11.4.25	Pedram Hekmati (Auckland) Correction terms, involutions and Seiberg-Witten theory Abstract: Correction terms are numerical invariants of 3-manifolds derived from Floer theory. In Seiberg-Witten Floer theory, involutions play a special role, as they can couple to the intrinsic charge conjugation symmetry and yield different flavours of equivariant Floer cohomology. In this talk, I will explain how this leads to three distinct families of correction terms and highlight some of their applications. This is joint work with David Baraglia.
25.4.25	BACH Seminar in Bochum
9.5.25	Florian Zeiser (Nijmegen) (Infinitesimal) Rigidity for foliations Abstract: A common question for geometric structures is that of rigidity, i.e., given two geometric structures sufficiently close, are they equivalent? In this talk we discuss this question for regular foliations on a closed manifold. In the first part we define the necessary terms, give an overview of the current state of the art and highlight its relation with the rigidity for group actions. Generally, there are two issues: 1) most results require the foliation to have compact leaves; 2) there is a lack of examples. In the second part of the talk, we take a step towards addressing those issues, by outlining a construction of infinitesimally rigid foliations with dense leaves. This is based on joint work with Stephane Geudens.
16.5.25	David Miyamoto (MPI Bonn) Integrating Banach Lie algebras to diffeological groups Abstract: Lie's third theorem states that every finite-dimensional Lie algebra integrates to a Lie group. This is no longer true in infinite dimensions: there exist Banach Lie algebras which do not arise as the Lie algebra of any Banach Lie group. We will show how this obstruction to integration vanishes by generalizing from "Banach" to "diffeological" Lie groups. Along the way, we will introduce diffeological spaces, their tangent functor, and the Lie functor on (the subcategory of elastic) diffeological groups.
23.5.25	Chiara Esposito (Salerno) Equivariant formality and reduction Abstract: In this talk, we discuss the reduction-quantization diagram in terms of formality. First, we propose a reduction scheme for multivector fields and multidifferential operators, phrased in terms of L-infinity morphisms. This requires the introduction of equivariant multivector fields and equivariant multidifferential operator complexes, which encode the information of the Hamiltonian action, i.e., a G-invariant Poisson structure allowing for a momentum map. As a second step, we discuss an equivariant version of the formality theorem, conjectured by Tsygan and recently solved in a joint work with Nest, Schnitzer, and Tsygan. This result has immediate consequences in deformation quantization, since it allows for obtaining a quantum moment map from a classical momentum map with respect to a G-invariant Poisson structure.
30.5.25	Francesco Cattafi (Würzburg) Pseudogroups and geometric structures Abstract: The space of (local) symmetries of a given geometric structure has the natural structure of a Lie (pseudo)group. Conversely, geometric structures admitting a local model can be described via the pseudogroup of symmetries of such local model. This philosophy can be made precise at various levels of generality (depending on the definition of "geometric structure") and using different tools/methods. In this talk I will present some aspects of a new framework, which includes previous formalisms (e.g. G-structures or Cartan geometries) and allows us to prove integrability theorems. A main novelty of this point of view consists of the fact that it uncovers the (beautiful!) hidden structures behind Lie pseudogroups and geometric structures. Indeed, the relevant objects which make this approach work are Lie groupoids endowed with a multiplicative "PDE-structure", their principal actions, and the related Morita theory. Poisson geometry provides the guiding principle to understand those objects, which are directly inspired from, respectively, symplectic groupoids, principal Hamiltonian bundles, and symplectic Morita equivalence. This is based on a forthcoming book written jointly with Luca Accornero, Marius Crainic and María Amelia Salazar.
6.6.25	BACH Seminar in Köln
13.6.25	Maxim Braverman (Northeastern) Background cohomology and symplectic reduction Abstract: We consider a Hamiltonian action of a compact Lie group G on a complete Kähler manifold M with a proper moment map. I define a regularized version of the Dolbeault cohomology of a G-equivariant holomorphic vector bundle, called the background cohomology. I show that the background cohomology of a prequantum line bundle over M `commutes with reduction', i.e. the invariant part of the background cohomology is isomorphic to the usual Dolbeault cohomology of the symplectic reduction.
20.6.25	Madeleine Jotz (Würzburg) A geometrisation of N-manifolds Abstract: Lie 2-algebroids are geometrised by linear Courant algebroids, while symplectic Lie 2-algebroids correspond to mere Courant algebroids. These correspondences due to Li-Bland, Severa and Roytenberg rely on the underlying equivalence of [2]-manifolds with metric double vector bundles. The latter yields a dictionary between graded geometric structures on [2]-manifolds, like homological vector fields, Poisson and symplectic structures, and corresponding `classical geometric' structures on the corresponding metric double vector bundles. Metric double vector bundles dualise to double vector bundles equipped with a (signed) involution. The latter can then be understood as S2-symmetric double vector bundles - recovering Pradines' `inverse' symmetric double vector bundles. Similarly, positively graded manifolds of degree n are equivalent to n-fold vector bundles equipped with a (signed) Sn-symmetry. This talk explains this correspondence and then discusses some examples. This work is partly joint with Malte Heuer and with Leonid Ryvkin.
11.7.25	Pedro Frejlich (UFRGS, Porto Alegre) Dirac products and concurrence Abstract: We discuss two canonical operations on Dirac structures Land R - the tangent product L * R and the cotangent product L ⊛ R. The latter is especially interesting in that it suggests (even mandates) a notion of compatibility between Dirac structures ("concurrence"). In this talk I want to illustrate the usefulness of the notion of concurrence to clarify old constructions in differential geometry, with special emphasis on Poisson and complex Dirac structures. Time permitting, we will also discuss ongoing work concerning the role of concurrence in reduction schemes and in the Nijenhuis condition in the Dirac world. From joint works with collaborators: D. Aguero, A. Arsie, D. Marínez Torres and I. Mencattini.

H. Geiges, 7.10.24