Joshua Sack

Teaching

Research Interests

• Discrete Mathematics: enumerative combinatorics (focusing on permutation patterns); game theory (combinatorial games, logic and games, and rationality and solution concepts); discrete quantum structures (quantum lattice-ordered sets; quantum graphs; quantales); probabilistic graphical models; logic
• Applied Logic: applications of logic to multi-agent systems, process theory, belief dynamics, game theory; development of new combinations of epistemic, probabilistic, temporal, and dynamic logics; coalgebraic modal logic; graded modal logic; quantum logic; characteristic formulae for fixed-point Hennessy-Milner logics; justification logic.
• Theoretical Computer Science: multi-agent systems (belief dynamics and strategic interaction); process theory (structural operational semantics and compositional techniques for model checking); quantum computation and information; optimization
• Algebra: rings of real-valued continuous functions; rings of real-valued measurable functions
• Topology: rings of real-valued continuous functions on different types of Tychonoff spaces; 3-manifolds (idempotents in the category of tangles)
• Mathematical Biology: computational models of immune-cell tumor-cell interaction