TCC Metric Diophantine Approximation

Via MS Teams, Tuesdays 10am to 12, see https://www.maths.ox.ac.uk/groups/tcc/tcc-current-courses

Lecture 1: October 11

Lecture 2: October 18

Lecture 3: October 25

Lecture 4: November 1

Lecture 5: November 15

Lecture 6: November 22

Lecture 7: November 29

Lecture 8: December 6

  1. Continued fractions. Including Dirichlet's theorem, diophantine exponents, and badly approximable numbers. SLIDES

  2. Lebesgue theory. Including Khintchine's theorem, the Duffin–Schaeffer conjecture (Koukoulopoulos–Maynard theorem), Borel–Cantelli lemmas, and zero-one laws. SLIDES 1, SLIDES 2, SLIDES 3

  3. Hausdorff theory. Including the Jarník–Besicovitch theorem and the mass transference principle. SLIDES

  4. Higher-dimensional theory. Including the Khintchine–Groshev theorem, Littlewood's conjecture, and Bohr sets. SLIDES

Pass SHEET 1 and SHEET 2. Send via email by December 2, midday.