Nihil Shah

I am a theoretical computer scientist and mathematician. My research explores the use of categorical semantics to provide new approaches to problems in mathematical logic, computational complexity, and quantum information. My first work along these lines were seminal contributions to the game comonads project. This project uses a categorical abstraction (comonads), successful in abstract algebra and programming language theory, to formalise a key technique in logic (model-comparision games). This project has been successful in formalising games for wide-range of logics and discovering new results relating combinatorial parameters with logical resources.

Currently, my work involves studying the piecewise algebraic structures ubiquitious in quantum information. In particular, I would like to understand computational complexity and geometry of various problems associated with these structures.

I am currently based at Cambridge University where I’m at Research Associate at the Department of Computer Science and Technology. I received my DPhil/PhD and MSc. from University of Oxford. I previously studied pure mathematics at University of California, Berkeley.

Nihil Shah Picture

Publications

Conference papers
  • 2024 — Mathematical Foundations of Programming Semantics (MFPS)
    Linear Arboreal Categories
    with Samson Abramsky, and Yoàv Montacute
    doi BibTeX Abstract
  • 2024 — Symposium on Logic in Computer Science (LICS)
    No Go Theorems: Directed Containers That Do Not Distribute Over Distribution Monads
    with Amin Karamlou
    doi BibTeX Abstract
  • 2023 — Symposium on Logic in Computer Science (LICS)
    A Categorical Account of Composition Methods in Logic
    with Tomáš Jakl, and Dan Marsden
    doi BibTeX Abstract
  • 2022 — Symposium on Logic in Computer Science (LICS)
    The Pebble-Relation Comonad in Finite Model Theory
    with Yoàv Montacute
    doi BibTeX Abstract
  • 2018 — Computer Science Logic (CSL)
    Relating Structure and Power: Comonadic Semantics for Computational Resources
    with Samson Abramsky
    doi BibTeX Abstract
Journal papers
  • 2025 — Logical Methods in Computer Science (LMCS)
    A Categorical Account of Composition Methods in Logic
    with Tomáš Jakl, and Dan Marsden
    doi BibTeX Abstract
  • 2024 — Logical Methods in Computer Science (LMCS)
    The Pebble-Relation Comonad in Finite Model Theory
    with Yoàv Montacute
    doi BibTeX Abstract
  • 2021 — Journal of Logic and Computation (JLC)
    Relating Structure and Power: Comonadic Semantics for Computational Resources
    with Samson Abramsky
    doi BibTeX Abstract

Teaching & Mentorship

University of Cambridge
  • Lent 2024 - Topics in Logic in Complexity
University of Oxford
  • Michaelmas 2023 - Algorithms and Complexity
  • Trinity 2021 - Logic and Proof
  • Michaelmas 2021 - Categories, Proofs and Processes
  • Michaelmas 2020 - Functional Programming
Other
  • TA for Game Comonads in Finite Model Theory research project at Adjoint School 2023
  • Spring 2016 - Marker for Philosphical Logic at UC Berkeley

Talks and news