Topics of the workshop:

1. Modelling: Schrödinger/Dirac/Wave operators with singular point-like perturbations; modelling as asymptotic limits and resolvent approximations; new models of contact interactions corresponding to today-feasible experimental realisations; new transmission models of classical and quantum particles.
2. Linear analysis:  modified Sobolev spaces adapted to the (fractional) powers of the linear operator of contact interaction; dynamical properties; propagators; dispersive, smoothing, and Strichartz - like estimates; wave operators; spectral projection estimates and asymptotics of eigenvalues and eigenfunctions; Strichartz type estimates; self-adjoint realisation of Laplace-Beltrami operators on generic almost Riemannian manifolds, including sub-Riemannian geometry of structures with tangency points.
3. Nonlinear analysis: non-linear (semi-linear) Schrödinger-type equations with contact-type singular perturbations of differential operators; well-posedness; blow-up phenomena; norm-growth; ground states; asymptotic stability; standing waves; invariant measures; derivation of point-perturbed NLS from many-body models.
4.Related tools and techniques: Functional-analytic, operator-theoretic, and PDE-oriented methods on models and problems whose applicability and insight extends to the workshop's main subject area.