Generalized punctual Hilbert schemes and 𝔤-complex structures

We define and analyze various generalizations of the punctual Hilbert scheme of the plane, associated to complex or real Lie algebras. Out of these, we construct new geometric structures on surfaces whose moduli spaces share multiple properties with Hitchin components, and which are conjecturally homeomorphic to them. For simple complex Lie algebras, this generalizes the higher complex structure. For real Lie algebras, this should give an alternative description of the Hitchin–Kostant–Rallis section.

Geometric characterization of continuously defective elastic crystals

We show how some differential geometric structures associated with a concept of a homogeneous space appear naturally in a kinematic model of continuously distributed defects in an elastic crystal solid and discuss how one can use them to describe the defectiveness of such a continuum.

Hydrogen evolution reaction on Co-Ni core-shell nanoclusters in different sizes: A DFT investigation from geometric structures to electronic structures

Nanoclusters have broad prospects in the application of hydrogen evolution reaction (HER) electrocatalysis. Its high specific surface area, surface geometry effect, electronic properties, and quantum size effect often make the nanoclusters have higher activity than ordinary electrocatalytic materials. However, it is still challenging to design and regulate nanoclusters and make them have better HER performance. In this work, through first-principles calculation from geometric structures to electronic structures, we try to understand the basic physical and chemical properties and HER performance of nanoclusters composed of transition metals Co and Ni. We optimize the electronic structure and promote effective charge transfer by adjusting the size of nanoclusters and constructing core-shell alloying. First-principles studies reveal that the geometric size and electronic structures of Co-Ni nanoclusters can significantly affect the performance of the hydrogen evolution reaction. We found that Co@Ni12 (|ΔGH*|=0.01eV) shows the best HER performance. The Gibbs free energy of hydrogen adsorption of Co-Ni nanoclusters is positively related to the size of the clusters, and the ΔGH* can be adjusted within a certain range by changing the electronic structures of the clusters. Our research helps to understand and design high-efficiency nanocluster electrocatalysts, paving the way for the rational design and synthesis of advanced electrocatalysts for HER.