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Three quick recipes with fully extended oriented 2d TQFTs

Domenico Fiorenza

Abstract

It always happens: you have a talk for dinner and nothing prepared. Your signature dish never fails, but you have served it too many times already and you'd like to surprise your guests with something new. Try these quick, light and colourful reinterpretations of haute cuisine classics, like (nonabelian) Fourier transforms and the Plancherel theorem for finite groups.

Three quick recipes with fully extended oriented 2d TQFTs

Abstract

It always happens: you have a talk for dinner and nothing prepared. Your signature dish never fails, but you have served it too many times already and you'd like to surprise your guests with something new. Try these quick, light and colourful reinterpretations of haute cuisine classics, like (nonabelian) Fourier transforms and the Plancherel theorem for finite groups.

Paper Structure

This paper contains 11 sections, 60 equations.

Table of Contents

  1. The ingredients
  2. Basic preparations
  3. Amuse-bouche: the isomorphism between the centres
  4. Hors d'oeuvre: nonabelian Fourier transforms
  5. Raw ingredients
  6. Nonabelian is too spicy? here's the abelian recipe
  7. Getting high with higher Fourier transforms
  8. The main course: the Plancherel theorem
  9. The inverse Fourier transform
  10. Sweet ending: the 1d Ising model
  11. Acknowledgments and further readings