
• Frank Neumann: Rational homotopy types and Hodge theory of moduli stacks of principal G-Bundles
  
  For a semisimple complex algebraic group G we determine the rational cohomology and the Hodge-Tate structure of the moduli stack of principal G-bundles over a connected smooth complex projective variety X of a certain special type using the homotopy theory of topological stacks and transcendental methods. The illustrative example will be that of an algebraic curve. This is joint work in progress with Pedro Luis del Angel Rodríguez (CIMAT).
• Simone Noja: Formal moduli and splitting obstructions of complex supermanifolds
  
  Unlike smooth supermanifolds, complex supermanifolds need not be split: their geometry is not, in general, reducible to the geometry of ordinary complex manifolds together with vector bundles on them. In this talk, I will discuss a deformation-theoretic approach to the splitting problem for complex supermanifolds. Starting from Green's obstruction tower, I will explain how the successive splitting obstructions are encoded by a finite-step filtered Maurer--Cartan problem and, after homotopy transfer, by a minimal filtered \(L_\infty\)-model. I will also describe how the affine Atiyah class recovers the same obstruction tower, with the Donagi--Witten component as its primary part. Time permitting, I will discuss new applications to the geometry of the supermoduli stack of super Riemann surfaces, with motivations from perturbative superstring theory. This talk is based on a joint work with M. Corrêa [arXiv:2605.03166]
• Chiara Pagani: Push-forward of Hopf-Galois extensions
  
  Using the framework of twisted tensor product algebras, we identify conditions under which covariant extensions of modules along morphisms inherit algebra structures. In this setting, we investigate the push-forward of Hopf–Galois extensions as an algebraic analogue of the pullback of principal bundles.
• Kasia Rejzner: Perturbative AQFT with boundary
  
  In this talk I will discuss the results obtained together with Michele Schiavina, concerning perturbative algebraic quantum field theory (pAQFT) in the presence of boundary. The main idea is to use the smoothened boundary modelled by an appropriate choice of test function smearing the interaction Lagrangian. The resulting formalism can be understood as a smoothened version of the Cattaneo-Mnev-Reshetikin (CMR) framework.
• Andrea Rivezzi: On the quantization-dequantization correspondence for (co)Poisson Hopf algebras
  
  In this talk, I will present a novel construction for quantizing co-Poisson Hopf algebras in an arbitrary symmetric monoidal category. The construction builds on and unifies ideas from works of Cartier, Drinfeld, Etingof–Kazhdan, and Ševera. We further show that reversing this construction yields an explicit dequantization procedure. This is joint work with J. Schnitzer (arXiv:2602.03810).
• Alexander Schenkel: Global derived geometry of lattice gauge fields
  
  Ideas and techniques from derived geometry have heavily influenced many recent developments in (quantum) field theory, leading to novel concepts such as factorization algebras, homological refinements of the traditional framework of algebraic QFT, and the powerful BV-BFV formalism. A common shortcoming of most (if not all) of these developments is that they are intrinsically perturbative, even at the level of classical fields, as they are based on the concept of formal moduli problems in derived geometry. The main reason for this limitation is that (quantum) field theories involve functional-analytic objects, such as spaces of distributional sections of vector bundles, which lie outside the scope of currently established frameworks for global derived geometry. In this talk I will explain how classical lattice field theories, which are defined on a discrete approximation of the spacetime manifold, admit a non-perturbative and global description within the standard framework of derived algebraic geometry. In particular, I will provide rather explicit and computable descriptions of the derived critical loci of classical Yang-Mills theory on the two-dimensional lattice, and show that their associated dg-categories of quasi-coherent complexes, playing the role of observables in this context, assemble into a locally constant prefactorization algebra on the lattice. This talk is based on joint work with M. Benini and T. Fernández [arXiv:2409.06873, to appear in Selecta Mathematica].