Anthea Monod

I am a Reader (Associate Professor) in Mathematics and Machine Learning at the Department of Mathematics at Imperial College London.

My research uses theory from pure mathematics (algebraic geometry and algebraic topology) to develop computational and statistical methods for data that have complex structures, or that live in complex spaces.
Research Interests:

Applied and Computational Topology including Topological Data Analysis
Applied Algebraic Geometry including Algebraic Statistics
Geometric Statistics and Geometric Deep Learning
Theoretical Machine Learning
Mathematical Biology

Contact: a [dot] monod [at] imperial [dot] ac [dot] uk
Office: Roderic Hill 318

£10 million to study the mathematics of AI:
I use pure mathematics (algebraic topology and algebraic geometry) to advance understanding of deep learning and modern AI technology. My research in this direction is supported by a £10M EPSRC Mathematical and Computational Foundations of Artificial Intelligence Hub [EP/Y028872/1]. I am a Co-Director of the Erlangen AI Hub alongside Michael Bronstein and Jeff Giansiracusa and the Imperial PI. You can read the press release about it here.

News & Upcoming Stuff

My PhD student Inés García-Redondo successfully defended her PhD entitled "Topological Invariants for Data: Duality, Stability and Applications to Machine Learning" on 4 September 2025. Many congratulations, Inés!
I have been promoted: As of 1 September 2025, I am a Reader (Associate Professor) in Mathematics and Machine Learning!
My PhD student Roan Talbut's paper on Tropical Gradient Descent was just accepted for publication in the Journal of Global Optimization!
Our paper Tropical Geometry of Phylogenetic Tree Space: A Statistical Perspective has been accepted to the Vietnam Journal of Mathematics in the special issue in memory of Andreas Dress! Joint work with Bo Lin, Rudy Yoshida, and Qiwen Kang
Our paper on Confidence Bands for Multiparameter Persistence Landscapes has just been accepted to Geometric Science of Information (GSI'25) taking place this year in St-Malo, France! Joint work with Inés García-Redondo and Qiquan Wang
I am an editor for the newly launched Association for Mathematical Research (AMR) journal Applied & Computational Topology & Geometry (ACTG)!
New preprint on the arXiv where we propose persistent homology as an interpretability tool for studying activation spaces of LLMs! Joint work with Aideen Fay, Inés García-Redondo, Qiquan Wang, and Haim Dubossarsky
New preprint where we propose entirely new graph kernels based on the genus of a graph via tropical geometry is up on the arXiv, check it out! Joint work with Yueqi Cao
Our paper on Tropical Fréchet Means has been accepted to the International Symposium on Symbolic and Algebraic Computation (ISSAC 2025) taking place this year in Guanajuato, Mexico! Joint work with Bo Lin, Kamillo Ferry, Carlos Améndola and Rudy Yoshida
New preprint on Computing the Tropical Abel–Jacobi Transform and Tropical Distances for Metric Graphs is live on the arXiv! Joint work with Yueqi Cao
In addition to being on the Scientific Advisory Committee, I will also be mentoring a project on Cycle Matching for High Dimensional Neural Activation Patterns together with Omer Bobrowski at LOGML 2025
My paper Generalized Morse Theory of Distance Functions to Surfaces for Persistent Homology has been accepted for publication in Advances in Applied Mathematics! Joint work with Anna Song and Ka Man (Ambrose) Yim
My MSc student Naomi Rosenberg won a Marjorie McDermott Women's Scholarship – Congratulations, Naomi!
My term as a UKRI–EPSRC Mathematical Sciences Early Career Forum member has been extended to 2026. I am honored to continue to serve the British mathematical community by voicing the needs of early career mathematicians in the UK to the EPSRC as well as to advocate for the EPSRC within the UK mathematical landscape.

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