Recent Advances in Geometric Structures¶
Overview¶
The conference Recent Advances in Geometric Structures will be held at Hokkaido University on July 6, 2026, from 10:00 to 17:00.
This conference is organized in conjunction with the visit of Professor Graham Smith as a JSPS Invitational Fellow.
Registration¶
Registration Form
Registration is open until July 3, 2026.
Place and how to get there¶
Hokkaido University, School of Science Building 4, Room 501
Fourth floor
Speakers¶
- Graham Smith
- Kentaro Ito
- Yoshihiko Matsumoto
- Shinpei Baba
Schedule¶
July 6, 2026, Monday¶
| Time | Speaker | Title |
|---|---|---|
| 10:00--11:00 | Kentaro Ito | Complex earthquakes and pieces of hyperbolic planes in \(\mathrm{SL}(2,\mathbb{C})\) |
| 11:30--12:30 | Shinpei Baba | Complex projective structures on Riemann surfaces and the intersections of their holonomy varieties |
| 14:30--15:30 | Graham Smith | TBA |
| 16:00--17:00 | Yoshihiko Matsumoto | CR-invariant energy of Legendrian knots in the Heisenberg group |
Abstracts¶
Kentaro Ito¶
Complex earthquakes and pieces of hyperbolic planes in \(\mathrm{SL}(2,\mathbb{C})\)
It is known that earthquake deformations of Fuchsian groups are induced by pleated hyperbolic planes in \(\mathrm{SL}(2,\mathbb{R})\), the anti-de Sitter space. We are interested in an extension of this theory to deformations of quasi-Fuchsian groups induced by surfaces in \(\mathrm{SL}(2,\mathbb{C})\). At the very beginning of this study, in this talk, we consider pieces of hyperbolic planes in \(\mathrm{SL}(2,\mathbb{C})\) inducing complex earthquake deformations of Fuchsian groups.
Shinpei Baba¶
Complex projective structures on Riemann surfaces and the intersections of their holonomy varieties
A complex projective structure on a Riemann surface has a holonomy representation from its fundamental group in \(\mathrm{PSL}(2,\mathbb{C})\). Given different diffeomorphic marked Riemann surfaces, we discuss projective structures on those surfaces that share the same holonomy.
Graham Smith¶
TBA
Yoshihiko Matsumoto¶
CR-invariant energy of Legendrian knots in the Heisenberg group
We introduce an energy functional for Legendrian knots in the 3-dimensional Heisenberg group, which carries a natural contact structure. This is an analogue of the energy for ordinary knots in Euclidean 3-space due to O'Hara (1991). Whereas O'Hara's energy, more precisely the one of exponent \(-2\), is invariant under Möbius transformations, our energy for Legendrian knots is invariant under the action of \(\mathrm{PU}(2,1)\), the group of CR automorphisms of the one-point compactification of the Heisenberg group.
I would like to explain carefully how the energy should be defined so as to achieve the \(\mathrm{PU}(2,1)\)-invariance, and how R-circles, a distinguished class of Legendrian unknots and knots, arise as energy minimizers. Time permitting, I will also discuss some open problems. This talk is based on joint work with Jun O'Hara, Chiba University.
Organizers¶
Shimpei Kobayashi and Jun-ichi Inoguchi
Hokkaido University