Our work concerns the development and study of precise mathematical formalisms that can be employed for the design, specification, and verification of computer programs. This is in a tradition of mathematical semantics that was started in the UK in the 1960s by Peter Landin, Christopher Strachey, and Dana Scott. This kind of semantics encompasses many mathematical theories, foremost among them order theory, topology, logic, game theory, and category theory, all of which feature in the work of the Birmingham Theory Group. The rich and often surprising interplay between these mathematical areas and programming concerns gives rise to wonderful opportunities for deep and conceptual research.

PhD opportunities

See our poster here.

We welcome applicants for PhD studies in any of these areas. Please email for more information, or contact individual researchers.


 Research areas
Benedikt Ahrens semantics of type theory, computer theorem proving,
categorical structures in programming
Martín Escardó topology, computation with infinite objects,
constructive mathematics, intuitionistic type theory
Dan Ghica game semantics, heterogeneous computing, model checking
Achim Jung mathematical structures in the foundations of computing: logic, topology, order
Paul Levy denotational semantics, computational effects and call-by-push-value,
nondeterminism, category theory, coalgebra, game semantics
Dave Parker formal verification, probabilistic model checking
Uday Reddy semantics of state, separation logic
Eike Ritter security protocol verification
Hayo Thielecke abstract machines, concurrent and functional programming, software security
Jamie Vicary (from January 2018) quantum computing, higher-dimensional algebra, category theory,
quantum field theory, formal proof
Steve Vickers constructive mathematics and topology, category theory and toposes
Noam Zeilberger categorical semantics of type systems and λ-calculus,
substructural logic and proof theory, interactions with combinatorics

Research staff

Marco Devesas Campos

Alex Smith

Honorary research fellows

Valeria de Paiva

Reinhold Heckmann

Claudio Hermida

Paul Taylor

PhD Students

Student Supervisor
Michael ArntzeniusDan Ghica and Neel Krishnaswami (University of Cambridge)
Auke BooijMartín Escardó
Steven CheungDan Ghica
Yuning FengPaul Levy
Bram GeronPaul Levy
Sina HazratpourSteve Vickers
Tomáš JaklAchim Jung and Aleš Pultr (Charles University in Prague)
Xiaodong JiaAchim Jung
Cory KnappMartín Escardó
Koko MuroyaDan Ghica
Anna Laura SuarezAchim Jung and Steve Vickers