Research

I am working on programmable self-assembly, with a focus on the three-dimensional polycube model. My research explores how complex three-dimensional structures can emerge from simple local interaction rules, and how properties such as symmetry, assembly complexity, and designability shape the space of achievable structures.

Using large-scale simulations and theoretical analysis, I study genotype–phenotype maps in self-assembling systems and investigate the fundamental principles that govern minimal assembly design.

Is symmetry always simple?

Many structures, from crystals to jigsaw puzzles, can be built in more than one way, and the space of possible assembly sequences turns out to be surprisingly rich mathematically. I work on combinatorial problems that count the different ways a discrete structure can be grown while remaining connected at every step. With Abdurrahman Hadi Erturk and Ard Louis, we derived an exact formula for the number of successive vertex orderings of a connected graph, and used the same framework to enumerate the ways a jigsaw puzzle can be assembled, some sequences connected throughout, others passing through disconnected intermediate stages.

Before moving into self-assembly, I worked on problems in condensed matter and statistical physics: strain engineering of quantum spin liquids for my master's thesis at TU Dresden (with Prof. Matthias Vojta), and magnetism in graphene fractals and Anderson localisation in disordered systems at IISER Tirupati (with Dr Sudipta Dutta and Dr Sambuddha Sanyal).