My research was centered around various aspects of abstract algebra varying from representation theory, group theory, topological groups and category theory. The last project I worked on in UEA with Dr Vanessa Miemietz was connected to 2-categories, monoidal categories, Hopf algebras and higher representation theory.
My PhD thesis was on smooth representations of locally compact (lctd) topological groups, with the aim in mind to apply the results on complete Kac-Moody over finite fields. This is also the main topic of my thesis. Representations are mainly studied geometrically - by looking at continuous actions of the lctd groups on simplicial sets. Having worked on this project for 4 years, I naturally developed an interest in topological Kac-Moody groups, p-adic algebraic groups and their buildings.
Basic Hopf Algebras and Symmetric Bimodules, with V. Miemietz, Journal of Pure and Applied Algebra, 227 (7), link.
Generalised Comodule-Contramodule Correspondence, with J. Jones and D. Rumynin, link.
Cocompact Lattices in Locally Pro-p-Complete Kac-Moody Groups, with I. Capdeboscq and D. Rumynin, to appear in Sbornik Mathematics (Matematicheskii Sbornik) 211, (2020), DOI:10.1070/SM9311.
Frobenius Reciprocity for Topological Groups, Communications in Algebra 47 (5), 2102 -- 2117, link.
Kac-Moody Groups and Cosheaves on Davis Building, with D. Rumynin, Journal of Algebra 515, 202 -- 235, link.
I was a teaching assistant for the following undergraduate courses:
Advanced Linear Algebra (academic years 2015/2016, 2016/2017, 2018/2019), University of Warwick.
Algebra II: Groups and Rings (academic years 2016/2017, 2017/2018, 2018/2019), University of Warwick.
Tensors, Spinors and Rotations (academic year 2015/2016), University of Warwick.
I have also led the seminars for the following Masters level courses:
Ring theory (academic year 2015/2016), University of Warwick.
Lie groups (academic year 2016/2017), University of Warwick.
Representation theory (academic year 2017/2018), University of Warwick.
Lie algebras (academic year 2018/2019), University of Warwick.
Additionally, I was a supervisor for 5 small group of students: 3 groups of first year students and 2 groups of second year students.