In the first call of Grant Period One, we received nine applications in total, and accepted seven of them. Two people applied for a Young Innovator and Research conference grant, the other seven applied for a Short-Term Scientific Mission grant.

The STSM grantees and their projects are the following.

• Aasifa Rounak will visit the Centre for Applied Dynamic Research (CADR) at the University of Aberdeen for 6 weeks. The goal is to advance the area of stochastic interrogation of mechanical systems exhibiting discontinuous nonlinearities, both numerically and experimentally, with a focus on the mass-excited impact oscillator and a double pendulum system. Aasifa Rounak’s work aligns with perspectives and methodologies developed across WG1 and WG3.
• Sema Yayla will visit the TU Wien for one month to study the long-time dynamics of the nonlocal Swift-Hohenberg equations. The goal is to prove the existence of its global attractor in 3D and analyze the stability of global attractors. This aligns with the mSPACE objective to understand the long-time behavior of multiscale systems.
• Setenay Akduman will visit the FernUniversität Hagen for 3 weeks to study shape optimization problems for elasticity systems arising in roof-like geometries, with a particular focus on open-book structures. Motivated by recent results on the existence of optimal shapes in architectural elasticity problems, the project seeks to identify geometries that maximize structural stability through energy minimization. This contributes to the activities of WG1 and WG2.
• Martina Vittorietti will visit the Charles University for 7 days to study the asymptotic behavior of estimators for Poisson–Laguerre tessellations and to develop tools for statistical inference in this setting. The proposed Short-Term Scientific Mission contributes to the Action’s overarching challenge of constructing a unified mathematical framework for the analysis of multiscale, geometrically structured spaces using analytic, combinatorial, and stochastic approaches, with a strong focus on applications.
• John Fernley will visit the Aarhus University for one month to develop and prove results on the role of geometry in variants of the voter model. The goal is to clarify the underlying mechanisms of consensus and ergodicity in the presence of strong geometric heterogeneity. The study of Laplace-type behaviour and spectral properties on hyperbolic structures connects to the core mission of WG1. By interpreting hyperbolic graphs as idealized heterogeneous media where geometry induces stronginhomogeneity, the project also contributes to the probabilistic foundations emphasized in WG4.
• Catherine Drysdale will visit the Institute of Biology Paris Seine of Sorbonne University for one month. The goal is to develop a computational model of the CA2 subregion of the mouse hippocampus by integrating available experimental data with domain-specific experimental expertise. A core deliverable will be a reproducible pipeline for constructing intrinsic CA2 coordinates using Laplace–Beltrami eigenfunctions derived from an appropriate atlas. This directly addresses the Action’s aims to translate applied-science problems into spectral-geometry and gradient-flow frameworks, bridge discrete and continuous metric representations, and harness the synergy between spectral theory and optimal transport.

The YRI Conference grantee is:

• Gilad Sofer received support to visit the programme ‘Geometric spectral theory and applications’ at the Isaac Newton Institute for Mathematical Sciences in Cambridge to present a poster on the Spectral Flow and Robin domains on Metric Graphs.