23.03.2018

Blog

Current events

Inverse days (12-14 December, Oulu)

Finnish mathematical days (4-5 January 2018, Joensuu)

Reading group fall 2017

The reading group will discuss microlocal analysis and its applications. References for the basic theory (roughly in ascending order of difficulty):

  • J. Wunsch: Microlocal analysis and evolution equations
  • M. Wong: An introduction to pseudo-differential operators
  • X. Saint-Raymond: Elementary introduction to the theory of pseudodifferential operators
  • N. Lerner: A first course on pseudo-differential operators
  • G. Eskin: Lectures on linear partial differential equations
  • A. Grigis, J. Sjöstrand: Microlocal analysis for differential operators - an introduction
  • M. Shubin: Pseudodifferential operators and spectral theory
  • M. Taylor: Partial differential equations, vol. II
  • L. Hörmander: The analysis of linear partial differential operators, vol. III

References for the applications:

(Please note that the notes below are not in final form and may be somewhat rough.)

26.09. Introduction to microlocal analysis (Mikko Salo)

10.10. Pseudodifferential symbols (Jesse Railo)

24.10. Pseudodifferential operators (Jere Lehtonen)

31.10. Elliptic pseudodifferential operators (Valter Pohjola)

07.11. The Dirichlet-to-Neumann map as a pseudodifferential operator (Tony Liimatainen)

14.11. The normal operator of the geodesic X-ray transform (Joonas Ilmavirta): paper and rough notes

21.11. L^2 boundedness of pseudodifferential operators (Giovanni Covi)

Reading group 2016-2017

(Please note that the notes below are not in final form and may be somewhat rough.)

10.10. Geodesic flows, notes 1: symplectic geometry

17.10. Geodesic flows, notes 2: geodesic flow as Hamilton flow

31.10. Geodesic flows, notes 3: symplectic and volume-preserving maps

07.11. Geodesic flows, notes 4: the Sasaki metric

14.11. Geodesic flows, notes 5: symplectic isoperimetric inequalities

21.11. Geodesic flows, notes 6: the Sasaki metric in local coordinates

06.02. Geodesic flows, notes 7: recap

13.02. Geodesic flows, notes 8: derivatives on the unit sphere bundle

20.02. Geodesic flows, notes 9: commutator formulas

06.03. Fractional Calderón problem, notes 1: motivation (slides from a colloquium talk)

14.03. Fractional Calderón problem, notes 2: introduction (slides from a seminar talk)

03.04. Fractional Calderón problem, notes 3: Sobolev spaces and fractional Laplacian (section 2 of the paper in the link)

10.04. Fractional Calderón problem, notes 4: Sobolev spaces and fractional Laplacian (section 2 of the paper in the link)

18.04. Fractional Calderón problem, notes 5: well-posedness for fractional Laplacian (section 2 of the paper in the link)

02.05. Fractional Calderón problem, notes 6: the DN map for fractional Laplacian (section 2 of the paper in the link)