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Welcome to my homepage!
Welcome to my homepage!
I am a mathematician, working in group theory: the mathematics of symmetry. Here is my CV.
I am currently a Herchel-Smith Fellow at the DPMMS in Cambridge, working in Henry Wilton's group, as well as a Henslow Fellow of the Cambridge Philosophical Society based at Wolfson College.
Previously I did my PhD at ETH Zurich with Alessandra Iozzi (see my MGP).
In October 2026 I will start as an Assistant Professor at Heriot-Watt, in Edinburgh.
Non-sofic groups
On 1 August 2026, OpenAI announced the solution of 10 major open problems, including the first construction of a non-sofic group. The proof crucially relies on work of Kun and Kun--Thom to prove the technical Proposition 2.3, which shows that a certain configuration of property (T) and non-LEF groups are such that the container group cannot be sofic. This is then applied to a construction involving elementary matrices over the binary Leavitt algebra - which have (T) by work of Ershov--Jaikin-Zapirain - and Thompson's group V - which is not LEF.
Below is an alternative construction of groups in this configuration, which avoids Leavitt algebras and Thompson groups, and gives torsion-free examples. The introduction also contains some more comments about the solution.
A torsion-free non-sofic group, 4 pages.
The first version was added to this homepage in the evening of 1 August 2026, and should appear on the arXiv on 4 August 2026.
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