Prof Bavula's research interests are noncommutative Noetherian rings and their modules (especially rings of differential operators and D-modules), dimensions (the Krull dimension, the global homological dimension, the Gelfand-Kirillov dimension, the filter dimension), graded and filtered algebras, groups of algebra automorphisms, various properties of elements of rings and associated algebraic objects (like derivations and associated algebras, etc).

Prof Bavula is particularly interested in simple infinite dimensional Noetherian non-commutative algebras and in various classification problems associated with them.