Zamrik.com

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 Website

This site collects what I produce: research papers, technical blog posts, book manuscripts, and course notes in applied mathematics and mathematical finance. The research section organises work by area — stochastic analysis, stochastic optimal control, mean field games, market modelling, agent-based models. The blog is where ideas get worked out before they become papers, or where they go when they have nowhere else to be. Books and courses will have their own sections as they accumulate. There is also a Visions gallery: a leisure practice running in parallel, where mathematics gives way to image.

All of it under the jurisdiction, blessings, and revelations of Sheogorath — Daedric Prince of Madness, Lord of the duality of Order and Chaos, whose realm divides into Dementia and Mania. The mathematics lives in Dementia. The Visions in Mania. The border kept deliberately open, where my keyboard, pen, and coffee sit.

Consulting

I take on consulting work in quantitative modelling, optimal policy and control theory, agent based models, and the mathematics of financial systems. The problems I find most interesting are the ones that resist standard approaches — models where the stochastic structure is genuinely complex and irreducible, numerical schemes that need to be built rather than borrowed, and analytical frameworks where the existing literature runs out.

If you are building something that requires serious mathematics — a pricing library, a stochastic control problem, the extraction of optimal policy under uncertainty, a multidimensional PDE solver, a high dimensional model calibration engine, a model that needs to actually work under real market conditions — get in touch, you will see something new for sure.