I work in category theory and logic and I am especially interested in the interplay of logic, category theory, and algebraic topology, such as in synthetic homotopy theory. I have studied topos theory, internal languages and categorical semantics to enhance our understanding of the relationships between logic, type theory and homotopy theory, and make new bridges between these disciplines.
My other research interests include programming languages, verification, formalization of mathematics, and machine learning.
I advocate interdisciplinary approaches in research in mathematics, logic, and computer science.
I was born in Qeshm Island in Iran. I have lived in the USA, Netherlands, UK, Canada, and Iran. I speak English, Dutch, and Persian.
Academic Profile
I am currently a postdoctoral research fellow in Emily Riehl’s group at the Department of Mathematics of the Johns Hopkins University. My current research focuses on the burgeoning field of synthetic homotopy theory. I am interested in exploring the application of methods from synthetic homotopy theory in simplicial, cubical, equivariant homotopy theory, and K-theory. I am also working on formalization of Reedy categories in the Lean proof assistant.
From Nov 2019 until Nov 2020, I was a Research Fellow at the University of Leeds Logic group working on the project Univalent type theories: models, equalities, and coherence in collaboration with Nicola Gambino (University of Manchester, formerly at Leeds) and Steve Awodey (Carnegie Mellon University) to develop a Kripke-Joyal style forcing semantics for Homotopy Type Theory. This semantics extends the usual Kripke-Joyal Semantics for IHOL (Higher Order Intuitionistic Logic) in toposes.
I earned my PhD in theoretical computer science from University of Birmingham under supervision of Steve Vickers. My PhD thesis investigated the bicategorical aspects of classifying toposes arising from the stricter syntactical aspects of a subclass of essentially algebraic theories corresponding to the logic of Arithmetic Universes. My thesis studies point-free generalized spaces (modeled by Grothendieck toposes over varying bases) under the three principles of geometricity, predicativity, and base-independence. More on this in my research profile. It was examined by Peter Johnstone and Martín Escardó.
Prior to joining Birmingham I was at Western University in London (Canada) where I did my masters in pure mathematics. I learnt intuitionistic logic and topos theory from John Lane Bell – In fact, I first heard about topos theory and intuitionistic logic in his classical philosophy of mathematics course.) I also learnt differential geometry from Martin Pinsonnault.
Other interests
I play football (soccer, for my American audience) as a midfielder. I go hiking for long hikes. I am fond of remote places in the mountains. And I like to go to Arts museums.
I am an avid reader of philosophy and history and enjoy discussing them. If you ever have the misfortune of talking to me about a non-math subject, you likely hear the word “Nietzsche” more than once. The fourfold works of Nietzsche (Thus Spoke Zarathustra), Heidegger (Being and Time), Foucault (The Order of Things), and Sloterdijk (Critique of Cynical Reason) have influenced my thinking.
The best novel I have read thus far is Robert Musil’s “Der Mann ohne Eigenschaften” from 1921. Musil’s wit is unsurpassable, and he understood the human condition in modernity like no other being.
Another interest of mine is the history of mathematics, in particular the history of the foundation and practice of mathematics in 19th and early 20th century. This includes Frege’s logicism, Dedekind’s foundational work in algebra and arithmetic, Klein’s Erlangen Program in geometry, Husserl’s phenomenology of mathematical thinking, and the formalist project of Hilbert and the ensuing axiomatic (re)turn in mathematics. These movements, specially the last one, find a strong reaction in Brouwer’s intuitionism, Weyl’s predicativism and his mediation between intuitionism and formalism, and Cassirer’s structuralist account of mathematical knowledge. You can read more here. Occasionally, I write some of my thoughts on range of issues of philosophical nature on my blog.