Álvaro del Pino Gomez (Utrecht University)

Thurston’s jiggling

In the mid 1970s, Thurston settled the existence problem for foliations of codimension 1 (showing that any manifold of vanishing Euler characteristic has such a foliation) and the classification problem for higher-codimension foliations. In this talk I will explain one of the ingredients of the proof, called jiggling.

If time allows, I will comment on some on-going work joint with A. Fokma and L. Toussaint generalising jiggling. Our main observation is that jiggling is the first example of an “h-principle without homotopical assumptions” and can indeed be related to other h-principle techniques, like convex integration.

Francesca Arici (Leiden University)

Sfeermakers or on sphere bundles in noncommutative geometry

The theory of C*–algebras offers an elegant setting for many problems in mathematics and physics. In view of Gel’fand duality, their study is often referred to as non-commutative topology: general noncommutative C*–algebras are interpreted as non-commutative spaces. Many classical geometric and topological concepts can be translated into operator algebraic terms, leading to the so-called noncommutative geometry (NCG) dictionary. 

In this talk, I will describe how circle and sphere bundles, central objects in the development of algebraic topology, can be realised in terms of modules over operator algebras.

Oliver Lorscheid (University of Groningen)

Moduli spaces in matroid theory

Families of matroids have appeared in different disguises during the last few decades: combinatorial flag varieties arise from flag matroids, Macphersonians appear as spaces of oriented matroids, Dressians consist of valuated matroids. With the advent of F1-geometry, we are able to understand these spaces from an algebro-geometric perspective as rational point sets of moduli spaces of (flag) matroids and place them into a larger landscape of geometric objects stemming from combinatorics. In this talk, I will give an impression of my joint works with Matthew Baker and with Manoel Jarra on the topic.