Plane quartics, bitangents, and symmetric determinantal representations

It is a beautiful fact that a general plane quartic in the complex projective plane has 28 bitangents. How do we write down these bitangents? It is also a beautiful fact that a general plane quartic in the complex projective plane has 36 symmetric determinantal representations (i.e. there are 36 inequivalent ways to write the equation of the quartic as a determinant of a symmetric 4×4 matrix whose entries are linear forms in 3 variables).

This talk will go over some of the classical theory of plane quartics, including relationships between bitangents and symmetric determinantal representations, theta characteristics, configurations of 8 points in P^3, and more.