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# Abstract Julian Quast

Julian Quast will speak on

The deformation space of $G$-valued pseudocharacters

Abstract: Pseudocharacters are a way to axiomatize characters of representations. We start with an introduction to pseudocharacters for $GL(n)$ and explain V. Lafforgue’s definition of $G$-valued pseudocharacters for any split reductive group $G$. We define the deformation ring of $G$-valued pseudocharacters for any linear algebraic group $G$. Then we show using results from invariant theory that for the classical groups $Sp(n)$ and $O(n)$ if $p \neq 2$ this deformation ring is noetherian. The construction generalizes that of Chenevier for $G=GL(n)$ using determinants.