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

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.

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.

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