MV-algebras and Łukasiewicz logic, approached through algebraic semantics, categorical equivalences, and geometric representations.
Broad interest in Stone-type dualities and “concrete” duality theory as a unifying toolkit across algebra and logic.
Algebraic structures and their representation
Abelian lattice-ordered groups (especially with strong unit) and related ordered structures, studied via representation/duality techniques and concrete geometric models.
Commutative semirings (“rigs”) and related “rig geometry” (structure, primes, axiomatizations, and categorical properties).
Arithmetic polyhedral & piecewise-linear geometry
Piecewise linear geometry, rational polyhedra and Z-maps.
