COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Differential Geometry and Topology Seminar > Cubic fourfolds, K3 surfaces, and mirror symmetry

## Cubic fourfolds, K3 surfaces, and mirror symmetryAdd to your list(s) Download to your calendar using vCal - Nick Sheridan, Cambridge
- Wednesday 25 October 2017, 16:00-17:00
- MR13.
If you have a question about this talk, please contact Ivan Smith. While many cubic fourfolds are known to be rational, it is expected that the very general cubic fourfold is irrational (although none have been proven to be so). There is a conjecture for precisely which cubics are rational, which can be expressed in Hodge-theoretic terms (by work of Hassett) or in terms of derived categories (by work of Kuznetsov). The conjecture can be phrased as saying that one can associate a `noncommutative K3 surface’ to any cubic fourfold, and the rational ones are precisely those for which this noncommutative K3 is `geometric’, i.e., equivalent to an honest K3 surface. It turns out that the noncommutative K3 associated to a cubic fourfold has a conjectural symplectic mirror (due to Batyrev-Borisov). In contrast to the algebraic side of the story, the mirror is always `geometric’: i.e., it is always just an honest K3 surface equipped with an appropriate Kähler form. After explaining this background, I will state a theorem: homological mirror symmetry holds in this context (joint work with Ivan Smith). This talk is part of the Differential Geometry and Topology Seminar series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- Differential Geometry and Topology Seminar
- MR13
- School of Physical Sciences
- bld31
Note that ex-directory lists are not shown. |
## Other listsSummer Hebrew Ulpan Invitation The obesity epidemic: Discussing the global health crisis## Other talksSouthern Africa; Northern Cape On the climate change conversation The importance of seed testing Source-and-Sink Models for Molecular Conduction Fukushima and the law Well-posedness of weakly hyperbolic systems of PDEs in Gevrey regularity. |