3:30 pm, Seminar Hall
The Singular tuples of matrices is not a null cone
K.V. Subrahmanyam
Chennai Mathematical Institute.
19-09-19

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Abstract

We say an m tuple of $n \times n$ matrices (X_1, X_2,\ldots,X_m) is a singular tuple if the(complex) linear span of $X_1,X_2,\ldots,X_m$ contains only matrices with determinant zero. A natural question is if there some reductive group $G$ acting linearly on C^{mn^2} such that the null cone for the action is precisely singular tuples of matrices. Recently Vishwambara Makam and Avi Wigderson showed that this is not possible if either m \geq 3 or n \geq 3. I will give a sketch of their proof.