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Seminar on Geometric Complex Analysis
Seminar information archive ～05/20｜Next seminar｜Future seminars 05/21～
| Date, time & place | Monday 10:30 - 12:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
2026/06/08
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Yoshihiko Matsumoto (The Univ. of Osaka)
CR-invariant energy of Legendrian knots in the Heisenberg group (Japanese)
https://forms.gle/8ERsVDLuKHwbVzm57
Yoshihiko Matsumoto (The Univ. of Osaka)
CR-invariant energy of Legendrian knots in the Heisenberg group (Japanese)
[ Abstract ]
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 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 PU(2,1)-invariance, and how R-circles, a distinguished class of Legendrian (un)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).
[ Reference URL ]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 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 PU(2,1)-invariance, and how R-circles, a distinguished class of Legendrian (un)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).
https://forms.gle/8ERsVDLuKHwbVzm57
