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Group Theory and Its Applications -- Introduction to beautiful modern mathematics

About the lecturer

I graduated from the Department of Mathematics of Nagoya University and Graduate School of Mathematical Sciences of the University of Tokyo. I have been an Assistant Professor at Tokyo Metropolitan University, an Associate Professor at Nagoya University and I became a Professor of Kavli IPMU in 2017. During these times, I visited University of Warwick (UK), University of Mannheim (Germany), Institute of Advanced Study (Princeton, US), Newton Institute (Cambridge, UK) and so on. I recieved the Special Takebe Prize from the Mathematical Society of Japan in 2001 for my reseach on crepant resolution and the McKay correspondence. I am also a member of the Science Council of Japan and also a Professor of the Ohara Ikebana school.

Syllabus

1 Subject Group Theory and Its Applications -- Introduction to beautiful modern mathematics
2 Field Algebra
3 Key words Group, Symmetry, Ring, Algebraic Geometry, Singularity, McKay correspondence
4 Unit 1
5 Lecturer Yukari Ito
6 Period June 14 - 18, 21 - 25, 2021
7 Time 5:00-6:30pm (Japan Standard Time)
8 Lecture style Online (live virtual class)
9 Evaluation Criteria Group, Symmetry, Ring, Algebraic Geometry, Singularity, McKay correspondence
10 Evaluation methods We will have small exercises during the lecture. Students will write a report after all the sessions. I will evaluate all of these and give the final assessment.
11 Prerequisites If you are interested in mathematics, in particular, algebra, you will no doubt enjoy this lecture. If you know something about basic algebra like group, polynomial ring, then it will be easy to understand this lecture. However, I will introduce every definition during the lectures and I will not be assuming any knowledge of algebra.
12 Contents Each session contains a lecture and an exercise. The contents of the lectures consist of Group Theory, Representation Theory of Finite Groups, Introductive Algebraic Geometry and Singualrties. I would like to introduce recent research related with group theory like McKay correspondence. I am planning to teach the following contents in this lecture:
1) Introdcution to Algebra
2) Definition of Group
3) Normal subgroup
4) Properties of groups
5) Application to the art in Japan
6) Representaion of finite groups
7) Characters 
8) Introductive Algebraic Geomtery
9) Singularity
10) McKay correspondence.
13 Required readings I will not use any textbooks during the lecture and I will introduce some books or papers which are related with the contents of my lecture for further studies.
14 Reference readings -
15 Notes on Taking the Course ※Students are asked to have their camera turned on during the lecture.
     

Contact

UTokyo Global Unit Courses
International Exchange Group, Education and Student Support Department,
The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8652 JAPAN

Please send all inquiries regarding the courses to the following email address:

utokyo-guc.adm(at)gs.mail.u-tokyo.ac.jp *Please change (at) to
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