This PhD position at Leiden University's Mathematical Institute is part of the ERC project 'Enumerative and Arithmetic Geometry of Logarithmic Curves,' supervised by Prof.dr. David Holmes. The research focuses on the moduli spaces of curves and abelian varieties, which are central objects in algebraic and arithmetic geometry. The project integrates various perspectives, including modular curves, Shimura varieties, and moduli spaces of flat structures, with applications in enumerative geometry (notably log Gromov-Witten theory and counting curves with tangency conditions) and arithmetic geometry (such as understanding rational points on abelian surfaces). The specific research direction for the PhD candidate will be tailored to their background, interests, and the project's progress at the time of joining. The candidate will join a vibrant and expanding group specializing in enumerative and logarithmic geometry, within a broader community at Leiden focused on algebra, geometry, and number theory. The institute offers a collaborative environment with local reading groups and participation in national and international algebraic geometry seminars, as well as opportunities to attend schools and workshops. The Mathematical Institute is internationally oriented and dedicated to advancing mathematical knowledge and its applications. The position offers a four-year contract, a competitive salary (€3059–€3881 gross per month), holiday and end-of-year bonuses, a pension scheme, full reimbursement of public transport commuting costs, flexible working hours, generous leave, and a laptop. Applicants must hold a Master’s degree in mathematics with a strong background in algebraic geometry or number theory and demonstrate proficiency in English. The application requires a CV, Master’s transcripts, a completed application form (LaTeX required), an optional Master’s thesis, and a motivation letter. The deadline for applications is 4 January 2026. For more information, candidates can contact Prof.dr. David Holmes at holmesdst@math.leidenuniv.nl or visit the provided links for details about the institute and employment conditions.