I'm Sam Mellick.

We are organising a conference at Jagiellonian University: Perspectives In Ergodic Theory RandOmness and GeometrY (PIEROGY). It will take place from the twelfth to the sixteenth of January in 2026. Click the link to register and find out more!

Critically important cultural information: Pierogi are a kind of dumpling Poland is famous for.

1. Unimodular random graphs with Property (T) have cost one, joint with Łukasz Grabowski and Héctor Jardón-Sánchez. See arXiv (submitted)
2. Exactness and the topology of the space of invariant random equivalence relations, joint with Héctor Jardón-Sánchez, Antoine Poulin, and Konrad Wrobel. See arXiv (submitted)
3. Indistinguishability of cells for the ideal Poisson Voronoi tessellation, solo dolo. See arXiv (to appear in Proceedings of the AMS)
4. Gaboriau's criterion and fixed price one for locally compact groups, solo dolo. See arXiv (to appear in Transactions of the AMS)
5. Poisson-Voronoi tessellations and fixed price in higher rank, joint with Mikolaj Fraczyk and Amanda Wilkens. See arXiv (submitted -- can you guess where?)
6. On the Existence of Balancing Allocations and Factor Point Processes, joint with Ali Khezeli. See arXiv (to appear in ALEA)
7. Point processes, cost, and the growth of rank in locally compact groups, joint with Miklós Abért. See arXiv (published in Israel Journal of Mathematics).
8. The Palm groupoid of a point process and factor graphs on amenable and Property (T) groups , solo dolo. See arXiv (to appear in a forthcoming survey on the connection between connected Cayley factor graphs and measure equivalence)

Recently I cotaught a minicourse at the IHES on my work around fixed price. You can find the first video here and the (very incomplete!) exercise sheets here. Feel free to contact me if you have any questions (particularly about the exercises).

A lot. What can I say? I get around. IHES, Centre de Recherches Mathématiques, Centre International de Rencontres Mathématiques, Université Paris Cité...
Tumbleweed...
Computing the cost on nondiscrete groups with factors of IID @ UT Austin Groups and Dynamics online seminar (watch on YouTube)
Visualising actions, computing cost, and fixed price for G x Z @ “Descriptive Dynamics and Combinatorics” of McGill University (slides)
The cost of point processes, invited guest @ DYOGENE Project of Centre Inria de Paris.
Point processes on groups, their cost, and fixed price for G x Z @ Ergodic and Geometric Group Theory of École Polytechnique Fédérale de Lausanne

I'm a big fan. If you want to simulate a conversation with me, tell your favourite LLM to poorly summarise one of its articles considered unusual. I reckon their list of common misconceptions should be a mandatory part of the school curriculum, too.