Higher Geometric Structures along the Lower Rhine XVIII
23-24 January 2025 - Radboud University Nijmegen

Date

The workshop starts Thursday 23 January 2025 at 14:00 and ends Friday 24 January 2025 at 16:30.

Location

The talks on Thursday are in room HG00.303 and those on Friday are in HG00.622. Both rooms are in the Huygensgebouw, Heyendaalseweg 135, Nijmegen, The Netherlands (Travel Directions)

Program

23 January (rooom HG00.303) 24 January (room HG00.622)
  • 09:45 - 10:00: Coffee
  • 10:00 - 11:00: Nandy
  • 11:15 - 12:15: Obster
  • 12:15 - 14:00: Lunch break
  • 14:00 - 15:00: Aintablian
  • 15:00 - 15:30: Coffee break
  • 15:30 - 16:30: Hebestreit

Registration

If you like to attend the workshop, please register here so that we can estimate the number of participants. There is no registration fee and the registration is open until 5 January 2025.

Description

This is the eighteenth in a series of short workshops jointly organized by geometers and topologists from Bonn, Cologne, Nijmegen, and Utrecht, all situated along the Lower Rhine. The focus lies on the development and application of new structures in geometry and topology such as Lie groupoids, differentiable stacks, Lie algebroids, generalized complex geometry, topological quantum field theories, higher categories, homotopy algebraic structures, higher operads, derived categories, and related topics.

Previous Meetings

Earlier editions of these workshops were: I (MPIM Bonn), II (Nijmegen), III (Utrecht), IV (MPIM Bonn), V (Nijmegen), VI (Utrecht), VII (Leuven), VIII (MPIM Bonn), IX (Nijmegen), X (Utrecht), XI (MPIM Bonn), XII (Nijmegen), XIII (Utrecht), XIV (MPIM Bonn), XV (Nijmegen), XVI (Utrecht), XVII (MPIM Bonn)

Organizers

The workshop series is organized by Christian Blohmann, Marius Crainic, Ioan Mărcuț, Ieke Moerdijk, and Steffen Sagave, and the local organizer for this workshop is Steffen Sagave.

Titles and abstracts

  • Lory Aintablian (MPIM Bonn): tba
    Abstract:

    tba

  • David Gepner (Johns Hopkins): tba
    Abstract:

    tba

  • Aaron Gootjes-Dreesbach (U Utrecht): Jet configuration spaces and weightings
    Abstract:

    Blowing up the diagonal of \(M^2\) for a manifold \(M\) yields a configuration space that remembers the collision axis of collided configurations. Fulton and MacPherson famously generalized this construction to configurations of more than two points. In joint work with Á. del Pino, we build configuration spaces for jets of maps \(M\to N\) in the same spirit, but adapted to the main structure on jet space: The Cartan distribution and the Lie filtration it generates. Higher jet orders necessitate the use of weighted blow-ups, which we tackle within the recent differential-geometric framework of weightings due to Loizides and Meinrenken. In this talk, I first intuitively illustrate this motivation and our construction. I will then give an introduction to weightings and discuss how we use them as far as time allows.

  • Fabian Hebestreit (U Bielefeld): tba
    Abstract:

    tba

  • Josefien Kuijper (U Utrecht): The Dehn invariant for spherical scissors congruence as spectral Hopf algebra
    Abstract:

    The Dehn invariant is known to many as the satisfying solution to Hilbert’s 3rd problem: a three-dimensional polyhedron \(P\) can be cut into pieces and reassembled into a polyhedron \(Q\) if and only if \(Q\) and \(P\) have not only the same volume, but also the same Dehn invariant. Generalised versions of Hilbert’s 3rd problem concern the so-called scissors congruence groups of euclidean, hyperbolic and spherical geometry in varying dimensions, and in these contexts one can define a generalised Dehn invariant. In the spherical case, Sah showed that the Dehn invariant makes the scissors congruence groups into a graded Hopf algebra. Zakharevich has shown that one can lift the scissors congruence group to a \(K\)-theory spectrum. In this talk I will discuss a lift of the Dehn invariant to the spectrum level, and we will see how it gives rise to a spectral version of Sah’s Hopf algebra.

    This talk is based on joint work in progress with Inbar Klang, Cary Malkiewich, David Mehrle and Thor Wittich.

  • Ahina Nandy (RU Nijmegen): tba
    Abstract:

    tba

  • Lennart Obster (U Coimbra): A cohomology theory for multiplicative tensors
    Abstract:

    Multiplicative tensors (possibly symmetric or exterior) are sections of certain vector bundles compatible with a multiplication of a Lie group(oid). Examples include multiplicative differential forms (e.g. symplectic forms), multiplicative multivector fields (e.g. multiplicative Poisson structures), multiplicative complex structures and multiplicative Ehresmann connections. The infinitesimal counterparts of multiplicative tensors are called infinitesimally multiplicative tensors. Infinitesimally multiplicative tensors are sections of certain vector bundles compatible with a Lie bracket of a Lie algebra/oid. In the talk we will describe a cohomology theory for tensor powers of vector bundles over Lie groupoids. In this (global) cohomology theory, multiplicative tensors appear as cocycles. Similarly, we describe the infinitesimal counterpart of this cohomology theory. The plan is to discuss some properties of these cohomology theories, including the relation between the global and infinitesimal theories, and to talk about a few applications.