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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Nihil Shah | Mathematician</title>
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<body>
<div class="container">
<header class="row" style="margin-top: 4rem; margin-bottom: 2rem; text-align: center;">
<div class="six columns">
<h2 style="margin-bottom: 0;">Nihil Shah</h2>
<nav>
<a href="./">Home</a> |
<a href="./files/cv.pdf" target="_blank">CV (PDF)</a> |
<a href="mailto:me@nihil.io">Email</a>
</nav>
</div>
<div class="five columns social-links">
<a href="https://orcid.org/0000-0003-2844-0828" title="ORCID"><i class="fab fa-orcid"></i></a>
<a href="https://scholar.google.com/citations?hl=en&user=GFfwRwYAAAAJ" title="Google Scholar"><i class="fas fa-graduation-cap"></i></a>
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</header>
<hr>
<div class="row about-container">
<div class="eight columns about-text">
<p>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.</p>
<p>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.</p>
<p>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.</p>
</div>
<div class="three columns">
<img src="./images/profile.jpg" alt="Nihil Shah Picture" class="profile-pic">
</div>
</div>
<hr>
<div class="row section">
<div class="twelve columns">
<h4>Publications</h4>
<h5>Conference papers</h5>
<ul class="pub-list">
<li class="pub-item">
<div class="pub-meta">
<span class="pub-year">2024</span> — <span class="pub-venue">Mathematical Foundations of Programming Semantics (MFPS)</span>
</div>
<div class="pub-title">Linear Arboreal Categories</div>
<div class="pub-info">
<div class="pub-authors">with Samson Abramsky, and Yoàv Montacute</div>
<div class="pub-actions">
<a href="https://doi.org/10.46298/entics.14830" class="button button-primary acad-btn" target="_blank">
<i class="fas fa-link"></i>doi
</a>
<a href="./files/bib/linear_arboreal.bib" class="button acad-btn" download>
<i class="fas fa-quote-right"></i> BibTeX
</a>
<a href="./files/abstract/linear_arboreal.txt" class="button acad-btn" target="_blank">
<i class="fas fa-align-left"></i> Abstract
</a>
</div>
</div>
</li>
<li class="pub-item">
<div class="pub-meta">
<span class="pub-year">2024</span> — <span class="pub-venue">Symposium on Logic in Computer Science (LICS)</span>
</div>
<div class="pub-title">No Go Theorems: Directed Containers That Do Not Distribute Over Distribution Monads</div>
<div class="pub-info">
<div class="pub-authors">with Amin Karamlou</div>
<div class="pub-actions">
<a href="https://doi.org/10.1145/3531130.3533335" class="button button-primary acad-btn" target="_blank">
<i class="fas fa-link"></i>doi
</a>
<a href="./files/bib/no_go.bib" class="button acad-btn" download>
<i class="fas fa-quote-right"></i> BibTeX
</a>
<a href="./files/abstract/no_go.txt" class="button acad-btn" target="_blank">
<i class="fas fa-align-left"></i> Abstract
</a>
</div>
</div>
</li>
<li class="pub-item">
<div class="pub-meta">
<span class="pub-year">2023</span> — <span class="pub-venue">Symposium on Logic in Computer Science (LICS)</span>
</div>
<div class="pub-title">A Categorical Account of Composition Methods in Logic</div>
<div class="pub-info">
<div class="pub-authors">with Tomáš Jakl, and Dan Marsden</div>
<div class="pub-actions">
<a href="https://doi.org/10.1109/LICS56636.2023.10175751" class="button button-primary acad-btn" target="_blank">
<i class="fas fa-link"></i>doi
</a>
<a href="./files/bib/categorical_fvm_conference.bib" class="button acad-btn" download>
<i class="fas fa-quote-right"></i> BibTeX
</a>
<a href="./files/abstract/categorical_fvm.txt" class="button acad-btn" target="_blank">
<i class="fas fa-align-left"></i> Abstract
</a>
</div>
</div>
</li>
<li class="pub-item">
<div class="pub-meta">
<span class="pub-year">2022</span> — <span class="pub-venue">Symposium on Logic in Computer Science (LICS)</span>
</div>
<div class="pub-title">The Pebble-Relation Comonad in Finite Model Theory</div>
<div class="pub-info">
<div class="pub-authors">with Yoàv Montacute</div>
<div class="pub-actions">
<a href="https://doi.org/10.1145/3531130.3533335" class="button button-primary acad-btn" target="_blank">
<i class="fas fa-link"></i>doi
</a>
<a href="./files/bib/pebble_relation_comonad_conference.bib" class="button acad-btn" download>
<i class="fas fa-quote-right"></i> BibTeX
</a>
<a href="./files/abstract/pebble_relation_comonad.txt" class="button acad-btn" target="_blank">
<i class="fas fa-align-left"></i> Abstract
</a>
</div>
</div>
</li>
<li class="pub-item">
<div class="pub-meta">
<span class="pub-year">2018</span> — <span class="pub-venue">Computer Science Logic (CSL)</span>
</div>
