|Speaker:||Sjoerd Beentjes (U of Edinburgh)|
|Title:||A proof of the Donaldson-Thomas crepant resolution conjecture|
|Date:||Tue, Jun 18, 2019, 15:30 - 17:00|
|Place:||Seminar Room A|
Donaldson-Thomas (DT) invariants are integers that enumerate curves in a given Calabi-Yau 3-fold. Let X be a 3-dimensional Calabi-Yau orbifold, and let Y be a crepant resolution of its coarse moduli space. When X satisfies the Hard Lefschetz condition, i.e., the fibres of the resolution are at most 1-dimensional, the Crepant Resolution Conjecture (CRC) of Bryan-Cadman-Young gives a precise relation between the generating functions of DT invariants of X and Y.
In this talk, I will give a brief introduction to DT invariants and present some examples. Then I will discuss joint work with John Calabrese and Jørgen Rennemo in which we interpret the relation of the CRC as an equality of rational functions, and prove it using the motivic Hall algebra and Joyce's wall-crossing formula.