1.2   Research

I am part of Theory Lab 5 at EDIC, the computer science department of EPFL, where I am a doctoral candidate under Mika Göös. Our group works on concrete complexity theory, where we ask things like

• Query Complexity: How many questions does one need to ask to determine … ?
• Communication Complexity: How much talking is required to jointly solve … ?
• Circuit Complexity: How small is the smallest machine that computes … ?
• Proof Complexity: How long is the shortest proof of … ?

At the moment, I am specifically interested in the interaction between constant-cost communication complexity and algebraic circuit complexity.

Publications

1. Sign-Rank of k-Hamming Distance is Constant (FOCS 2025)
   with Mika Göös, Nathan Harms and Dmitry Sokolov.
   arχiv, ECCC, slides
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   In a nutshell: Two ants on a cube can determine if they are very close to each other using way less communication than was previously believed.

More information can be found on my Google Scholar page.

Once Upon a Time

1. Transfinite Context-Free Generative Grammars (2022)
   Cambridge Mathematical Tripos Part III Essay
   pdf
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   In a nutshell: A certain classical characterisation of languages can be generalised to languages with words of infinite length

2. On the Probabilistic Method and Permutations (2019)
   High School Graduation Project
   pdf, poster
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   In a nutshell: It is surprisingly useful to use randomness in the proofs of statements that are entirely deterministic.

Other Research Interests

• Reverse mathematics & new foundations
• Model theory & non-standard analysis
• Large cardinal axioms & incompleteness
• Computer formalisation & automated theorem proving

I am also loosely affiliated with a research effort led by Timothy Gowers on Human Oriented Automated Theorem Proving