<div class="pub-title">Relating Structure and Power: Comonadic Semantics for Computational Resources</div>
<div class="pub-info">
<div class="pub-authors">with Samson Abramsky</div>
<div class="pub-actions">
<a href="https://doi.org/10.4230/LIPIcs.CSL.2018.2" class="button button-primary acad-btn" target="_blank">
<i class="fas fa-link"></i>doi
</a>
<a href="./files/bib/relating_structure_and_power_conference.bib" class="button acad-btn" download>
<i class="fas fa-quote-right"></i> BibTeX
</a>
<a href="./files/abstract/relating_structure_and_power.txt" class="button acad-btn" target="_blank">
<i class="fas fa-align-left"></i> Abstract
</a>
</div>
</div>
</li>
</ul>
<h5>Journal papers</h5>
<ul class="pub-list">
<li class="pub-item">
<div class="pub-meta">
<span class="pub-year">2025</span> — <span class="pub-venue">Logical Methods in Computer Science (LMCS)</span>
</div>
<div class="pub-title">A Categorical Account of Composition Methods in Logic</div>
<div class="pub-info">
<div class="pub-authors">with Tomáš Jakl, and Dan Marsden</div>
<div class="pub-actions">
<a href="https://doi.org/10.46298/lmcs-21(4:10)2025" class="button button-primary acad-btn" target="_blank">
<i class="fas fa-link"></i>doi
</a>
<a href="./files/bib/categorical_fvm_journal.bib" class="button acad-btn" download>
<i class="fas fa-quote-right"></i> BibTeX
</a>
<a href="./files/abstract/categorical_fvm.txt" class="button acad-btn" target="_blank">
<i class="fas fa-align-left"></i> Abstract
</a>
</div>
</div>
</li>
<li class="pub-item">
<div class="pub-meta">
<span class="pub-year">2024</span> — <span class="pub-venue">Logical Methods in Computer Science (LMCS)</span>
</div>
<div class="pub-title">The Pebble-Relation Comonad in Finite Model Theory</div>
<div class="pub-info">
<div class="pub-authors">with Yoàv Montacute</div>
<div class="pub-actions">
<a href="https://doi.org/10.46298/lmcs-20(2:9)2024" class="button button-primary acad-btn" target="_blank">
<i class="fas fa-link"></i>doi
</a>
<a href="./files/bib/pebble_relation_comonad_journal.bib" class="button acad-btn" download>
<i class="fas fa-quote-right"></i> BibTeX
</a>
<a href="./files/abstract/pebble_relation_comonad.txt" class="button acad-btn" target="_blank">
<i class="fas fa-align-left"></i> Abstract
</a>
</div>
</div>
</li>
<li class="pub-item">
<div class="pub-meta">
<span class="pub-year">2021</span> — <span class="pub-venue">Journal of Logic and Computation (JLC)</span>
</div>
<div class="pub-title">Relating Structure and Power: Comonadic Semantics for Computational Resources</div>
<div class="pub-info">
<div class="pub-authors">with Samson Abramsky</div>
<div class="pub-actions">
<a href="https://doi.org/10.1093/logcom/exab048" class="button button-primary acad-btn" target="_blank">
<i class="fas fa-link"></i>doi
</a>
<a href="./files/bib/relating_structure_and_power_journal.bib" class="button acad-btn" download>
<i class="fas fa-quote-right"></i> BibTeX
</a>
<a href="./files/abstract/relating_structure_and_power.txt" class="button acad-btn" target="_blank">
<i class="fas fa-align-left"></i> Abstract
</a>
</div>
</div>
</li>
</ul>
</div>
</div>
<hr>
<div class="row section">
<div class="six columns">
<h4>Teaching & Mentorship</h4>
<div class="news-box">
<h5 id="university-of-cambridge">University of Cambridge</h5>
<ul>
<li>Lent 2024 - Topics in Logic in Complexity</li>
</ul>
<h5 id="university-of-oxford">University of Oxford</h5>
<ul>
<li>Michaelmas 2023 - Algorithms and Complexity</li>
<li>Trinity 2021 - Logic and Proof</li>
<li>Michaelmas 2021 - Categories, Proofs and Processes</li>
<li>Michaelmas 2020 - Functional Programming</li>
</ul>
<h5 id="other">Other</h5>
<ul>
<li>TA for Game Comonads in Finite Model Theory research project at <a href="https://adjointschool.com/2023.html">Adjoint School 2023</a></li>
<li>Spring 2016 - Marker for Philosphical Logic at UC Berkeley</li>
</ul>
</div>
</div>
<div class="six columns">
<h4>Talks and news</h4>
<div class="news-box">
<ul>
<li>27-29 May 2026 - University College London, Attending the <a href="https://aminkaramlou.github.io/ric/">Workshop on Resources and Computation</a></li>
<li>20 Mar 2026 - University of Cambridge, <a href="https://talks.cam.ac.uk/talk/index/246703/">Talk (Logic & Semantics Seminar)</a> on partial Boolean algebras</li>
<li>20 Feb 2026 - University of Birmingham, <a href="https://researchseminars.org/talk/TheoryCSBham/70/">Invited Talk (Theory Seminar)</a> on mixed distributive laws</li>
</ul>
</div>
</div>
</div>
<hr>
<footer class="row" style="margin-top: 5rem; padding-bottom: 2rem; color: #7f8c8d; font-size: 1.2rem;">
<div class="twelve columns">
<p>© 2026 Nihil Shah. Created with Hakyll and Skeleton CSS.</p>
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