Asymptotic Analysis
Where: Skoltech #422
When: Tuesday, 12:30 - 15:30
Who: Konstantin Tikhonov
Contact: tikhonov at itp dot ac dot ru
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.