Algebra and Dynamics

Math 275 - Tu Th 10:00-11:30 pm - 209 Science Ctr
Harvard University - Spring 2003

Advanced topics in dynamical systems with algebraic features, such as:
maps on projective space and algebraic surfaces, Coxeter groups, flows on homogeneous spaces and polygonal billiards.
Instructor: Curtis T McMullen

  • J. E. Fornaess, Dynamics in Several Complex Variables, AMS - CBMS Lectures, 1996.
  • Morosawa, Nishimura, Taniguchi and Ueda, Holomorphic Dynamics, Cambridge University Press, 2002
  • Barth, Peters and van de Ven, Compact Complex Surfaces, Springer-Verlag, 1984
  • G. van der Geer, Hilbert modular surfaces, Springer-Verlag, 1987
  • J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge University Press, 1990
  • S. Tabachnikov, Billiards , Soc. Math. France, 1995
  • M. B. Bekka and M. Mayer, Ergodic theory and topological dynamics of group actions on homogeneous spaces, Cambridge University Press, 2000
Other useful references
  • Doyle, Elkies, Gross, McMullen: Various papers
  • Ghys, Dynamique des flots unipotents sur les espaces homogènes, Sem. Bourbaki 1991/92; Asterisque 206
  • Hubbard and Papadopol, Superattractive fixed-points in Cn , Indiana Univ. Math. J. 43 (1994), 321-365.
  • Briend and Duval, Deux caractérisations de la mesure d'équilibre d'un endomorphisme de Pk(C) , Publ. Math. IHES 93 (2001), 145-159.
  • Masur and Tabachnikov, Rational billiards and flat structures
Prerequisites. Intended for advanced graduate students.

Topics may include:
  • Rational maps with icosahedral symmetry
  • Solving quintic polynomials
  • Currents and cohomology
  • Dynamics of endomorphisms of Pn
  • Dynamics on K3 surfaces
  • Unimodular lattices
  • Coxeter groups
  • Salem numbers
  • Unipotent flows on homogeneous spaces
  • Ratner's theorem
  • Gaps in Sqrt[n] mod 1
  • Moduli of Riemann surfaces
  • Teichmüller geodesic flow
  • Billiards
  • Hilbert modular surfaces
  • Teichmüller curves
  • Thu, 30 Jan. First class
  • M-F, 22-30 Mar. Spring recess.
  • Thu, 1 May. Last class

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