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Mon, 13 Mar 2023
14:15
14:15
L4
Categorical and K-theoretic Donaldson-Thomas theory of $\mathbb{C}^3$
Tudor Pădurariu
(Columbia University)
Abstract
Donaldson-Thomas theory associates integers (which are virtual counts of sheaves) to a Calabi-Yau threefold X. The simplest example is that of $\mathbb{C}^3$, when the Donaldson-Thomas (DT) invariant of sheaves of zero dimensional support and length d is $p(d)$, the number of plane partitions of $d$. The DT invariants have several refinements, for example a cohomological one, where instead of a DT invariant, one studies a graded vector space with Euler characteristic equal to the DT invariant. I will talk about two other refinements (categorical and K-theoretic) of DT invariants, focusing on the explicit case of $\mathbb{C}^3$. In particular, we show that the K-theoretic DT invariant for $d$ points on $\mathbb{C}^3$ also equals $p(d)$. This is joint work with Yukinobu Toda.
The second series of our short films, ‘Me and My Maths’, is now running on our social media with even higher viewing figures than the first series. You can watch a compilation of the first four films via the video below.
Starring: Kylie and Chloe, Andrea, Doyne, and Kate Wenqi.
Me and My Maths. Short films about people who also do maths.