Let $A$ be a differential bigraded $k$-algebra and let $e \in A$ be an idempotent. Under suitable assumptions on the pair $(A,e)$, we define the graded Higgs category $\mathcal H^{\mathbb Z}(A,e)$ and the graded relative cluster category $\mathcal C^{\mathbb Z}(A,e)$. We show that $\mathcal H^{\mathbb Z}(A,e)$ carries a Frobenius extriangulated structure, and that its stable category admits a silting object. Examples arise from Keller--Scherotzke's work on graded singular Nakajima categories and from graded maximal Cohen--Macaulay modules over isolated singularities. This is a report on ongoing joint work with Li Fan.

This talk will take place in hybrid mode at the Institut Henri Poincaré.