Manuel Hauke: The Duffin-Schaeffer conjecture and beyond

Abstract:

Khintchine’s Theorem is one of the cornerstones in metric Diophantine Approximation. The question of removing the monotonicity condition on the approximation function in Khintchine’s Theorem led to the recently proved Duffin-Schaeffer conjecture. In this talk, I will discuss asymptotic formulae for the number of good approximations, generalizations to higher dimensions and inhomogeneous variants, and demonstrate the deep connection to analytic number theory that lies in the heart of the corresponding proofs. This talk is partially based on joint work with B. Borda and C. Aistleitner.