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.
Researchers across the Erlangen AI Hub continue to showcase their work on the international stage. This season, Hub members presented at the IEEE Conference on Decision and Control (CDC 2025) and NeurIPS 2025, one of the world’s leading AI gatherings. Their contributions span advances in autonomous systems, the mathematical foundations of control, and the growing use of generative AI in finance. The highlights are captured below.
Advances in Abstraction-Based Control at CDC 2025
Designing safe, reliable controllers for autonomous systems, from drones to self-driving vehicles, remains a fundamental challenge in AI. At CDC 2025, Erlangen Hub PDRA Thom Badings and Co-Investigator Alessandro Abate presented new research advancing abstraction-based control, a principled approach for computing correct-by-construction control policies under uncertainty.
Their two papers deliver key contributions:
Strengthening the mathematical foundations A refined abstraction framework capable of computing provably safe control policies even when system dynamics are uncertain. This work enhances both precision and scalability for complex autonomous platforms.
Introducing data-driven abstraction methods New techniques for constructing abstractions directly from empirical data, reducing reliance on fully specified analytical models and enabling robust control in partially known environments.
These developments push forward the frontier of reliable autonomous decision-making and contribute to the Hub’s broader mission to develop rigorous foundations for trustworthy AI.
Further reading: Probabilistic Alternating Simulations for Policy Synthesis in Uncertain Stochastic Dynamical Systems https://arxiv.org/abs/2508.05062 • Data-Driven Abstraction and Synthesis for Stochastic Systems with Unknown Dynamics: https://arxiv.org/abs/2508.15543
Generative AI for Finance: Rama Cont at NeurIPS 2025
At the NeurIPS 2025 Workshop on Generative AI in Finance, Erlangen Hub Co-Investigator Rama Cont delivered an invited talk on how generative models are transforming quantitative finance.
Financial markets are noisy, nonlinear, and highly interdependent, making simulation and risk assessment especially challenging. Cont presented recent work demonstrating how GAN-based models can emulate complex market behaviour, generate realistic scenarios, and support robust risk management.
His talk covered several key generative approaches developed by Cont and collaborators, including:
VolGAN for stochastic volatility surfaces
Tail-GAN for modelling rare but high-impact tail events
YieldGAN for yield curve dynamics
Data-driven hedging with generative models, a method using conditional generative models to compute hedge ratios across simulated market scenarios
The last of these was the focus of his presentation and recent paper, which proposes a non-parametric approach to hedging that outperforms classical delta and delta-vega strategies, even years after the training period.
The workshop itself featured leading voices from academia and industry, reflecting the rapid growth of AI-driven approaches in financial modelling.
NeurIPS 2025 was among the most competitive editions of the conference to date, with just 24.5% of submissions accepted. Against this backdrop, Erlangen AI Hub Director Michael Bronstein appeared as a co-author on nine accepted papers, presented across poster and spotlight sessions.
These contributions span generative and diffusion models, flow-based methods, equivariant and graph neural architectures, optimisation, and inference. All are core areas in the mathematical foundations of modern AI, and together, they reflect sustained engagement with both the theory and practice of scalable learning systems.
In a conference landscape increasingly shaped by large North American corporations and Chinese research institutions, this level of representation places Bronstein as a key figure in small group of Europe-based researchers maintaining strong technical visibility at NeurIPS, while highlighting the continued contribution of UK and European research to foundational questions shaping the field.
