Recent Progresses about Special Holonomy Manifolds

References/Resources
Several videos with many interesting lectures and seminars can be found online on the website

https://sites.duke.edu/scshgap/lectures-videos/

For those interested in reading about string backgrounds


 * 1) Lecture notes by Gauntlett - here the case of M-theory is discussed in some detail

2020-03-04: Some questions about special holonomy (Michele)
I will give a gentle introduction to certain topics of interest in the context of special holonomy manifolds both from the physics and from the math point of view.

2020-03-25: Boxcounting - Part 1 (Nicolò)
We will explore aspects of the DT/GW correspondence in the context of CY3.

Lecture notes

References:


 * 1) Worldsheet perspective: https://arxiv.org/pdf/hep-th/9309140.pdf, https://arxiv.org/pdf/hep-th/9307158.pdf,
 * 2) Target perspective: https://arxiv.org/pdf/hep-th/9809187.pdf, https://arxiv.org/pdf/math/0312059.pdf, https://arxiv.org/pdf/1404.2323.pdf
 * 3) Donaldson, Thomas 96
 * 4) Lecture notes by Okounkov and Thomas

2020-04-08: Boxcounting - Part 2 (Nicolò)
Conclusion of the discussion of the DT/GW correspondence in the context of CY3 - example of three-dimensional complex plane.

2020-05-06: A gentle introduction to G(2) special holonomy (Michele)
Introduction to aspects of G(2) special holonomy. Examples (Joyce Orbifolds, Twisted Connected Sums, and Bryant-Salamon G(2) cones).

Notes can be found at the following link

2020-05-13: G2-manifolds from Calabi-Yau 3-folds (Lorenzo Foscolo, UCL)
Abstract: I will discuss joint work with Mark Haskins and Johannes Nordström on the construction of families of 7-dimensional Ricci-flat manifolds with holonomy G2 close to a limiting Calabi-Yau 3-fold. These results provide a geometric counterpart to physical results about the duality between M-theory and Type IIA String theory. In the non-compact setting we are able to produce infinitely many new complete non-compact G2-manifolds (only a handful of examples was previously known). If time permits I will discuss work in progress on the construction of compact G2-manifolds from Calabi-Yau 3-folds with nodal singularities and explain how this construction can be extended to produce the first known compact G2-spaces with isolated conical singularities.

Exceptionally, this talk was recorded: please find the recording here

2020-06-17: Toric ideas for special geometries (Andrew Francis Swann, Aahrus University)
Abstract: The moment map is a powerful tool in symplectic geometry, with compact symplectic toric manifolds being described by their Delzant polytope. The talk will show how several properties of this picture can be carried over to special geometries via the concept of multi-moment map. The Spin(7) case gives master equations that specialise for smaller dimensional Ricci-flat geometries. Related ideas may be applied to nearly Kähler manifolds in dimension 6.

This is joint work with Thomas Bruun Madsen and Giovanni Russo

Slides of this talk are available here

2020?: Boxcounting - Part 3 (Nicolò)
Discussion of the DT partition function for CY4 (cancelled by the speaker)