# Colloquium abstracts

**Pradeep Das**

TIFR, Mumbai

October 15, 2020

**K"ahler Geometry of Moduli of Representations of Quivers**: In this talk, I shall discuss some holomorphic aspects of moduli spaces of finite dimensional semistable representations of a finite quiver. Namely, I shall describe the construction of a natural Hermitian holomorphic line bundle on the stratified moduli space of semistable representations, and show that the curvature of this line bundle on each stratum of the moduli space is a scalar multiple of the K"ahler form of that stratum. I shall then recall the definition of the tensor product $Q otimes Q'$ of two quivers $Q$ and $Q'$, and define the tensor product $V otimes W$ of a representation $V$ of $Q$ with a representation $W$ of $Q'$, and discuss the semistability of $V otimes W$. Moreover, I shall describe a relation between the natural line bundles on the moduli spaces of representations of $Q, Q'$ and $Q otimes Q'$.