Undergraduate courses

  • A first course in number theory (used for Math 319)
  • A first course in mathematics (used for Math 327)

    Graduate courses

  • Algebra I and II (Math 520 and 521)
  • Topics in number theory I: algebraic number theory (Math 519)
  • Topics in number theory II: modular forms (Math 519)
  • Topics in number theory III: p-adic interpolation (Math 519)
  • Topics in number theory IV: Analogies between numbers and functions (Math 519)
  • Algebraic curves I
  • Algebraic curves II
  • Algebraic geometry (Math 531)

    Talks, mini-courses

  • Differential calculus with integers (IHES 2011)
  • Correspondences, Fermat quotients, uniformization (Bonn, 2010)
  • Galois groups arising from arithmetic differential equations (Luminy, 2010)
  • Lectures on arithmetic differential equations (Leiden, 2009)
  • Differential algebra and diophantine geometry (Princeton, 1993)

    Short notes

  • Group actions
  • G(2,4), etc
  • SL(2,F)
  • Complex multiplication
  • Introduction to a course on zetas
  • Dwork's approach to congruence zeta
  • Schemes, moduli schemes
  • The totally ramified direction
  • Fractal dimension
  • Areas and volumes
  • Projective non-free modules
  • Introduction to "elliptic curves" or "modular forms"
  • Explicit computation of H^1(elliptic curve,O)
  • Turing, Godel, Matjiasevich
  • Some number theory exercises
  • Some algebra exercises
  • Langlangs philosophy
  • History of Galois theory
  • Some basic Galois groups
  • S_p as Galois group
  • Finite generation of invariants
  • History of p-adic analysis
  • Jordan normal form, etc
  • Artin-Hasse exponential
  • Plane curves
  • Probabilities
  • Particles and fields
  • SO(3), SU(2), etc
  • Lorentz transformations, E=mc^2
  • Gauge, matter, gravitation
  • Planck units
  • Universal gravitation
  • Classical vs quantum mechanics
  • Groups and quantum mechanics
  • Linear algebra of quantum mechanics
  • Penrose diagram: mind/physics/mathematics
  • Galois groups Galois-style
  • Disciplines in modern university
  • Artin substitution
  • Interior, exterior, and Lie derivatives
  • Addition formulae