The project advanced understanding of string theory through both mathematical analysis and computational approaches. The research focussed on two complementary areas that together provided new insights into quantum effects in string theory.
The first major area of work involved analysing string theory through geometric structures. The Fellow studied worldsheet string models in spaces with special geometric properties, known as G2 and Spin(7) structures. This investigation revealed that certain physical quantities, specifically the partition functions that count string vibrations, have a remarkable "topological" property - they remain unchanged when the underlying geometry is deformed. The Fellow also developed and expanded the mathematical framework of "generalised geometry," which proved particularly well-suited for describing the complex spaces that appear in string theory. This led to a groundbreaking proof of the existence of certain deformed string theory solutions that incorporate quantum corrections.
The second focus area involved developing new mathematical tools to understand quantum corrections. The Fellow created new frameworks that revealed how quantum effects modify string theory solutions, including the development of a "generalised holomorphic structure" approach. This work established unexpected connections between string theory and other areas of mathematics, particularly geometric flows. The research also produced first-time calculations of fundamental quantities in certain string theory models, providing concrete results in previously intractable areas.
These research achievements have been extensively shared with the scientific community through seventeen peer-reviewed papers published in leading journals. The work has been presented at major international conferences, including prestigious venues such as Strings, StringMath, and StringPheno. The Fellow organised workshops and seminars at both host institutions, delivered graduate-level lectures on the new mathematical techniques, and engaged in public outreach activities to communicate these complex ideas to broader audiences.
The project has had significant impact through knowledge transfer and collaboration. The research, conducted first at the University of Chicago and then at Sorbonne Université, has created lasting partnerships between these institutions. Graduate students have been trained in these advanced mathematical techniques, ensuring the continuation of this research direction. The tools and frameworks developed during the project have found applications beyond theoretical physics, contributing to both physics and mathematics.
The comprehensive approach of the project - combining mathematical innovation, computational methods, and international collaboration - has created lasting impact in both theoretical physics and mathematics. The established partnerships between European and American institutions continue to facilitate scientific exchange, while the mathematical tools developed are being actively used by researchers around the world to advance our understanding of fundamental physics.
