Dr Ittay Weiss
I'm a Senior Lecturer in Mathematics with research interests in topology and category theory.
I am a Senior Lecturer in the School of Mathematics and Physics at the University of Portsmouth. I studied Mathematics at the Hebrew University where I completed my BSc and my MSc, and then continued to pursue a PhD in Mathematics at Utrecht University under the supervision of Prof. Ieke Moerdijk. Upon completion of my PhD I worked for a short while as an actuarial advisor and promptly returned to academia as an Assistant Professor of Mathematics at Utrecht University on a three year contract. I then joined the University of the South Pacific as a Lecturer in Mathematics, where I was later promoted to Senior Lecturer, before joining the University of Portsmouth department of mathematics.
My research is concentrated in three areas of study: homotopy theory, general topology, and category theory. My homotopy theory research involves the study of algebraic structures called operads, which are of fundamental importance in algebraic topology (and other areas). During my PhD, under the guidance of Professor Ieke Moerdijk, I developed the theory of dendroidal sets, which forms a generalisation of simplicial sets. The theory of dendroidal sets is still gaining momentum quickly as a central technique in operad theory. My main interest in the area is the problem of the geometric realisation of dendroidal sets.
In general topology, I am interested in the feasibility and utility of a metric formalism due to Flagg. While it is well-known that not every topological space is metrisable, in 1997 Flagg (building on earlier work of Kopperman) introduced the notion of value quantale and proved that every topological space is metrisable, provided the axioms are suitably weakened and the distance function is allowed to take values in a value quantale. It turns out that in a precise sense Flagg's formalism is equivalent to classical topology, raising the question how useful Flagg's metric formalism is. Since 2012, I have been applying the metric formalism in general topology, showing the formalism is quite useful.
Lastly, the notion of generalised inverse limit in topology was introduced by Ingram and Mahavier in 2006, and quickly received much attention due to the natural framework it offers, its elegance, and its applicability in dynamics and mathematical economy. The concept is a generalisation of the inverse limit of an inverse system, a concept well-known to be a specific instance of the notion of limit in a category. I am developing a category theoretic formalism, and extension of the usual one, in order to fully re-establishing the link with category theory. I am interested in further developing the category theoretic notions, fuelled by phenomena in classical generalised inverse limits, as well as in applying categorical techniques for solving classical problems in the field.
I have taught modules across most of the spectrum of the undergraduate curriculum (from introductory mathematics, calculus, and linear algebra to logic, set theory, and Galois theory) as well as postgraduate modules in metric geometry and topology. Prior to joining the University of Portsmouth I had taught Mathematics in three different universities, using three different languages, catering to students of various backgrounds. I am interested and involved in curriculum improvements and re-design, seeking to employ new technology for the benefit of learners and teachers. I designed and wrote an advanced calculus module for the Saylor Foundation (US based non-profit organisation). I am also the co-author of the Springer undergraduate textbook "A Primer on Hilbert Space Theory".