ColMar Interactions 2022
The seminar "Interactions" joins the teams of two universities: that of Cologne, and that of Marburg, therefore the name "ColMar Interactions". The goal is to explain some very recent developments in the field of equivariant topology and equivariant symplectic geometry. The organisers are:
- Oliver Goertsches (goertsch@mathematik.uni-marburg.de)
- Panagiotis Konstantis (pako@mathematik.uni-marburg.de)
- Silvia Sabatini (sabatini@math.uni-koeln.de)
This is an online seminar. If you would like to participate, please write an email to pako@mathematik.uni-marburg.de to receive the login data.
Schedule
02.06.2022, 14:30-16:00 (GMT +2), Hiroaki Ishida (Kagoshima University),
"Double sided torus actions and complex geometry on SU(3)"
Abstract: In this talk we construct complex structures on SU(3) which is not left invariant but invariant under the double sided torus action. We also construct invariant Kähler orbifold structures on quotients of SU(3) by subtori of the double sided torus. This talk is based on the joint work with Hisashi Kasuya, arXiv:2110.08533.
09.06.2022, 14:30-16:00 (GMT +2), Grigory Solomadin (HSE University),
"On independent GKM-graphs without nontrivial extensions"
Abstract: A GKM-manifold M with the T-torus action is called an action in j-general position if for any fixed point x\in M of the T-action any j weights of the tangent representation at x are linearly independent. Apart from j=2 required by the definition of a GKM-manifold, this property has nice implications for the topology of the corresponding orbit space M/T (Ayzenberg, Masuda '19) and for the related objects like face poset (Ayzenberg, Masuda, S. '22). An extension problem (e.g. see Kuroki '19) seeks for a maximal (with respect to an extension of the T-action) GKM-action of a torus T' on M with an equivariant (proper) embedding T \to T' in order to reduce the complexity 1/2 \dim M-\rank T of the action. It seems to be a challenging task to find a GKM-manifold M^{2n} that is both j-independent and non-extendible for every n>=j>=2, for instance, in the class of homogeneous GKM-manifolds studied by Guillemin, Holm and Zara '06. In the talk I will describe a purely combinatorial example of a k-independent (n,k)-type (i.e. n-regular graph and k is the rank of the axial function) GKM-graph without nontrivial extensions that cannot be realized by a GKM-manifold for any n=k=3 or n>= k>= 4, and tell about the methods involved. The talk is based on arXiv:2205.07197.