Speaker
Description
In the first part, I will introduce our in progress work on the Seiberg duality conjecture in geometric level. Consider a quiver with potential. It has been proved by many people that its quasimap I function is preserved under quiver mutation in some sense. In this work, we further consider the behavior of the scheme under quiver mutation, and we have proved that the scheme is also preserved under quiver mutation.
In the second part, I will talk about an expected application of this result to the relation between cluster algebra and quantum cohomology rings. Considering the given quiver, one can construct a cluster algebra. One the other hand, one can consider the quantum cohomology ring of the quiver variety when it is smooth. We claim an algebra homomorphism from the cluster algebra to the quantum cohomology ring. This is a joint work with Zijun Zhou and Yaoxiong Wen.
