My broad background is in operator algebras, and most of my recent work has been in ergodic theory. 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 trying to extend these results beyond amenable groups.
I am quite keen to see how random walks on groups can be used to obtain results that are of interest in various fields. I also have some results regarding dilations of semigroup representations that I am writing up.
Publications during my PhD:
"Dilations of a class of semigroup representations to the boundary", draft in preparation
"Ergodic Average Dominance for Unimodular Amenable Groups", with R. Xia and J. Zacharias, 2025, 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