Donaldson-Thomas invariants, wall-crossing and categorifications

It is an important subject to study algebraic curves inside algebraic varieties, both in classical algebraic geometry and also enumerative geometry inspired by string theory. The Donaldson-Thomas theory is one of curve counting theories on Calabi-Yau 3-folds, and has developed in these 20 years from several aspects of mathematics and mathematical physics. Among them, the wall-crossing in derived category turned out to be a key phenomena in proving deep structures of generating series of Donaldson-Thomas invariants.
In the first one hour, I will review the classical aspect of counting curves inside algebraic varieties, and explain how it leads to modern enumerative geometry such as Gromov-Witten invariants, Donaldson-Thomas invariants.
In the second one hour, I will explain wall-crossing phenomena in Donaldson-Thomas theory, and its categorification in the case of the resolved conifold.

*Please contact Keita Mikami's mail address to get access to the Zoom meeting room.