The mathematics of G_2 conifolds for M-theory


Karigiannis, S. (2013). The mathematics of G_2 conifolds for M-theory. Perimeter Institute. https://pirsa.org/13100126


Karigiannis, Spiro. The mathematics of G_2 conifolds for M-theory. Perimeter Institute, Oct. 25, 2013, https://pirsa.org/13100126


          @misc{ pirsa_PIRSA:13100126,
            doi = {10.48660/13100126},
            url = {https://pirsa.org/13100126},
            author = {Karigiannis, Spiro},
            keywords = {},
            language = {en},
            title = {The mathematics of G_2 conifolds for M-theory},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {oct},
            note = {PIRSA:13100126 see, \url{https://pirsa.org}}

Spiro Karigiannis University of Waterloo


G_2 manifolds play the analogous role in M-theory that Calabi-Yau manifolds play in string theory. There has been work in the physics community on conjectural "mirror symmetry" in this context, and it has also been observed that singularities are necessary for a satisfactory theory. After a very brief review of these physical developments (by a mathematician who doesn't necessarily understand the physics), I will give a mathematical introduction to G_2 conifolds. I will then proceed to give a detailed survey of recent mathematical developments on G_2 conifolds, including desingularization, deformation theory, and possible constructions of G_2 conifolds. This includes separate joint works of myself with Jason Lotay and with Dominic Joyce.