Seminars & Colloquia Calendar

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Special Colloquium

Invariants of Calabi-Yau manifolds

Aleksander Doan - Columbia University

Location:  Zoom
Date & time: Monday, 22 November 2021 at 11:30AM - 12:30PM

Abstract: One of the central problems of geometry is to classify manifolds which admit special geometric structures. Calabi-Yau manifolds provide a particularly interesting class of examples. Since their discovery forty years ago they have stimulated extraordinary research activity, leading to new, beautiful mathematics and surprising connections with physics. A distinctive feature of Calabi-Yau manifolds is that they lie at the intersection of three branches of geometry: algebraic, differential, and symplectic. As a result, there is an abundance of examples of these manifolds as well as tools we use to understand them. The talk will focus on invariants of Calabi-Yau manifolds, which are defined by counting holomorphic curves. In particular, I will discuss a recent proof, joint with E. Ionel and T. Walpuski, of the Gopakumar-Vafa finiteness conjecture, which concerns the algebraic structure of these invariants. I will then outline a proposal for defining a new invariant, which counts holomorphic curves together with solutions to partial differential equations originating from gauge theory; the technical challenges of this proposal will lead us to explore uncharted territories in geometry and analysis. 

This talk is for the local Rutgers Math Community only, Zoom links will be sent by the Department Chair via email.

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