Séminaires : Séminaire d'Algèbre

In the first part, I will introduce our work in progress on the Seiberg duality conjecture at the 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 behaviour of the representation scheme under quiver mutation. In the second part, I will talk about an expected application of this result to the relation between cluster algebras and quantum cohomology rings. From a 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 expect that there is an algebra homomorphism from the cluster algebra to the quantum cohomology ring. This is a joint work with Zijun Zhou and Yaoxiong Wen.

This talk will take place on Zoom only.