Research by T. Zamrik

Research Interests

My research is rooted in the analysis and solution of the most mathematically demanding systems arising in modern applied mathematics. I work at the intersection of stochastic analysis, partial differential equations, and stochastic optimal control — fields whose deep interplay gives rise to some of the hardest open problems in the discipline.

At the forefront of my interests is the development and application of theory in mean field games, stochastic partial differential equations (SPDEs), differential games, and spatio-temporal agent-based models: settings where classical analytical tools must be rebuilt from the ground up, and where the coupling between randomness, nonlinearity, and infinite-dimensional structure is not a complication but the essential feature. I am concerned not merely with existence and uniqueness, but with forcing explicit, structured solutions out of equations that are seemingly impervious to crack.

What unifies my work is a commitment to solving systems that resist reduction — where the complexity is irreducible, and where the mathematics must rise to meet it. A refusal to settle for partial answers — a conviction that the most resistant equations, given the right tools and the right perspective, will yield.

About this research

The notebook and most of the papers are free to read; a few papers are restricted. Every paper can be cited, and each carries its own serial number, printed on the paper and in its address, so a citation always points at one document. Where a paper’s code is published, it is on GitHub, at github.com/Dr-Zamrik, so its numbers can be re-run rather than taken on trust.

The notebook is a personal blog space where useful and fun snippets of applied mathematics are kept; some evolve into formal research.