Waseda Special Lectures 2025

Special Lecturer (series of lectures)

Jost-Hinrich Eschenburg (University of Augsburg, Germany)

Theme:  Exceptional Symmetric Spaces

Abstract:  See here.
(revised ver: Lecture 1, Lecture 2)

Slides: Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7, Seminar on Penrose Tiling.

This lecture course will contain the following subjects: 

(1) Basics for symmetric spaces

(2) Roots and curvature

(3) Symmetric subspaces and their congruence classes

(4) Classical symmetric spaces: Grassmannians and structure spaces

(5) Normed division algebras

(6) Spin groups and Spin representations

(7) Rosenfeld planes

(8) Polarity on Rosenfeld planes

(9) Structure spaces for Rosenfeld planes

Moreover, there is a lecture on Penrose tilings for students and even a broader auditory. 

Invited Lecturers

Hiroyuki Tasaki (Tokyo Metropolitan University & University of Tsukuba, Japan)

Title: Polars and antipodal sets

Abstract: In this lecture I explain the concepts of polars and antipodal sets in compact symmetric spaces introduced by Chen-Nagano. These are defined using symmetry only and fundamental concepts in the theory of symmetric spaces. I show all polars and antipodal sets in compact classical Lie groups. These polars are Grassmann manifolds and these antipodal sets induce all antipodal sets in Grassmann manifolds.  I also mention the cases of quotient groups of compact classical Lie groups and spin groups.

Masahiro Morimoto (Tokyo Metropolitan University, JSPS PD, Japan)

Title: The parallel transport map over affine symmetric space

Abstract: In the 1990s, C.-L. Terng and G. Thorbergsson investigated a natural Riemannian submersion from an infinite dimensional Hilbert space onto a compact Riemannian symmetric space G/K. This map is called the parallel transport map over G/K. Later, N. Koike extended their theory to the case that G/K is a Riemannian symmetric space of non-compact type. In this talk, I will explain my research on the extension of those theories in the framework of affine differential geometry. In particular, the parallel transport map over an affine symmetric space is defined and shown to be an affine submersion with horizontal distribution in the sense of Abe and Hasegawa. Its relation to weakly reflective submanifolds in symmetric spaces will also be discussed.

Related Research Activity (Short Communications)

Waseda Young Researchers Meeting on Geometry 2025

Organizers

Martin Guest (Waseda University, professor emeritus)

Katsuhiro Moriya (University of Hyogo)

Yoshihiro Ohnita (Waseda University & OCAMI)

Takashi Sakai (Tokyo Metropolitan University)

Yuichiro Sato (Waseda University)

Hiroshi Tamaru (OCAMI, Osaka Metropolitan University)

Makiko Sumi Tanaka (Tokyo University of Science)

Support

WIMS, Waseda University

OCAMI, Osaka Metropolitan University

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

Contact

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

Link

Waseda Special Lectures 2024

Image Credits: David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss. An aperiodic monotile