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Colloquium
Seminar information archive ～05/25｜Next seminar｜Future seminars 05/26～
| Organizer(s) | AIDA Shigeki, OSHIMA Yoshiki, SHIHO Atsushi (chair), TAKADA Ryo |
|---|---|
| URL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium_e/index_e.html |
2025/06/20
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
Yuichi Ike (Graduate School of Mathematical Sciences, The University of Tokyo)
The square peg problem and microlocal sheaf theory (JAPANESE)
Yuichi Ike (Graduate School of Mathematical Sciences, The University of Tokyo)
The square peg problem and microlocal sheaf theory (JAPANESE)
[ Abstract ]
The square peg problem asks whether every Jordan curve in the plane admits four distinct points that form the vertices of a square. This problem was proposed by Toeplitz in 1911, but it is still open. This problem can be generalized to the rectangular peg problem, which asks about the existence of a rectangle with a given aspect ratio. Greene and Lobb gave an affirmative answer to the rectangular peg problem for any smooth Jordan curve using symplectic geometry, and later improved the result using spectral invariants in Floer theory. In this talk, I will explain that we can solve the rectangular peg problem for any rectifiable Jordan curve using microlocal sheaf theory. This is joint work with Tomohiro Asano.
The square peg problem asks whether every Jordan curve in the plane admits four distinct points that form the vertices of a square. This problem was proposed by Toeplitz in 1911, but it is still open. This problem can be generalized to the rectangular peg problem, which asks about the existence of a rectangle with a given aspect ratio. Greene and Lobb gave an affirmative answer to the rectangular peg problem for any smooth Jordan curve using symplectic geometry, and later improved the result using spectral invariants in Floer theory. In this talk, I will explain that we can solve the rectangular peg problem for any rectifiable Jordan curve using microlocal sheaf theory. This is joint work with Tomohiro Asano.
