Preprints
We present a general construction of eventually periodic projective resolutions for modules over quotients of rings of finite left global dimension by a regular central element. Our approach utilizes a construction of Shamash, combined with the iterated mapping cone technique, to systematically ‘purge’ homology from a complex. The construction is applied specifically to the integral group rings of groups with finite virtual cohomological dimension. We demonstrate the computability of our method through explicit calculations for several families of groups including hyperbolic triangle groups and mapping class groups of the punctured plane.
In Preparation
Cohomology of Heckoid groups,
with Thomas Csizmadia and Jeroen Schillewaert
Euler characteristics for groups of type VFP via Gorenstein projective approximations,
with Alex Martsinkovsky
Theses
My Master's Thesis: Rigidity in semisimple Lie groups
Visting Scholar
Throughout my higher education experience, I have had the opportunity to travel to several Universities for research visits.
In the Summer of 2025, I was a visitor at The University of Auckland, under the supervision of Professor Jeroen Schillewaert. We studied the (co)homology of Heckoid groups by constructing explicit free resolutions. We have continued to work on this project together with Thomas Csizmadia.
In the Spring of 2024, I visited the University of Aberdeen with Dr. Irakli Patchkoria. Whilst in Aberdeen I learned a considerable amount about Euler characteristics of groups and other ideas from homological algebra and algebraic topology.
In the Summer of 2023, I was a research visitor at The University of Auckland, visting Professor Jeroen Schillewaert. We explored applications of group cohomology in geometric group theory; particularly for hyperbolic groups.
In the summer of 2018, I had a summer scholarship and research visitor position at Australia National University. I worked with Dr. Asilata Bapat and Dr. Anand Deopurkar. Our work focused on identifying dense orbits in the representation space of a particular class of extended Dykin quivers.