I am a mathematician working in the foundation of mathematics and its connection to theoretical computer science. My main research interests include constructive mathematics and type theory, category theory and categorical logic, and higher category theory. I am also interested in applications of these areas to topology and algberaic 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 Iran, Canada, UK, and the Netherlands. I speak Persian, English, and Dutch.
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. Here is my page at Leeds: https://eps.leeds.ac.uk/maths/staff/6531/dr-sina-hazratpour
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 was about some of 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 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, related to the history of mathematics, is the history of the foundation and practice of mathematics in 19th and early 20th century. This includes for example Dedekind’s foundational work in algebra and arithmetic, Klein’s Erlangen Program in geometry, Frege’s logicism, Husserl’s phenomenology of mathematical thinking, the Formalism project of Hilbert and the ensuing axiomatic (re)turn in mathematics, 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. Ocassionally, I will write some of my thoughts on range of issues of philosphical nature on my blog.