The world faces an era of ‘permacrisis’, marked by overlapping challenges such as climate change, conflicts, economic instability, and recurrent disease outbreaks, which disrupt health systems and deepen inequalities. Primary Health Care (PHC) is vital for addressing immediate health needs and social determinants, fostering resilience, and promoting equity during such crises. This opinion piece highlights PHC’s unique role in ensuring essential services, reducing barriers to care, and integrating health with broader social and environmental policies. In conflict-affected and climate-impacted regions, PHC supports community resilience, promotes health equity, and adapts to systemic shocks. Investing in PHC infrastructure, empowering community health workers, early disease detection, promoting climate-adaptive health practices and delivering integrated care can advance health for all. PHC offers a sustainable pathway to resilient health systems capable of navigating the complexities of a rapidly changing world.

We define a class of amenable Weyl group elements in the Lie types B, C, and D, which we propose as the analogs of vexillary permutations in these Lie types. Our amenable signed permutations index flagged theta and eta polynomials, which generalize the double theta and eta polynomials of Wilson and the author. In geometry, we obtain corresponding formulas for the cohomology classes of symplectic and orthogonal degeneracy loci.

Accurate estimation of dark matter halo masses for galaxy groups is central to studies of galaxy evolution and for leveraging group catalogues as cosmological probes. In this work, we present a comprehensive evaluation and calibration of two complementary halo mass estimators: a dynamical estimator based on a modified virial theorem (MVT) and an empirical summed stellar mass to halo mass relation (sSHMR), which uses the summed mass of the three most massive group galaxies as a proxy for halo mass. Using a suite of state-of-the-art semi-analytic models (SAMs; Shark, SAGE, and GAEA) to produce observationally motivated mock light-cone catalogues, we rigorously quantify the accuracy, uncertainty, and model dependence of each method. The MVT halo mass estimator achieves negligible systematic bias (mean $\Delta = -0.01$ dex) and low scatter (mean $\sigma = 0.20$ dex) as a function of the predicted halo mass, with no sensitivity to the SAM baryonic physics. The calibrated sSHMR yields the highest precision, with mean $\Delta = 0.02$ dex and mean $\sigma = 0.14$ dex as a function of the predicted halo mass but exhibits greater model dependence due to its sensitivity to varying baryonic physics and physical prescriptions across the SAMs. We demonstrate the application of these estimators to observational group catalogues, including the construction of the empirical halo mass function and the mapping of quenched fractions in the stellar mass–halo mass plane. We provide clear guidance on the optimal application of each method: the MVT is recommended for GAMA-like surveys ($i \lt 19.2$) calibrated to $z \lt 0.1$ and should be used for studies that require minimal model dependence, while the sSHMR is optimal for high-precision halo mass estimation across diverse catalogues with magnitude limits of $Z \lt 21.2$ or brighter and to redshifts of $z \leq 0.3$. These calibrated estimators will be of particular value for upcoming wide-area spectroscopic surveys, enabling robust and precise analyses between the galaxy–halo connection and the underlying dark matter distribution.

Under the assumption that the adjusted Brill-Noether number $\widetilde {\rho }$ is at least $-g$, we prove that the Brill-Noether loci in ${\mathcal M}_{g,n}$ of pointed curves carrying pencils with prescribed ramification at the marked points have a component of the expected codimension with pointed curves having Brill-Noether varieties of pencils of the minimal dimension. As an application, the map from the Hurwitz scheme to ${\mathcal M}_g$ is dominant if $n+\widetilde {\rho } \geq 0$ and generically finite otherwise, settling a variation of a classical problem of Zariski.

In the second part of the paper, we study the analogous loci of curves in Severi varieties on $K3$ surfaces, proving existence of curves with nongeneral behaviour from the point of view of Brill-Noether theory. This extends previous results of Ciliberto and the first-named author to the ramified case. We apply these results to study correspondences and cycles on $K3$ surfaces in relation to Beauville-Voisin points and constant cycle curves.

In 1934 C.V. Raman, Nobel Prize laureate in physics, founded the Indian Academy of Sciences in an attempt to create a single unified national scientific society for India. Instead, due to actions of Raman, the Royal Society and other British and Indian scientists, three distinct Indian science academies emerged and have persisted to the present day. Taking place against a background of British imperialism, Indian nationalism and scientific internationalism, Raman’s actions provide a fascinating case study of scientific production and the shaping of scientific networks in (British) India. This paper scrutinizes this hitherto unexplored late imperial stage of the Indian scientific landscape and highlights the versatile role of British imperialism in influencing the founding and functioning of the Indian Academy of Sciences under Raman. The latter’s national and international career and leadership testify to a complex relationship where the personal and the political became intertwined with science in (British) India.

We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and description often rely on specific knowledge of the parent object and its automorphisms. In many cases, questions of reproducibility and comparison arise. Here we present a categorical framework that addresses these questions. We prove that every characteristic structure is the image of a functor equipped with a natural transformation. This shifts the local description in the parent object to a global one in the ambient category. Through constructions in representation theory, such as tensor products, we can combine characteristic structure across multiple categories. Our results are constructive and stated in the language of a constructive type theory which facilitates their implementation in proof checkers.