http://sole.dimi.uniud.it/~dikran.dikranjan/

RESEARCH INTERESTS

Algebraic aspects of Topological Groups, Rings and Modules

• Algebraic structure of topological groups
• Description of linear compactness of rings through endomorphisms
• Minimal topologies on rings and their connection to Krull dimension

Combinatorial aspects of (topological and abstract) groups

• Connections between the algebraic structure of topological groups and some of their functorial posets
• Large and small sets in (topological and abstract) groups
• Combinatorial properties of continuous maps between groups endowed with functorial topologies

Compact groups and their generalizations

• minimal groups and compact representations of groups
• countably compact groups and pseudocompact groups
• compact group close to Lie groups
• the impact of compactness-like properties of the topological groups on their dimension and (dis)connectedness

Category theory

• Closure operators and their application to algebra, topology and discrete mathematics
• Dualities between categories of topological modules

Uniform and quasi uniform spaces

• Uniform continuity and its generalizations
• Cowell-poweredness of categories of quasi uniform spaces