ICTP Joint Math & Physics Seminar - Wednesday, 19 March, at 13:30 - VENUE: Room A - Galileo Guest House

[ICTP Math Section]

_*ICTP Joint Math & Physics Seminar*_

Wednesday 19 March, at 13:30

VENUE: *Room A, Galileo Guest House
*


Speaker: Daniel Baldwin (ICTP)


Title: Kummer-type HyperKähler Orbifolds and Joyce-Karigiannis G2-Manifolds


Abstract: The talk will be split in two parts, discussing two projects 
broadly related to constructing and classifying special holonomy 
orbifolds and manifolds.

Firstly, motivated by finding a new compact hyperKähler manifold, we 
study hyperKähler orbifolds of Kummer-type (i.e. orbifolds obtained as 
quotients of tori) associated to the maximal torus of E8 and classify 
such spaces. We then study their singular sets in an attempt to find an 
example which can be desingularised to a smooth hyperKähler manifold. 
The methods developed pave the way for a larger project to classify all 
special holonomy Kummer orbifolds.

Secondly, we study 7-manifolds of holonomy SU(2) \rtimes F and partially 
classify them. Orbifold limits of such spaces have singular sets of the 
type considered by Joyce and Karigiannis who showed that (1707.09325), 
under certain conditions, such singular spaces can be desingularised to 
smooth, compact, G2-manifolds. We obtain a complete understanding of the 
physics of these spaces in the context of M-theory, although this will 
not feature much in the talk. As a bonus we discover an unexpected 
isomorphism between two seemingly unrelated moduli spaces: the space of 
Ricci flat metrics on these 7-manifolds and the space of flat 
connections on compact, flat 3-manifolds.

Relevant papers: 2501.03692, 2309.12869, 2312.12311

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