A sample of some specific interests:

• Importance sampling ∩ Markov chain Monte Carlo: IS is often viewed as a classical, somewhat “naive” method that struggles with complex problems such as high dimensions. Yet it remains central to applications ranging from Boltzmann generators and LLM training to estimating rare outputs of generative models. More advanced methods, such as Sequential Monte Carlo, are fundamentally based on IS. I remain interested in the mathematical properties of IS estimators: when they can work in high dimensions, which population- and sample-based metrics are appropriate, how they behave with infinite variance or heavy-tailed targets, and how combinations such as MCMC-IS can be understood. Ultimately, MC methods are used wherever an accurate answer matters, and understanding how much an answer can be trusted requires mathematics.
• Monte Carlo ∩ generative models: What is the role of Monte Carlo methods in understanding the properties of generative models, like LLMs, diffusion models, etc.? For instance, we have been working on estimating probabilities of rare outputs in masked diffusion language models.
• …and adjacent ideas: I like continuosly learning new concepts from neighbouring fields. There are so many interesting ideas still to explore!

Please do not hesitate to contact me for talking about research.