Abstract:
In this talk, I will discuss the quantization of algebraic curves via a matrix
model. An algebraic curve is obtained as the spectral curve, and
a quantum spectral curve is obtained as a (time-dependent) differential
operator which annihilates the expectation value of a determinant
operator. It is known that in terms of 2d conformal field theory,
this quantum curve associated with the determinant operator is expressed
as the BPZ equation for a level 2 degenerate field. By generalizing this
discussion to higher levels, I will show that we can construct infinite family
of quantum curves. I will also show that these quantum curves can be
reconstructed by means of the topological recursion. This is based on
a work with Piotr Sulkowski.