Mathematics

This talk is about the coherent-constructible correspondence (CCC). CCC is a version of homological mirror symmetry for toric varieties. It equates the derived category of coherent sheaves on a toric variety and the category of constructible sheaves on a torus that satisfy some condition on singular support. Recently, Harder-Katzarkov conjectured that there should be a version of CCC for toric fiber bundles and they proved their conjecture for P^1-bundles. I will explain how we can prove (half of) their conjecture for P^n-bundles. If time permits, I will give a more precise version of the conjecture for arbitrary toric fiber bundles.