My research projects fall into three distinct categories, each rooted in a shared foundation: my strong connection to a physics approach characterized by meticulous and often extensive analytical calculations to clarify the behavior of physical systems. The categories listed on this site include scattering in photonic crystal devices, memristive devices, and stochastic genetic networks. While stochastic genetic networks can also be classified as devices, they are uniquely constructed using molecular pathways.
Prior to receiving my Fulbright research grant in 2020, my work primarily centered on statistical physics applied to gene regulatory networks. During that time, I also began exploring the scattering of electromagnetic waves in the context of photonic devices. Both of these research areas can be traced back to my earlier work on physical models solvable using the Bethe Ansatz, where the Yang-Baxter equation proves to be a powerful tool. This equation is so versatile that it encompasses both statistical physics (such as Ising-like models) and quantum scattering matrix theory (including Zamolodchikov’s quantum field scattering matrices). While my work in electromagnetism and statistical physics does not employ techniques from the Yang-Baxter framework, it is still geared toward obtaining closed-form analytical solutions.
The timing of my Fulbright grant aligned with the COVID-19 pandemic, granting me the mental space to concentrate deeply on a complex problem in photonic devices. During this period, I successfully derived a closed-form analytical solution to Maxwell’s equations on a lattice framework proposed by Pendry and MacKinnon. Moreover, during my Fulbright research in Brazil in 2022, I collaborated with a condensed-matter group dedicated to the experimental and theoretical study of memory devices. My background in various mathematical-physics disciplines proved highly relevant to the group’s work, and their research focus deeply inspired and motivated me.
In my research, I deeply value and find great joy in working alongside my collaborators, whose contributions I truly appreciate.