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What use has a mathematician for symmetry?

What use has a mathematician for symmetry?. Mogens Flensted-Jensen SEST Friday 2 December 2011. The general opinion about mathematicians. The general opinion about students among mathematicians. Main Theorem:. Main Theorem:. Mathematics is Modelling.

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What use has a mathematician for symmetry?

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  1. What use has a mathematician for symmetry? Mogens Flensted-Jensen SEST Friday 2 December 2011

  2. The general opinion about mathematicians

  3. The general opinion about studentsamong mathematicians

  4. Main Theorem:

  5. Main Theorem:

  6. Mathematics is Modelling

  7. But: Simple calculations can lead to complicated numbers

  8. Mathematics is Teaching Teaching of mathematics to non-mathematicians:

  9. Mathematics is Research • Doing mathematical research is a kind of art: • You must understand (to a certain extend) the known mathematical world (theory) • You must see some “interesting” unexplored region • You must begin to explore such a region • You design or discover the right “map” of the region (i.e. formulate a hypothesis) – This is the “art” part • You must prove it rigorously – This is where you need craftsmanship and ingenuity

  10. In mathematics we talk about “beauty” when the “art” of designing the “map” gives a result, which is • Build on easy accessible concepts • Easy to conceive and understand the structure and the content • Has not been understood before • Is difficult to prove rigorously

  11. Symmetric Spaces

  12. Mercer Oak, near Institute for Advanced Study

  13. My topic: Harmonic Analysis The classical theory • On R: • Fourier Integrals (xexp(λx)) • On T=R/Z: • Fourier Series (t exp(2πnt)) • On Rand T: • Fourier Inversion Formula • Plancherel Formula • On R: • Paley-Wiener Theorem

  14. Modern Highlight 1: Harish-ChandraPlancherel Formula for G • Discrete series • Asymptotic expansions • Spherical functions Key Paper:

  15. Modern Highlight 2: HelgasonGeometric Analysis on G/K • Spherical functions and Paley-Wiener theorems • Poisson transform: Helgason conjecture Key paper:

  16. Symmetric Spacesinmathematical terms U/K G/K A Symmetric Space is an affine manifold for which the geodesic reflection in any point is an affine isomorphism G/H

  17. My simple idea for the construction of the discrete spectrum for G/H (1980):

  18. Mittag-Leffler Institute,Djursholm, Stockholm, Sweden 1970-71 and 1995

  19. Plancherel Formula for G/H MLI November 1995 Henrik Schlichtkrull And Erik van den Ban Paley-Wiener Theorem for G/H MLI November 1995 Patrick Delorme

  20. I did not talk much about symmetry and mathematics Anyway Thank You for your patience. Mogens

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