2019 Special courses on advanced topics in Mathematics J

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Academic unit or major
Mathematics
Instructor(s)
Hattori Kota 
Course component(s)
Lecture
Day/Period(Room No.)
Intensive ()  
Group
-
Course number
ZUA.E344
Credits
2
Academic year
2019
Offered quarter
4Q
Syllabus updated
2019/3/18
Lecture notes updated
-
Language used
English
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Course description and aims

The main subject of the course is the geometry of Riemannian manifolds with special holonomy groups. We introduce the notion of holonomy groups on Riemannian manifolds then explain the examples of special holonomy such as Calabi-Yau, Hyper-Kähler, G2 or Spin(7) manifolds. The aim of this course is to understand the fundamental properties of these manifolds.

Student learning outcomes

Be familiar with Riemannian metrics and curvatures.
Be familiar with complex structures."

Keywords

Kähler manifolds, Calabi-Yau manifolds, Hyper-Kähler manifolds, G2 manifolds, Spin(7) manifolds

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
- - - -

Class flow

This is a standard lecture course. There will be some assignments.

Course schedule/Required learning

  Course schedule Required learning
Class 1 The following topics will be covered. - Riemannian manifolds and Levi-Civita connections - Holonomy groups - Curvatures - Complex manifolds - Calabi-Yau manifolds and Hyper-Kählermanifolds - Exceptional Holonomy groups" Details will be provided during each class session.

Textbook(s)

None required.

Reference books, course materials, etc.

None required.

Assessment criteria and methods

Assignments (100%).

Related courses

  • MTH.B301 : Geometry I
  • MTH.B302 : Geometry II
  • MTH.B331 : Geometry III
  • MTH.B341 : Topology

Prerequisites (i.e., required knowledge, skills, courses, etc.)

To have basic knowledge in the theory of differentiable manifolds.

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