My research interests lie at the interface of mathematical analysis and formal models of computation. Recent work focuses on formal foundations for reliable recursive agentic AI systems, especially causal-temporal execution structures and domain-theoretic semantics. Earlier work concerns PDEs, tensor transport equations in low regularity, optimal transport, Wasserstein gradient flows, and numerical schemes for gradient-flow dynamics.

• CTEGs: A Domain-Theoretic Model of Recursive Agent Execution

  Introduces CTEGs as a formal model of recursive agent execution records. The paper connects agent execution semantics with domain theory by viewing recursive execution as an ascending Kleene chain of typed temporal graphs, with applications to provenance, fault-tolerant execution traces, relational encodings, and tamper-evident verification. Submitted April 2026.

  Abstract: 'We introduce causal-temporal event graphs (CTEGs) as a formal model for fully resolved recursive agent execution records under single-parenthood causal semantics. We formalise direct event emissions and recursive subagent invocations as extension procedures on generic typed temporal graphs and show that the recursive closure ℰ∞ of the induced maximal dynamics starting from single causal roots consists entirely of finite sequences of CTEGs. A CTEG is a rooted arborescence whose nodes carry timestamps and event types, subject to the constraint that timestamps be strictly increasing along causal paths. We realise ℰ∞ as the increasing union of a recursive hierarchy ℰ₀ ⊆ ℰ₁ ⊆ ⋯ of agent execution levels parametrised by recursion depth, which is recognised as the ascending Kleene chain of a monotone operator φ admitting ℰ∞ as its least fixed point. Although the introduction of the full hierarchy is natural, stabilisation occurs already at ℰ₁ if one insists that the internal construction of a subagent execution trace be a delegated and opaque computational unit. The CTEG formalism supports compositional construction of globally well-formed execution traces from local agent behaviour without centralised coordination, preserves well-formedness under partial execution failure, and admits a natural relational database encoding. The arborescent structure of CTEGs is further compatible with cryptographic Merkle tree commitments for tamper-evident session verification.'

• Weak Solutions of the Linear Transport Equation for Rank Two Tensor Fields

  MSc thesis at the University of Oslo. Supervised by Prof. Snorre H. Christiansen. Nov 2024.

  Proves an existence theorem for transport equations acting on rank-two tensor fields under Sobolev regularity, extending the DiPerna–Lions scalar theory toward geometric PDE settings.

  Presentation: Slides giving a high-level overview of the arguments and contributions.

  Abstract: 'We formulate and prove an existence theorem for the linear transport equation for rank two tensor fields under Sobolev regularity, extending classical results of DiPerna & Lions (1989) in the scalar setting. The Lie derivative on tensors is extended to vector fields in H¹, where it is proved that control of Sym DV in L∞ is sufficient for existence of weak solutions starting at initial conditions in L². This is in contrast to the scalar case, where sufficient for existence are L∞-bounds on the divergence. Extensions to weak advection of differential forms have been considered, but this is to the best of our knowledge not the case for general, non-alternating or symmetric tensors. Our motivations stem from problems in general relativity and geometric flows, where evolution equations for the metric give rise to non-linear equations with transport terms of the type considered here.'

• Optimal Transport and Convergence of the JKO Scheme

  MSc thesis at the University of Oxford. Supervised by Dr. Jakub Skrzeczkowski in the group of Prof. José A. Carrillo. May 2025. Submitted version. Revised version upcoming.

  Gives a new proof of measurability of pointwise limits in second countable regular spaces via embeddings into the Tychonoff cube, contributing to a more categorically appropriate formulation of the topological foundations of optimal transport over traditional metric approaches.

  Observed and proved well-posedness of the Brinkman PDE in the space of tempered distributions by Malgrange–Ehrenpreis and a Fourier transform argument. Proved non-uniqueness in the space of Schwartz distributions by means of example, and that all solutions are smooth by elliptic regularity.

  Proved convergence of the JKO scheme for the Wasserstein gradient flow of the Brinkman functional, leading to existence of solutions to a non-local continuity equation with velocity potential linked through Brinkman's law. This repairs a fixed-point argument in the literature which proceeds by other means.

  The examiners further comment that 'the example with a geodesic connecting the Dirac mass at 0 with the uniform distribution on an interval giving infimum of the functional seems to be original'.

  Abstract: 'We review rudimentary aspects of optimal transport and Wasserstein spaces in the locally compact category with particular emphasis on topological conditions. We give a proof that measurability is preserved under pointwise limits into second countable regular spaces by embeddings into Tychonoff cubes. This class is large enough to encompass all Polish spaces and all separable Banach spaces. Although these embeddings are well-known, we are not aware of any proof of this result in the measure theory literature utilising this technique. We construct a counterexample to show that measurability is not preserved into general topological spaces. We conclude by proving convergence of the JKO scheme for the gradient flow of the Brinkman functional on the 2-Wasserstein space, following an outline in Ambrosio, Gigli, Savaré (2008). Finding some of their estimates unclear, we suggest clarifications and adaptations of their arguments based on similar estimates derived herein.'