Edit about me + added new preprint

Author: jmarkakis

_data/publications.yml

@@ -43,6 +43,12 @@ published:
 
 preprints:
 
+  - title: A type theory for invertibility in weak \(\omega\)-categories
+    authors: Thibaut Benjamin, Camil Champin, Ioannis Markakis
+    date: 2026
+    arxiv : https://arxiv.org/abs/2602.16602
+    abstract: We present a conservative extension ICaTT of the dependent type theory CaTT for weak \(\omega\)-categories with a type witnessing coinductive invertibility of cells. This extension allows for a concise description of the "walking equivalence" as a context, and of a set of maps characterising \(\omega\)-equifibrations as substitutions. We provide an implementation of our theory, which we use to formalise basic properties of invertible cells. These properties allow us to give semantics of ICaTT in marked weak \(\omega\)-categories, building a fibrant marked \(\omega\)-category out of every model of ICaTT.
+
   - title: "Beyond Eckmann-Hilton: Commutativity in Higher Categories"
     authors: Thibaut Benjamin, Ioannis Markakis, Wilfred Offord, Chiara Sarti, Jamie Vicary
     date: 2025

_pages/index.md

@@ -3,4 +3,8 @@ permalink: /
 title: "About me"
 ---
 
-I am a Research Associate at the [Computer Lab](https://www.cst.cam.ac.uk/) of the [University of Cambridge](https://www.cam.ac.uk/), working with [Prof. Jamie Vicary](https://www.cl.cam.ac.uk/~jv258/). My research interests lie in the intersection of mathematics and theoretical computer science. I am working on higher category theory using ideas from logic and dependent type theory. I am interested in applications of higher categories to topology and to the semantics of programming languages. Moreover, I am interested in the homotopy theory of higher categories, in particular the comparison of different models, and the homotopy hypothesis for globular models.
+I am a Research Associate at the [Computer Lab](https://www.cst.cam.ac.uk/) of the [University of Cambridge](https://www.cam.ac.uk/), working with [Prof. Jamie Vicary](https://www.cl.cam.ac.uk/~jv258/). My research interests lie in the intersection of mathematics and theoretical computer science.
+
+I am working on higher category theory using ideas from logic and dependent type theory. I am interested in applications of higher categories to topology and to the semantics of programming languages. Moreover, I am interested in the homotopy theory of higher categories, in particular the comparison of different models, and Grothendieck's homotopy hypothesis for globular models.
+
+I am also interested in artificial intelligence and its applications to mathematics, particularly in topology and formalisation. I believe that ideas from type theory and category theory can be leveraged to build better systems, and I am exploring how these mathematical foundations can inform the design of more efficient and principled approaches in AI.