Geometric Structures in Utrecht Utrecht University - Mathematics Department Home

Higher Geometric Structures along the Lower Rhine III

October 17-18, 2013 - Utrecht University

Organizers: Marius Crainic, Ieke Moerdijk, Christian Blohmann


This is the third in a series of  short workshops jointly organized by the Geometry/Topology groups in Bonn, 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, di fferentiable stacks, Lie algebroids, generalized complex geometry, topological quantum fi eld theories, higher categories, homotopy algebraic structures, higher operads, derived categories, and related topics. The first workshop took place in Bonn and the second in Nijmegen.


Camilo Arias Abad (Bonn)

Javier Gutiérrez (Nijmegen)

Matias del Hoyo (Utrecht)

Arturo Prat-Waldron (Bonn)

Gregor Schaumann (Universität Erlangen-Nürnberg)

Pavol Ševera (Université de Genève)

Anton Zeitlin (Columbia University)


Click here to register. For any inquiries, please send an email to

Financial Support

If you wish to apply for financial support, please fill out the corresponding field in the registration form.

Conference Dinner

There will be a conference dinner at the Faculty Club on Thursday at 6:30pm. The faculty club is located behind the dom tower at the very heart of the city center. Since it is a bit tricky to find the entrance, we will gather outside the lecture hall after the last lecture on Thursday and take the bus together to the city center.

Location: Utrecht University, Campus “de Uithof”

Registration and the lectures of the first day will take place in the Minnaert building in lecture Room 208 (after entering the building, go to the end of the hall and climb up one floor). The lectures of the second day will take place in room 322 of the BBL (Buys Ballotlaboratorium) building located just behind the Minnaert building. To arrive by public transportation, take bus number 11 from the train station or from the stop Oorsprongpark close to the Mitland hotel and get off at the stop “Botansiche tuinen”. From there it is a 3 minute walk.

Schedule, Titles and Abstracts

Thursday - October 17




12:30 - 14:00

MIN 208

Registration and informal gathering for lunch

14:00 - 15:00

MIN 208

Pavol Ševera - Moment maps, centers, moduli spaces

Abstract: I will explain how the theory of (generalized) moment maps can be replaced with the notion of left and right centers of quasi-Poisson manifolds and apply this point of view to moduli spaces of flat connections on surfaces with various boundary data. I will briefly discuss why it is beneficial for explicit deformation quantization of the resulting Poisson manifolds.

15:30 - 16:30

MIN 208

Javier Gutiérrez - On Ohkawa's theorem for combinatorial model categories

Abstract: A theorem due to Ohkawa states that the collection of Bousfield equivalence classes of spectra is a set. This fact has been studied and generalized to other triangulated categories by Neeman, Iyengar-Krause and Dwyer-Palmieri. In this talk, I will explain how to extend this result to arbitrary combinatorial model categories. This is a joint work with C. Casacuberta and J. Rosick ý.

17:00 - 18:00

MIN 208

Gregor Schaumann - A diagrammatic calculus for tricategories, dualities and strictification.

Abstract: We introduce a 3-dimensional diagrammatic calculus for tricategories that extends the calculus of ribbon diagrams to diagrams including surfaces in the cube. Orientation reversal of surfaces and lines corresponds to two duality operations on the tricategories. The singularity structure of the projection of the diagrams and the corresponding moves describe precisely the structure of the strict version of a tricategory with duals. The example of bimodule categories and applications to defects in 3-d topological field theories will be discussed. Part of this is joint work with Catherine Meusburger and John Barrett.


Drinks and dinner at the Faculty Club (see further details above)

Friday - October 18




10:00 - 11:00

BBL 322

Arturo Prat-Waldron - Geometric Quantization Revisited

Abstract: In this talk we will review the geometric quantization of certain symplectic supermanifolds arising from the variational calculus of one dimensional supersymmetric sigma models. We will discuss how this point of view fits in the Stolz-Teichner approach to cohomology theories via Euclidean Field Theories, and the possible extensions to higher dimensional sigma models.

11:30 - 12:30

BBL 322

Anton Zeitlin - Conformal invariance for sigma models, Courant algebroids and homotopy algebras.

Abstract: We discuss the G-infinity algebra associated to Courant algebroids with Calabi-Yau structure and its relation to the vanishing condition for the (covariant) Beta-functions of sigma models in string theory leading to field equations with corrections.

13:30 - 14:30


14:30 - 15:30

BBL 322

Matias del Hoyo - Metrics on stacks

Abstract: In a joint work with R. Fernandes we introduce a notion of Riemannian metrics for Lie groupoids, prove that any proper groupoid admits a metric, and show that the exponential maps of our metrics yield linearizations of the groupoid structures, providing both a simple proof and a generalization for the Weinstein-Zung Theorem. I will talk about these ideas from the stack perpective: our notion is Morita invariant, leading to stacky versions of metrics, normal coordinates and tubular neighborhoods.

16:00 - 17:00

BBL 322

Camilo Arias Abad - Higher dimensional analogues of braid representations