I am broadly interested in connections between mathematical logic and category theory, with an aim towards applications to computational complexity. My current research is on defining comonads that provide categorical semantics for logical and combinatorial (co)-resources. These comonads capture logical equivalences and combinatorial invariants of graphs/hypergraphs in a syntax-free, elegant, and compositional framework.
I completed my BA in pure Mathematics at University of California, Berkeley in 2015. I completed the MSc in Mathematics and Foundations of CS (MFocS) program with distinction in 2017.
I started my DPhil researching comonadic semantics for logical equivalence and graph-theoretic parameters in 2019. Between my masters and DPhil, I worked as a software engineer developing in Haskell and using the latest functional programming technologies/techniques. Outside of my research, I enjoy perfecting my skills in the kitchen and hiking in new high places.
Linear Arboreal Categories
Samson Abramsky‚ Yoàv Montacute and Nihil Shah
In CoRR. Vol. abs/2301.10088. 2023.
A game comonadic account of Courcelle and Feferman−Vaught−Mostowski theorems
Tomás Jakl‚ Dan Marsden and Nihil Shah
In CoRR. Vol. abs/2205.05387. 2022.
The Pebble−Relation Comonad in Finite Model Theory
Yoàv Montacute and Nihil Shah
In Christel Baier and Dana Fisman, editors, LICS '22: 37th Annual ACM/IEEE Symposium on Logic in Computer Science‚ Haifa‚ Israel‚ August 2 − 5‚ 2022. Pages 13:1–13:11. ACM. 2022.