Francesca Arici

This 4-year PhD position at the Mathematical Institute of Leiden University is part of the project 'New K-theoretic invariants in quantum theory' within the national consortium Emergence at all Scales (EAAS). The research is supervised by Dr. Francesca Arici and Dr. Bram Mesland at Leiden University, in collaboration with Dr. Irene Aguilera at the University of Amsterdam. The project is based in the Analysis and Dynamical Systems group and involves a 70/30 collaboration between Leiden and Amsterdam. The main goal is to interpret topological physics encoded by non-Hermitian and non-gapped Hamiltonians using noncommutative geometry. Key objectives include finding analytic expressions for families of numerical Hamiltonians modeling magnetic topological semimetals, classifying these Hamiltonians using operator algebra invariants such as K-theory and cyclic homology, and developing mathematical methods to derive robust topological invariants from numerical Berry curvature. The candidate will use analytical tools from operator algebras and noncommutative geometry, and analyze data from simulations of tight-binding Hamiltonians. The project aims to advance mathematical understanding of topology in quantum matter. The successful candidate will participate in scientific activities, meetings, and workshops of the EAAS consortium, collaborate across disciplines and institutions, and engage in science communication and outreach, including a pilot program for high school science teaching. EAAS is a national interdisciplinary initiative involving multiple Dutch and Ukrainian universities and Statistics Netherlands, focusing on emergent phenomena across scales in physics, mathematics, astronomy, history and philosophy of science, and social science. The Mathematical Institute at Leiden University is internationally oriented, with research themes in algebra, geometry, number theory, analysis, dynamical systems, probability, operations, dynamics, and statistics. The institute values inclusivity and diversity, and encourages applications from women and under-represented groups. The position offers a competitive salary (€3059 - €3881 gross per month), additional travel funding, holiday and end-of-year bonuses, pension scheme, public transport reimbursement, flexible working hours, and options for sabbatical or parental leave. All PhD candidates are part of the Leiden University Graduate School of Science. Applicants must have a Master’s degree in mathematics or theoretical physics, with expertise in noncommutative geometry, operator algebras, K-theory, operator theory, or mathematical physics. Familiarity with condensed matter theory and many-body quantum theory is a plus. Proficiency in English and willingness to perform numerical simulations are required. Applications should include a CV, transcripts, application form with referees, optional Master’s thesis, and a motivation letter. The review of applications begins on 5 January 2026 and continues until the position is filled.