Celebrating Three PhD Successes
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.