Asymptotic Analysis

Where: Skoltech #422
When: Tuesday, 12:30 - 15:30
Who: Konstantin Tikhonov
Contact:

Homework assignments and research papers for final presentations are available at Course Page.
Elementary introduction to some of the topics of this course can be found online at Complex Analysis with Physical Applications.

Syllabus


Part 1: Asymptotic series

5 September 2017

Lecture 1: Asymptotic series: introduction and motivation.

12 September 2017

Lecture 2: Borel summation.

19 September 2017

Lecture 3: Asymptotic evaluation of integrals.

26 September 2017

Lecture 4: Hyperasymptotics and resurgence.


Part 2: Examples from Quantum Mechanics and theory of Ordinary Differential Equations

3 October 2017

Lecture 5: WKB approximation, turning points and Stokes geometry for linear ODEs.

10 October 2017

Lecture 6: Phase integral methods in non-stationary, scattering and eigenvalue problems.

17 October 2017

Lecture 7: Anharmonic Oscillator.

24 October 2017

Lecture 8: Nonlinear connection problems.


Part 3: Examples from Quantum Field Theory

31 October 2017

Lecture 9: Effective action and derivative expansion.

7 November 2017

Lecture 10: Analytic continuation of path integrals.

14 November 2017

Lecture 11: Path integrals with multiple zero modes.

21 November 2017

Lecture 12: Complex saddle points in path integrals.


Part 4: Exam and Presentation of the Projects

28 November 2017

Exam and Presentation of the Projects.