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.