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Wall-crossing in Gromov-Witten theory

Algebraic Geometry and Number Theory

Speaker: Emily Clader, San Francisco State University
Related Webpage: https://sites.google.com/site/emilyclader/
Location: 1147 MSB
Start time: Tue, Oct 30 2018, 2:30PM

Gromov-Witten theory is a technique for counting curves in a variety, and while it admits beautiful structure, it is notoriously difficult to compute. Ciocan-Fontanine and Kim recently introduced a generalization of Gromov-Witten theory, the theory of "quasi-maps," which depends on an additional stability parameter varying over positive rational numbers. When that parameter tends to infinity, Gromov-Witten theory is recovered, while when it tends to zero, the resulting theory encodes information related to the "B-model." Ciocan-Fontanine and Kim proved a wall-crossing formula exhibiting how the theory changes with the stability parameter, and in this talk, we discuss an alternative proof of their result as well as a generalization to other gauged linear sigma models. This is joint work with Felix Janda and Yongbin Ruan.