Berlin-Hamburg-Hannover-Seminar am 19.06.2026

Melanie Bertelson (ULB) Non-squeezing and other global rigidity results in locally conformal symplectic geometry

Using generating functions quadratic at infinity for Lagrangian submanifolds of twisted cotangent bundles, we define spectral selectors for compactly supported lcs Hamiltonian diffeomor- phisms of the locally conformal symplectizations M and M’ of the standard contact manifolds R²ⁿ⁺¹ and R²ⁿ x S¹ respectively, and obtain several applications : the construction of a bi-invariant partial order on the group of compactly supported lcs Hamiltonian diffeomorphisms of M and M', of an integer-valued bi-invariant metric on the group of compactly supported lcs Hamiltonian diffeomorphisms of M', and of an integer-valued lcs capacity for domains of M'. The lcs capacity is used to prove a lcs non-squeezing theorem in M' analogous to the contact non-squeezing theorem in R²ⁿ x S¹ discovered in 2006 by Eliashberg, Kim and Polterovich.

Álvaro del Pino Gómez (Utrecht) Rigidity for submanifolds of fat manifolds

A connection on a principal bundle is said to be fat if it is maximally curved. This concept, which was introduced by Weinstein, translates almost verbatim to the setting of distributions (subbundles of the tangent bundle). There, fatness amounts to the strongest form of maximal non-integrability. In corank-1, fat distributions are the same as contact structures.

In this talk I will discuss recent joint work with Eduardo Fernández and Wei Zhou, in which we study submanifolds adapted to corank-2 fat distributions. Our starting observation is that these submanifolds, that we dub "prelegendrians", can be drawn via a "front projection", which allows us to construct many examples. This is sufficient to establish our main result: there are prelegendrians that are formally equivalent (i.e. they have the same smooth knotting type and the same algebraic topological invariants) but are not isotopic as prelegendrians. Equivalently, the h-principle fails for prelegendrians. This rigidty exploits the connection between fat structures and contact structures.

I will wrap the talk with a number of open questions in the study of fatness.