New PDRAs join Erlangen AI Hub

erlangenaihub on 1 October, 2026

A very warm welcome to the Erlangen AI Hub to our three new PDRAs who joined us in September: Konstantin Kueffner, Kelly Maggs, Gianmarco Parretti. They join a growing team of PDRAs across our University of Oxford departments (Mathematical Institute and Department of Computer Science), and we are delighted to have them on board.

Kelly Maggs completed a PhD in algebraic topology at EPFL where his supervisor was Kathryn Hess. He then transitioned to mathematical biology during a postdoc in Heather Harrington’s group at at the Max Planck Institute for Cell Biology and Genetics. His research goal is to develop a geometric, topological, and algebraic language for cellular processes compatible with modern machine learning.

Gianmarco Parretti’s research lies at the intersection of Artificial Intelligence and Formal Methods, aiming to improve the reasoning capabilities of autonomous agents. He received his PhD in AI at the University of Rome “La Sapienza” after defending a thesis titles Synthesis Under Environment Specifications for LTLf.

Konstantin Kueffner was a PhD student at the Institute of Science and Technology Austria, working under the supervision of Thomas A. Henzinger. His research lies in the intersection of formal verification, statistic, and machine learning, with a particular emphasis on uncertainty quantification. His research interests include: runtime verification, formal methods, stochastic processes amongst others.

We look forward to getting to know more about them and their work.

Mathematics and the Future of AI

Kevin Childs on 12 February, 2026

Intellectual leadership through deep foundations

In a new University of Oxford Expert Comment article, Erlangen AI Hub Co-Investigator Professor Peter Grindrod CBE, argues that mathematics is not peripheral to artificial intelligence, but central to solving its core challenges.

As AI systems increase in scale and complexity, concerns around reliability, bias, interpretability, and formal guarantees cannot be addressed by engineering alone. Mathematics provides the structure to reason rigorously about uncertainty, optimisation, stability, and limits. Through probability, geometry, topology, dynamical systems, and information theory, maths enables AI systems that are interpretable by design and grounded in provable principles.

At the Erlangen AI Hub, Professor Grindrod and colleagues are working precisely in this space: bringing deep mathematical ideas into direct engagement with real-world AI challenges. Maths provides the foundation to build systems that are more robust, transparent, and intellectually grounded, helping position the UK as a leader through intellectual depth rather than scale. Read the full article below.

Expert Comment: How and why mathematics will both underpin and lead the next generation of AI | University of Oxford

Celebrating Three PhD Successes

Kevin Childs on 15 December, 2025

We are delighted to celebrate the recent PhD successes of Dr Yueqi Cao, Dr Roan Talbut, and Dr Qiquan (Qi) Wang, three early-career researchers whose work spans tropical geometry, statistical topology, and the mathematics of complex data. Their achievements reflect not only their own creativity and depth of insight but also the vibrant research environment shaped by their supervisor, and Hub Co-Director Professor Anthea Monod, who’s algebraic topology and algebraic geometry contributes to the understanding of modern statistical and machine-learning problems.

Dr Yueqi Cao — Tropical Geometry and Metric Graphs

Dr Yueqi Cao successfully defended his PhD, From Graphs to Point Clouds: the Tropical Abel–Jacobi Transform and Persistent Homology for Metric Graphs. His thesis develops rigorous links between tropical geometry, persistent homology, and statistical approaches for metric graphs, offering new tools for understanding geometric structure and opening pathways for applications in cryptography, information geometry, and machine-learning tasks on graph-structured data.

Yueqi’s doctoral work has led to four published journal papers across computational mathematics, data science, and statistics, with several more under review. He now continues his research as a Digital Futures Fellow at KTH Stockholm.

Dr Roan Talbut — Tropical Geometry for Phylogenetic Statistics

Dr Roan Talbut, now a Postdoctoral Research Associate at the Erlangen Hub, defended their PhD titled Tropical Geometry for Phylogenetic Statistics. Their research provides deep new insights into the intersection of tropical geometry, probability, statistics, and optimisation, developing tools that bring greater interpretability and computational tractability to the analysis of evolutionary and biological data.

Roan’s PhD resulted in several peer-reviewed publications across data science, optimisation theory and pure mathematics, with further work in progress. They continue their academic journey at Durham University

Dr Qiquan (“Qi”) Wang — Statistical Topology Across Biology and AI

Dr Qiquan Wang successfully defended her PhD, The Shape of Data: Statistical Topology Across Biology and AI. Her thesis establishes new statistical frameworks for analysing data using topological invariants in both single- and multi-parameter settings, and has applications to biological systems and deep-learning architectures.

Qi’s research has led to five papers, including publications, with additional manuscripts under review. She now moves on to a postdoctoral fellowship at Queen Mary, University of London.

Recognising the Mathematical Foundations of Their Research

These PhD successes highlight the vibrancy of mathematical foundations research and the impact of early-career researchers contributing new ideas at the interface of mathematics and AI. We are proud to celebrate their achievements and look forward to seeing the exciting directions their work will take in the years ahead.