2019 Lecture on Advanced Science in English (Mathematics 5)

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Academic unit or major
Pajitnov Andrei 
Course component(s)
Day/Period(Room No.)
Intensive ()  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
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Course description and aims

In the early 1920s M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology.
Circle-valued Morse theory originated from a problem in hydrodynamics studied by S. P. Novikov in the 1980s. Nowadays, it is a constantly growing field of contemporary mathematics with applications and connections to many domains of geometry and topology.
The aim of this course is to give a systematic treatment of geometric foundations of the subject and recent research results.

Student learning outcomes

Students will be able to understand basics of Morse theory and circle-valued Morse theory.


Morse theory, circle-valued Morse theory

Competencies that will be developed

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

Class flow

Standard lecture course

Course schedule/Required learning

  Course schedule Required learning
Class 1 This course covers the fundamentals of Morse theory and circle-valued Morse theory and several topics such as: - Homology with local coefficients for the Morse-Novokov theory; - The Morse-Novikov theory for closed 1-forms; - Circle-valued Morse theory for knots and links, etc. Details will be provided in class.


None required

Reference books, course materials, etc.

A. V. Pajitnov, Circle-valued Morse Theory, Walter de Gruyter.

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.)

Students require the knowledge of manifolds and homology.



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