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 of constant-cost communication complexity with algebraic circuit complexity.

As a founding member of the Association for Human Mathematics, I have pledged to no use large language models in any core research capacity.

Publications

1. Sign-Rank of k-Hamming Distance is Constant (FOCS 2025)
   with Mika Göös, Nathan Harms, and Dmitry Sokolov
   arχiv, ECCC, slides
   
   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.

2. Algebraic Complexity Approach to Sign-Rank (pre-print)
   with Mika Göös, Kaave Hosseini, and Anastasia Sofronova
   ECCC
   
   In a nutshell: In a particular algebraic setting, deciding whether two patterns combine to form a rectangle requires a lot of communication.

More information can be found on my Google Scholar page.

Talks

1. Communication and Topology (2026)
   A “5 minute talk” from Complexity as a Kaleidoscope 2026
   YouTube
   
   In a nutshell: Communication is hard because spheres can’t be squished into planes.

Once Upon a Time

1. Transfinite Context-Free Generative Grammars (2022)
   Cambridge Mathematical Tripos Part III Essay
   pdf
   
   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
   
   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