Moduli Spaces and Vector Bundles, New trends

Tufts University, Medford MA

Investigators

Abstract

The grant will provide support for several early-career mathematicians based in the US to attend a five-day international conference, "Moduli Spaces and Vector Bundles, New Trends", to be held at the University of Warwick, U.K. The study of moduli spaces for curves and vector bundles continues to be at the forefront of Algebraic Geometry, and this conference will present recent developments of the theory of moduli spaces and explore further open questions. The award will allow the early-career mathematicians to attend lectures, present in poster sessions, discuss questions with experts in the field, and receive advice and mentorship that will enhance the ability to continue their work. The organizers of the conference have a track record of promoting diversity and encouraging the incorporation of new talent into the field, and women and members of under-represented minorities will be encouraged to participate. For more information, see the conference page http://vbac.wikidot.com/vbac2022. The main topic of the conference will be moduli theory and applications with an emphasis on questions related to vector bundles. One focus will be general theory of stability conditions in derived categories. The theory of Bridgeland stability has matured to provide a powerful tool to study classical problems in algebraic geometry and to analyze moduli spaces of sheaves. A second focus is non-reductive geometric invariant theory, which can be used to construct moduli spaces that include unstable objects or involve non-reductive group actions; important work on the cohomology of such quotients is in progress. Next, higher rank Brill–Noether theory, an ongoing enterprise, has already born some fruit in applications such as computing the Kodaira dimension of spaces of Pryms. The final subtopics, moduli of Higgs bundles and character varieties, are related via the non-abelian Hodge Theorem. World experts in these fields will participate in the conference and present their latest results. Discussions taking place during the conference are likely to lead to further progress in the field. This award will allow US scholars to travel to the UK to attend this impactful event. For more information, see the conference page http://vbac.wikidot.com/vbac2022. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.