Math 272

Instructor Prof. Rich Schwartz
When/Where Kassar 205, Tu-Th 1-2:20
summary This is a graduate topics class on piecewise isometries. List of Topics:

• general dissection: The Banach-Tarski Paradox.
  notes on the B.T. Theorem
• polyhedral dissection: The case of polygons, Pick's Theorem, The Dehn-Sydler Theorem
  notes on Dehn's theorem
  notes on Dehn-Sydler Theorem
  
• Quasi-Crystals: Penrose tiling, pentagrids, cut and project method
  De Bruijn's papers
• Sturmian Sequences: Continued Fractions, Renormalization
  Notes on Continued Fractions
  Smillie/Ulcigrai paper
  
• Outer billiards: General Properties, the regular pentagon, kites, rational polygons
  Tabachnikov's paper
  My paper on the pinwheel lemma
  preprint arXiv version of my book
  
• Rational Billiards: Hyperbolic geometry, translation surfaces,Veech examples
  See chapters 16 and 17 in my other book.