| I will discuss an ongoing joint work with Roberto Svaldi on boundedness of Calabi-Yau pairs. Recent works in the minimal model program suggest that pairs with trivial log canonical class should satisfy some boundedness properties. I will show that Calabi-Yau pairs which are not birational to a product are indeed log birationally bounded, if the dimension is less than 4. In higher dimensions, the same statement can be deduced assuming the BAB conjecture. If time permits, I will discuss applications of this result to elliptically fibered Calabi-Yau manifolds. |