Meeting “Lie theory and Poisson Geometry” (2022)
A. Balibanu, C. Esposito, M.A. Salazar, and I are organising a meeting on the role of Lie/representation theoretical aspects in the study of Poisson Geometry. We will have some great minicourses, as well as talks given by young participants. Our goal is to bring together young researchers on these fields. The event will take place on the week of 10th-14th January 2022, at CIRM (France). All the information can be found here. Registration and submission of abstracts are now closed.
Friday Fish seminar
The Friday Fish is the Differential Geometry seminar of Utrecht University. The online edition, started due to Corona, was organised by M. Crainic, M. Mol, and myself during the period summer 2020/summer 2021. We are currently running the seminar in a hybrid format with smaller audience. If you are interested in attending (or you are just curious about what we are doing), feel free to drop me an email. You can find more information in our webpage.
Dutch Differential Geometry and Topology seminar
This is a monthly seminar series organised together with F. Pasquotto, T. Rot and R. Vandervorst. Its aim is to show offer a panoramic view of different subfields within Differential Geometry to master students in Dutch universities. The sessions are structured as 2-hour minicourses, together with a break and a relaxed discussion afterwards. The 2021/22 edition started in September. You can find more information here.
Workshop “A topological theory of distributions” (2021)
During the week of 30th August-3rd September 2021, V. Franceschi, F. Pasquotto, M. Seri, and myself organised a workshop on the interactions between Subriemannian Geometry, the theory of hypoelliptic operators, and Contact Topology. It was meant to take place at the Lorentz Center (Leiden) but, due to covid, all activities (lectures and working groups) ended up taking place online.
You can find the details of the meeting in our webpage. The lectures were recorded; they can be found in the following playlist. During the working groups we had plenty of interesting discussions about open questions in the intersection of the three areas. All of these will eventually appear in a booklet we are preparing summarising the work carried out during the workshop.
15th Young Researchers Workshop on Geometry, Mechanics, and Control (2020)
These workshops give an opportunity to young researchers in Geometry, Mechanics, and Control to interact with one another and with experts from each of these fields. The 2020 edition was originally going to be held in Utrecht but, due to corona, had to take place online. Additional information, as well as videos and slides from the workshop can be found here.
Minicourses on tangent distributions (2019)
I have been using my NWO Veni to bring young researchers to Utrecht University for a couple of weeks to share their expertise with us using a minicourse format. The topics covered have to do with the theory of tangent distributions (contact or otherwise) and related topics (symplectic geometry, subriemannian geometry, and others).
This event has now been superseded by the Dutch Differential Geometry and Topology seminar.
November 27th – December 6th 2019
Lucas Dahinden is a postdoc based at the Ruprecht-Karls-Universität Heidelberg. His research deals with Contact Topology and Dynamics. During his visit he will give a minicourse on some recent extremely interesting developments regarding topological entropy.
- Title: Rigidity of topological entropy for positive contactomorphisms.
- Location: Uithof campus in Utrecht, Minnaert gebouw, room 0.15.
- Time: 29th November 2019. 11:00-13:00 and then 15:00-17:00.
- Abstract: In this series of talks I aim to present a result in Symplectic Geometry. Historically, Symplectic Geometry developed as the geometry behind Physics because it is the right framework to define the Hamiltonian equations. Nowadays, Symplectic Geometry is a research field on its own, with many subbranches and connections to other fields. We take a journey beginning with the definition of “symplectic”, to more and more specialized theories. We will follow the following structure:
1. Symplectic Geometry in general
2. Floer homology
3. Rabinowitz-Floer homology
4. The main result.
The proof of (4) uses the machinery introduced in (1-3), but I hope to show you that this machinery is also of independent interest by explaining ideas and mentioning other applications. The main result identifies a class of spaces on which a natural class of maps has positive topological entropy (i.e. they are chaotic in some sense).
For the non-experts: A generalization of geodesic flows on a generalization of rationally hyperbolic manifolds is always chaotic.
For the experts: In Liouville fillable contact manifolds with exponentially growing wrapped Floer homology, every positive contactomorphism has positive topological entropy.
April 2nd-16th 2019
Daniel Álvarez-Gavela is a postdoc at the IAS. His work deals with flexibility phenomena in contact and Symplectic Topology, Singularity Theory, and parametrised Morse theory. During his stay in Utrecht he gave two beautiful minicourses.
- Title: The flexibility of caustics and its applications to the arborealization of Lagrangian skeleta
- Location: Uithof campus in Utrecht, Buys Ballot gebouw, room 077.
- Time: 5th April 2019. 11:00-13:00 and then 14:30-16:30.
- Abstract: Starting with the results of Smale-Hirsch on immersion theory, there has been extensive work in the mathematics literature devoted to the problem of simplifying the singularities of smooth maps. The over-arching principle is that such a problem, a priori geometric in nature, often reduces to the underlying homotopy theoretic problem, to which the tools of algebraic topology can be applied. Recently it has been shown that such a reduction also exists for the problem of simplifying the singularities of Lagrangian and Legendrian fronts, also known as caustics. This latter problem is intimately linked to the problem of simplifying the singularities of the skeleta of Weinstein manifolds, which are the symplectic analogues of Stein manifolds (smooth affine complex varieties). In the best case scenario the simplification yields a skeleton with only arboreal singularities, which are a particularly natural and simple class of singularities for which the pseudo-holomorphic invariants of Weinstein manifolds become combinatorial.
- Title: K-theoretic invariants in symplectic and contact topology via parametrized Morse theory
- Location: Uithof campus in Utrecht, Buys Ballot gebouw, room 077.
- Time: 12th April 2019. 11:00-13:00 and then 14:30-16:30.
- Abstract: The generating family construction provides a link between the study of Lagrangian (resp. Legendrian) submanifolds of cotangent bundles (resp. 1-jet spaces) and the study of parametrized Morse theory on fibre bundles. By the work of Smale, Hatcher, Wagoner, Igusa, Waldhausen and others, the homotopy type of the space of (stable) h-cobordisms of a manifold can be computed in terms of K-theory using the tools of parametrized Morse theory. Therefore it is not surprising that K-theoretic invariants can be used to exhibit rigidity phenomena in symplectic (resp. contact topology). It is currently unclear the precise way in which the K-theoretic invariants are related to the invariants provided by pseudo-holomorphic curve theory. However, several new examples of the connection between K-theory and symplectic (resp. contact) topology have recently appeared in the literature, making the study of this connection a fertile topic for research.