Waseda Special Lectures

Special Lecturers (series of lectures)

Fran Burstall (5 lectures, University of Bath, UK)

Title: Topics in Integrable Geometry

Abstract: See here.

Lynn Heller (2 lectures, BIMSA, China)

Title: Integrable surface theory (Part 1)

Abstract: See here.

Sebastian Heller (2 lectures, BIMSA, China)

Title:  Integrable surface theory (Part 2)

Abstract: See here.

Invited Lecturers

Shoichi Fujimori (Hiroshima University, Japan)

Title: Deformations of minimal surfaces and their limits

Abstract: In this lecture, we consider various families of periodic minimal surfaces in Euclidean 3-space.  We study deformations and limits of families embedded minimal surfaces and show several results. We exhibit various graphics of examples as well.

Kosuke Naokawa (Hiroshima Institute of Technology, Japan)

Title: Singularities of developable surfaces and their discretizations 

Abstract: Cuspidal edges and swallowtails are typical singularities appearing on developable surfaces, which are ruled surfaces with zero Gaussian curvature in Euclidean 3-space. In this talk, we introduce properties of singularities of developable surfaces in smooth case and give formulations and criteria for discrete versions of such cuspidal edges and swallowtials. 

Reiko Miyaoka (Tohoku University, Japan)

Title: Dupin hypersurfaces related to Chern’s conjecture

Abstract: S.S.Chern asks if a closed minimal hypersurface in the sphere is isoparametric if it has constant scalar curvature. Here we show an affirmative answer for a closed Dupin hypersurface M with CMC weaker than minimality:

1. When g=3, M is isoparametric .

2. When g=4, M is isoparametric if M has constant scalar curvature.

3. When g=6, M is isoparametric if M has constant Lie curvatures. 

Here, the Lie curvature is the cross ratio of four principal curvatures, a Lie invariant discovered by the speaker (1989).

Yoshihiro Ohnita (Waseda University & OCAMI, Japan)

Title: Introduction to Harmonic Map Theory related to Integrable System Methods

Abstract: I will give an introductory survey on harmonic map theory of Riemann surfaces into Lie groups and symmetric spaces via related integrable system methods, such as  loop groups/infinite dimensional Grassmannian models and Higgs bundle moduli spaces.

Wayne Rossman (Kobe University, Japan)

Title: Transforming Discrete Constant Gaussian Curvature Surfaces

Abstract: I will talk about recent work with Thomas Raujouan and Naoya Suda on utilizing explicit parametrizations of discrete constant Gaussian curvature (CGC) surfaces of revolution in Euclidean 3-space for making explicit Bäcklund transformations to discrete CGC surfaces that are not rotational, thereby creating new examples. Time allowing, I will also comment on recent work with Joseph Cho, Thomas Raujouan and Masaya Hara on transforming surfaces with Weierstrass representations in various space forms. 

Related Research Activity

Waseda Young Researchers Meeting on Geometry 2024 

organized by Yuichiro Sato, September 18-19, 2024

Organizers

Katsuhiro Moriya (University of Hyogo)

Yoshihiro Ohnita (chair, Waseda University & OCAMI)

Wayne Rossman (Kobe University)

Yuichiro Sato (Waseda University)

Masashi Yasumoto (Tokushima University)

Support

- JSPS Grant-in-Aid for Scientific Research (C) No.22K03293 (Principal Investigator: Katsuhiro Moriya)

- JSPS Grant-in-Aid for Scientific Research (A) No.23H00083 (Principal Investigator: Martin Guest)

- JSPS Grant-in-Aid for Scientific Research (A) No.22H00094(Principal Investigator: Masa-hiko Saito)

- Waseda Institute for Mathematical Science (WIMS) 

- Osaka Central Advanced Mathematical Institute (OCAMI), Osaka Metropolitan University  

Contact

Yoshihiro Ohnita (Waseda U. & OCAMI) ohnita @omu.ac.jp