Symmetric matrices associated with oriented link diagrams.

Motivated by metaplectic invariants of Goldschmidt–Jones,
generalizing the cyclotomic invariants of Kobayashi–Murakami–Murakami,
I will explain a construction which associates to each oriented link
diagram a symmetric matrix with elements being quadratic polynomials
in one indeterminate with integer coefficients. Based on a slightly
modified S-equivalence of Trotter and Murasugi in the space of
symmetric matrices, the construction gives rise to an invariant
of oriented links. In particular, the signature of the matrix is
conjecturally related to the Tristram–Levine signature function.