In this talk, I will discuss two distinct research avenues from my lab. In the first part, I will discuss the electronic structure of the nodal line semimetal ZrSiTe. I will demonstrate that there are two different surface states in ZrSiTe - topological drumhead surface states and trivial floating band surface states that can be distinguished in ARPES experiments. I show that a non-trivial Berry phase that exists in a confined region within the Brillouin Zone which gives rise to the topological drumhead-type surface states. The Z2 structure of the Berry phase induces a Z2 'modular arithmetic' of the surface states, allowing surface states deriving from different nodal lines to hybridize and gap out, which can be probed by a set of Wilson loops. Our findings are confirmed by ab-initio calculations and angle-resolved photoemission experiments, which are in excellent agreement with each other and the topological analysis.

In the second part, I outline a topological classification of molecules and their chemical reactions, proposing that changes in topological invariants of molecules measure strong non-adiabatic couplings along the reaction path. As an example, we consider 0-dimensional molecular Hamiltonians in a real-space tight-binding basis with time-reversal symmetry and an additional spatial reflection symmetry.  I will discuss a possible classification in the presence of many-body interactions and propose that the topological properties can be explained by the presence of zeros of the interacting single particle Green's function.