Research Programmes

01. Knowledge, Evidence, and Representation

We are interested in how knowledge can be represented, acquired, and justified, particularly when an observer has access to only partial information about the system being studied.

Suppose two systems are indistinguishable under a particular collection of observations. What conclusions can we draw about them? How would those conclusions change if additional observations became available? And how do the assumptions we make about a system affect what we are able to infer from it?

These questions lead naturally to formal epistemology, epistemic and modal logic, probability, belief revision, and mathematical models of observation and inference.

We are also interested in how different representations of knowledge relate to one another, and how formal models can help distinguish what is known, what is inferred, and what remains undecidable from the available information.

02. Abstraction, Equivalence, and Mathematical Structure

This programme is concerned with the mathematical relationships between different structures, representations, and levels of abstraction.

A recurring direction is to investigate the conditions under which different mathematical objects or descriptions can be considered equivalent, which properties are preserved by transformations between them, and how more general structures can be constructed from particular realizations.

Our interests here include abstract algebra, category theory, higher category theory, type theory, homotopy type theory, and connections to geometry and topology.

We are particularly interested in structural approaches that allow us to reason about relationships between mathematical objects without depending on their particular representations. This includes questions about identity, equivalence, invariance, and the mathematical constructions through which different theories can be related.

The programme also provides room for purely mathematical investigations, including problems motivated by relationships between otherwise distinct areas of mathematics.

03. Information, Computation, and Interaction

We study the mathematical properties of systems that compute, communicate, and interact with one another.

Some of the questions concern the limits of computation and communication themselves. Others arise when several systems are composed together, particularly when their individual properties do not carry over straightforwardly to the resulting system.

We are interested in information flow, communication constraints, partial observability, distributed computation, and the formal analysis of interacting systems.

Theoretical tools include information theory, automata theory, computability and complexity theory, formal verification, probability, and mathematical models of distributed and interactive computation.

One direction within this programme concerns multi-agent systems, where communication, coordination, and information sharing introduce questions that cannot always be answered by analysing agents individually.

We are also interested in translating formal results into protocols, verification methods, and system designs whose properties can be understood mathematically.

04. Decision, Games, and Collective Behaviour

A system's ability to perform an action does not necessarily tell us whether it will choose to perform it.

This distinction motivates several questions about decision-making, rationality, incentives, and strategic interaction.

We are interested in how decisions depend on the information available to an individual or system, the objectives being pursued, and the behaviour expected from other participants. When several decision-makers interact, we also want to understand how their individual choices give rise to collective outcomes.

This programme brings together decision theory, game theory, Bayesian and epistemic games, mechanism design, social choice theory, bounded rationality, and causal approaches to decision-making.

The resulting questions extend across individual decision-making, strategic communication, coordination, and the design of mechanisms for systems involving several interacting participants.

We are particularly interested in identifying mathematical structures that explain these behaviours across different settings, rather than constructing models tied to one particular application.

05. Mathematical Foundations of Physical Theories

We are interested in theoretical and mathematical physics, particularly questions concerning the mathematical structures underlying physical theories and the relationships between different descriptions of physical phenomena.

One direction concerns quantum theory and its mathematical foundations, including Hilbert-space formulations, operator-theoretic approaches, and the algebraic structures used to describe quantum systems.

Another concerns spacetime and gravitation, where differential geometry, causal structure, and the mathematical formulation of general relativity provide several interesting problems.

We are also interested in statistical mechanics, emergence, and the relationships between descriptions of physical systems at different scales. Questions about coarse-graining, effective theories, and the preservation of structure across different levels of description are particularly relevant here.

The programme encompasses investigations within individual physical theories as well as mathematical approaches to relating them.

Our interests include geometry, topology, functional analysis, operator algebras, dynamical systems, and other areas of mathematics that arise naturally in theoretical physics.

06. Dynamics of Knowledge and Scientific Practice

This programme concerns how scientific knowledge develops, accumulates, and moves between individuals, research communities, and institutions.

As scientific knowledge grows, the amount of existing work required to contribute to a particular subject can also increase. At the same time, new methods of communication, representation, and computation can change how that knowledge is accessed, organized, and used.

We are interested in studying these relationships more formally.

This includes questions about the accumulation and distribution of knowledge, the effects of specialization, the organization of scientific collaborations, and the ways different communication structures influence collective understanding and discovery.

Relevant approaches include social epistemology, information theory, network theory, dynamical systems, mathematical models of collective knowledge, and empirical studies of scientific practice.

Another direction concerns how changes in scientific capabilities affect the institutions through which research is conducted. This includes research infrastructure, mechanisms for collaboration, the verification and communication of scientific results, and the development of policies informed by a better understanding of these processes.

We are interested in both the mathematical and empirical investigation of these questions and their consequences for how scientific research can be organized.