Lecturer

Kotaro Kawai (河井公大朗, Associate Professor, BIMSA)
Date

2026-02-25 ~ 2026-05-13
Schedule
Weekday    Time    Venue    Online    ID    Password
Wed    15:20-18:40    A3-4-312    Zoom    435 529 7909    BIMSA

Prerequisite

vector bundles and their connections, basics of Riemannian manifolds
Introduction

In this course, we give a detailed introduction to the theory of principal bundles. After defining principal bundles, we introduce connections and holonomy groups on them, and compare these notions with the corresponding theory of vector bundles. We then present the classification of holonomy groups of Riemannian manifolds and discuss the geometric structures appearing in the classification. If time permits, we will also cover the theory of characteristic classes via Chern-Weil theory.
Reference

D. D. Joyce, Riemannian holonomy groups and calibrated geometry. Oxford Graduate Texts in Mathematics, 12. Oxford University Press, Oxford, 2007. x+303 pp. ISBN: 978-0-19-921559-1
H. Konno, [Differential geometry] Bibun kikagaku (in Japanese), University of Tokyo Press, 2013.
Video Public

Yes
Notes Public

Yes
Audience

Advanced Undergraduate, Graduate
Language

English
Lecturer Intro

Kotaro Kawai got a bachelor's degree and a master's degree from the university of Tokyo, and received his Ph.D from Tohoku university in 2013. He was an assistant professor at Gakushuin university in Japan, then he moved to BIMSA in 2022. His research interests are in differential geometry, focusing on manifolds with exceptional holonomy.
TA

Anton Iliashenko (null)
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FROM 202.120.11.*