- Start Date
- End Date
- Meeting Type
- Summer School
- Contact Name
Chiu-Chu Melissa Liu - Columbia University
Course title: Gromov-Witten invariants, Fan-Jarvis-Ruan-Witten invariants, and Mixed-Spin-P fields
Cristina Manolache - Imperial College London
Course title: Boundary contributions to enumerative invariants
General description and aims of the school:
Gromov-Witten invariants, which "count" curves (with appropriate extra conditions) on smooth projective varieties, were introduced more than two decades ago; motivated by high energy physics, they ended up revolutionising enumerative algebraic geometry and provided a bridge to other branches of mathematics, such as integrable systems of differential equations.
Since then, their scope has been expanded in different directions (e.g. relaxing the smoothness conditions, replacing the variety by a stack, allowing torus actions), and techniques have been introduced for their computation; moreover, a plethora of other invariants using the same basic ideas has been introduced, leading to fruitful investigations on the relationships among them.
The aim of this school is to bring doctoral students, postdocs, and anyone interested from a review of the basic construction to current, state-of-the art research in this field, with a special focus on invariants for Calabi-Yau threefolds, the richest example both in algebraic geometry and in physics. Many important questions about these varieties are still unanswered, such as giving a mathematically rigorous definition of the Gopakumar-Vafa invariants (at the moment only available in the language of theoretical physics).
Valentina Beorchia, Trieste Ada Boralevi, Sissa Trieste Barbara Fantechi, Sissa Trieste
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