research:main

# Differences

This shows you the differences between two versions of the page.

 research:main [2019/12/31 22:17]ustun research:main [2020/03/13 18:56] (current)ustun [Submitted] Both sides previous revision Previous revision 2020/03/13 18:56 ustun [Submitted] 2020/02/18 23:59 ustun 2020/02/06 16:48 ustun 2019/12/31 22:17 ustun 2019/12/10 16:51 ustun 2019/12/10 16:46 ustun 2019/12/10 16:44 ustun 2019/12/06 00:47 ustun 2019/12/06 00:39 ustun 2019/12/04 13:24 ustun 2019/12/04 13:23 ustun [Preprints] 2019/08/29 21:16 external edit Next revision Previous revision 2020/03/13 18:56 ustun [Submitted] 2020/02/18 23:59 ustun 2020/02/06 16:48 ustun 2019/12/31 22:17 ustun 2019/12/10 16:51 ustun 2019/12/10 16:46 ustun 2019/12/10 16:44 ustun 2019/12/06 00:47 ustun 2019/12/06 00:39 ustun 2019/12/04 13:24 ustun 2019/12/04 13:23 ustun [Preprints] 2019/08/29 21:16 external edit Line 1: Line 1: ===== Interests ===== ===== Interests ===== I am interested in $G_2$ and Spin(7) manifolds. I am interested in $G_2$ and Spin(7) manifolds. - More specifically, I am working on problems related to their calibrated submanifolds (which are volume minimizing submanifolds of dimension 3 in $G_2$ case or 4 in Spin(7) case) and interactions with other geometric structures (e.g. contact structures). + More specifically, I am working on problems related to complexification of $G_2$ and Spin(7) manifolds and interactions of these geometries with other geometric structures (e.g. contact and symplectic structures). - I am also interested in Seiberg-Witten theory, low dimensional topology and applications of algebraic geometry and algebraic topology to these problems. + I am also interested in Seiberg-Witten theory, low dimensional topology and applications of algebraic geometry and algebraic topology to problems in differential geometry. ===== Publications ===== ===== Publications ===== Line 11: Line 11: [[https://doi.org/10.1016/j.jalgebra.2019.11.035|1) On the Complex Cayley Grassmannian]], Journal of Algebra 547 (2020) 519-537 [[https://doi.org/10.1016/j.jalgebra.2019.11.035|1) On the Complex Cayley Grassmannian]], Journal of Algebra 547 (2020) 519-537 + + ==== Accepted ==== + + 3) (joint with E. Windes) Two-Frame Fields on Simply Connected Spin 7-Manifolds - Proceedings of the 12th ISAAC Congress, March 2020