Principal Investigator: Eleny Ionel
This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The proposal is aimed at increasing understanding of the structure of the moduli spaces of stable holomorphic maps by combining ideas from several different fields of research. The core of the project seeks to use geometric and analytical methods to investigate what happens to these moduli during certain natural degenerations. In particular it leads to defining a version of Gromov-Witten invariants relative certain type of singular subspaces, including relative both a normal crossing symplectic divisor and a Lagrangian intersecting in a prescribed way. It also investigates how these invariants behave under appropriate smoothings of either the ambient space or of the divisor and the Lagragian.
The proposed work lies at the intersection of string theory and symplectic topology. String theory developed as a potential candidate for unifying general relativity and particle physics. The details of this theory have turned out to be extraordinarily rich, and have inspired many remarkable results in mathematics. But results in mathematics have also guided and inspired many new discoveries in string theory and mirror symmetry. It is hoped that this project will contribute to the growing interaction between various fields of mathematics and other sciences. In particular, one of the themes running through this proposal is that symplectic topology can contribute insights into string theory.
