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Luke Oeding
Luke Oeding
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Geometric Complexity Theory:

Theorem (Mulmuley and Sohoni [MS]) The permanent (respectively the determinant) polynomial is characterized by its symmetry group.

That is if $P$ is a homogeneous polynomial of degree $m$ in $m^2$ variables and its symmetry group $G_P$ also fixes the permanent (respectively the determinant), then $P$ must be a scalar multiple of the permanent (respectively the determinant).

Landsberg and Ressayre [LR][LR] made progress on Valiant's version of P vs NP using this result.

Geometric Complexity Theory:

Theorem (Mulmuley and Sohoni [MS]) The permanent (respectively the determinant) polynomial is characterized by its symmetry group.

That is if $P$ is a homogeneous polynomial of degree $m$ in $m^2$ variables and its symmetry group $G_P$ also fixes the permanent (respectively the determinant), then $P$ must be a scalar multiple of the permanent (respectively the determinant).

Landsberg and Ressayre [LR] made progress on Valiant's version of P vs NP using this result.

Geometric Complexity Theory:

Theorem (Mulmuley and Sohoni [MS]) The permanent (respectively the determinant) polynomial is characterized by its symmetry group.

That is if $P$ is a homogeneous polynomial of degree $m$ in $m^2$ variables and its symmetry group $G_P$ also fixes the permanent (respectively the determinant), then $P$ must be a scalar multiple of the permanent (respectively the determinant).

Landsberg and Ressayre [LR] made progress on Valiant's version of P vs NP using this result.

Source Link
Luke Oeding
Luke Oeding
  • 569
  • 2
  • 12

Geometric Complexity Theory:

Theorem (Mulmuley and Sohoni [MS]) The permanent (respectively the determinant) polynomial is characterized by its symmetry group.

That is if $P$ is a homogeneous polynomial of degree $m$ in $m^2$ variables and its symmetry group $G_P$ also fixes the permanent (respectively the determinant), then $P$ must be a scalar multiple of the permanent (respectively the determinant).

Landsberg and Ressayre [LR] made progress on Valiant's version of P vs NP using this result.

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