The title of my thesis is "Ergodic Theory and Random Walks on Groups". My broad background is in operator algebras, and most of my recent work has been in ergodic theory and dynamical systems. We recently gave a new proof of the pointwise ergodic theorem for unimodular amenable groups using random walk techniques that allows us to treat the classical and noncommutative versions on an equal footing. We are currently investigating further implications of these results, and trying to extend them beyond amenable groups. We are also developing random walk techniques to study measure bundles resulting from group actions on standard probability spaces. I am quite keen to see how random walks on groups can be used to obtain results that are of interest in various fields.
Publications during my PhD:
"2-colourings of the integers through lamplighter random walks", with C. A. Wilson, draft in preparation
"Dilating semigroup representations to the boundary quotient", 2026, link to preprint
"Ergodic Average Dominance for Unimodular Amenable Groups", with R. Xia and J. Zacharias, 2025, submitted, link to preprint
Previous publications as a Masters' student (in Physics):
"Construction of propagators for divisible dynamical maps'', with D. Chruściński, published in the New Journal of Physics in 2021, link to article
"Generic Contractive States and Quantum Monitoring of Free Masses and Oscillators'", with P. Bhasin and S. M. Roy, published in Physics News (Apr-Sep 2019), link to article
Other works not intended for publication, as a Masters' student:
"Apollo's Voyage: A New Take on Dynamics in Rotating Frames", with A. Dasgupta, 2020, link to preprint
"C*-Algebras, Completely Positive Maps, and Dilations", Masters' thesis under the supervision of S. Biswas, 2020, link to thesis