The mathematical knowledge used in graphics is mainly calculus (essential basis), linear algebra (model transformation basis), optimization theory and method (basis of writing papers and doing research), differential geometry, finite element, stochastic process and so on. More mathematical knowledge is constantly applied to this subject, of which the first three belong to the foundation.

The topic of your thesis may be too professional for graphics. For graphics, topics of interest may be:

On Monte Carlo method and its application (siggraph used it in an article in 2005 or 2006)

Statistics and parameter estimation of a class of stochastic processes

ILr Optimal Design of a Class of Spherical Harmonic Function Models

In fact, the mathematical foundation of the department of mathematics is generally enough for graphics. Just choose a topic that can prove your strength.

For example, the following topics are also good.

Quasi-linearization method for singularly perturbed turning point problem (a good basis for ordinary differential equations)

Differential transformation method and power series solution of second-order differential equations (a good basis for ordinary differential equations)

Asymptotic analysis of (undetermined) model solution;