Talk Abstract: The Flag variety is a basic object of geometry and linear algebra. It is a space that parameterizes flag: sequences of nested linear spaces. In the process of studying the topology of the space of polynomial curves on this space, we find a surprising connection to linear control systems. This led us to formulate conjectures which were proved with assistance from Google DeepMind.​

Talk Abstract: Take two points and pick a path between them "uniformly at random." Of course, there are infinitely many paths, and the question does not really make sense. However, there is a way to make sense of it: Brownian motion. Although this theory is rather classical in 1D, in two dimensions or more, things are much less understood. I will give a gentle overview of the type of problems we tackle in this area, and maybe even some theorems.

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Talk Abstract: In this talk, we present a framework for extracting "needles in the haystack" via agentic research workflows: decomposing a question into subqueries, routing them through multiple data collections, executing semantic search over vector embeddings, and using reflection loops to detect gaps and drive conditional repeat execution. We discuss the architecture of this system, including query routing, similarity search over chunks, reflection-based query expansion, and final synthesis. Finally, we show how the approach systematically uncovers deep patterns and hidden insights from large unstructured corpora, turning sparse signals into precise, cohesive reports.

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Talk Abstract: Wastewater surveillance resurged during the COVID-19 pandemic as a passive, low-cost, non-invasive method for monitoring community-level disease transmission with the potential to overcome biases inherent in other surveillance methods, such as those driven by healthcare-seeking behaviour. Past efforts have primarily focused on correlating wastewater pathogen levels with clinical indicators, demonstrating its ability to forecast reported cases, Emergency Department (ED) visits, and hospitalizations. Building on this foundation, we propose TARnISHED-WW (Time-series Analysis of Random Walkers for Infections Surveillance and Hospital ED visits), a novel framework that combines multiple pathogen wastewater viral load and clinical data to model overall ED visits latent multivariate Gaussian random walks that capture shared infection dynamics across regions. This framework incorporates signals from three major respiratory viruses: Influenza A, SARS-CoV-2 and Respiratory Syncytial Virus (RSV). Due to TARnISHED-WW's hierarchical Bayesian architecture, we can infer pathogen-specific contributions to ED visits, yielding an important indicator to support hospital and emergency services planning and public health surveillance. Our work demonstrates the potential of wastewater surveillance combined with advanced quantitative modelling to provide robust public health indicators and support health care preparedness and planning.

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Talk Abstract: Understanding what lies beneath the Earth’s surface is essential for addressing challenges such as locating critical minerals, managing groundwater, monitoring CO₂ storage, and tracking permafrost change. Much like how medical imaging techniques such as MRI or X-ray reveal internal structure non-invasively, geophysical surveys measure signals—electric, magnetic, seismic, or gravitational—that are influenced by the physical properties of the subsurface.

Recovering those properties from surface data leads to a PDE-constrained inverse problem, where we seek models of the Earth that reproduce the observed data while incorporating prior knowledge from geology, petrophysics, and complementary geophysical methods. In this talk, I will introduce the mathematical formulation of the geophysical inverse problem and discuss the strategies we use to tackle its inherent non-uniqueness and ill-posedness. I will also highlight current research directions, including how machine learning can be integrated with physics-based approaches, and show examples from applications in mineral exploration and environmental monitoring.

Talk Abstract: Not all of us will stay in academia. How do we prepare ourselves for the shift, especially when a lot of entry-level jobs have been replaced by AI? This is a discussion of life beyond academia and how to stay relevant as a math PhD in this competitive job market.

Talk Abstract: Sampling from complex probability distributions is a fundamental challenge in statistics and machine learning. When a target distribution is too complicated to sample from directly, annealing algorithms provide a solution: gradually transition from a simple, tractable distribution to the complex target through a sequence of intermediate annealing steps. This talk explores two complementary approaches to this problem: Sequential Monte Carlo and Parallel Tempering. We show how their performance depends on three key factors: the number of samples, the number of annealing steps, and the geometry of the probability distributions. Our main finding reveals a phase transition that determines when these algorithms work well and when they fail.

Talk Abstract: A maximum entropy method is described for estimating densities from quantum Monte Carlo simulations in high-energy physics. Standard approaches are prone to numerical overflow, limiting their reliability. We describe a dual self-scaling algorithm that is robust and efficient.

Talk Abstract: Quantifying the distribution of animals and understanding their movement behaviour is fundamental to their conservation. As such, ecologists increasingly collect movement data. However, characterising the distribution and behaviour of marine species is hindered by many formidable challenges. For example, marine species spend most of their life in areas difficult for us to reach (e.g., ocean depths), and many positioning systems (e.g., GPS) are not well-suited to the marine environment. Using species such as Arctic terns and narwhals, I will demonstrate how advanced statistical methods can improve our understanding of their ecology and inform management and conservation.

Talk Abstract: Accurate, robust and fast image reconstruction is a critical task in many scientific, industrial and medical applications. Deep learning is currently causing a revolution in modern image reconstruction, leading to powerful new techniques with seemingly breakthrough performance. In this talk, I will first briefly survey several different deep learning methodologies. Then I will highlight some of their pitfalls, in particular, their tendency to hallucinate – a serious problem for safety-critical applications such as healthcare. Finally, I will end with insights into how mathematics can help guarantee the robustness of deep learning-based methods.