I am a mathematician working in the foundation of mathematics and its connection to theoretical computer science. My main research interests include category theory and categorical logic, type theory, and higher category theory. I am also interested in applications of these areas to topology and algebraic topology. On the side, I recently started to learn more about topological data analysis and persistent homology.
I was born in Qeshm Island in Iran. I have lived in the US, Netherlands, UK, Canada, and Iran. I speak English, Dutch, and Persian.
I am currently a postdoctoral research fellow at the Department of Mathematics of the Johns Hopkins University. My PI is Emily Riehl. Our project is within the burgeoning field of (constructive) synthetic homotopy theory.
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 Prof. Nicola Gambino (University of Leeds) and Prof. 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.
Before that I was a PhD student in Theoretical Computer Science at the University of Birmingham under supervision of Prof. Steve Vickers . My PhD thesis investigated the bicategorical aspects of topos theory arising from the 2-categorical aspects of certain essentially algebraic theories corresponding to the logic of Arithmetic Universes. The idea was to carve out from the 2-category of Grothendieck toposes (over varying bases) the part that corresponds to the logic of Arithmetic Universes (finitary plus free algebras by means of list objects). It was examined by Prof. Peter Johnstone and Prof. Martín Escardó. The main contribution of my thesis was a study 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.
Prior to joining Birmingham I was at Western University in London (Ontario) where I did my masters in pure mathematics. I learnt intuitionistic logic and topos theory from John Bell (In fact, I first heard about topos theory and intuitionistic logic in his amazing philosophy of mathematics course.) I also learnt differential geometry from Martin Pinsonnault.
I am fond of remote places in nature, museums, hiking, and photography. I run a lot and I play football (for my American readers, this means soccer). I am an avid reader of philosophy and history of philosophical thoughts and enjoy discussing them. The fourfold Nietzsche (Thus Spoke Zarathustra), Heidegger (Being and Time), Foucault (The Order of Things), and Sloterdijk (Critique of Cynical Reason) have made the most impact on my thinking.
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.