Dr José Siqueira

Dr José Siqueira

BA MASt PhD

  • Position Bye Fellow
  • School Physical Sciences Department of Pure Mathematics and Mathematical Statistics
  • Personal website José Siqueira
  • Email jvp27@cam.ac.uk

Dr Siqueira is a mathematician working on the Foundations of Mathematics, particularly Category Theory and its relationship to Logic, Geometry, and Computation. Other interests include facets of mathematical thinking and how its understanding affects education, sciences, and languages (broadly construed).

Dr José Siqueira

After completing an undergraduate degree in mathematics in Brazil (with one year abroad at the University of Bristol), José moved to Cambridge to undertake Part III of the Mathematical Tripos, followed by a PhD at the Department of Pure Mathematics and Mathematical Statistics. He specialises in Category Theory, a subject classed as part of the Foundations of Mathematics. His research revolves around the abstract theory of distributive laws and categorifications of nonstandard proof methods (in the sense of nonstandard analysis).

Dr Siqueira has been lecturing in Part III of the Mathematical Tripos since Lent 2022 and acted as a College Lecturer and Director of Studies in Mathematics for Gonville & Caius from 2022 to 2024. He was also a Director of Studies for St Edmund's College (where he remains a Director of Studies and Associate Tutor) and Lucy Cavendish College before joining Wolfson in 2024.

2022: Doctor of Philosophy, University of Cambridge
2016: Master of Advanced Study in Pure Mathematics, University of Cambridge
2014: Bachelor of Mathematics, University of Brasília

The relationship between what we describe and the language that we use to do so is at the core of Logic as a discipline. The tools of category theory facilitate its study in two main ways: we can admit a richer semantics for our languages (by meaningfully interpreting symbols as something other than just sets and functions), and we can treat syntax and semantics on equal grounds, as both are just instances of categories. One of Dr Siqueira's research interests is in using modern ideas in categorical logic to gain insight on complicated logical phenomena by providing adequate categorical models. An ongoing project concerns understanding and expanding the scope of nonstandard proof techniques, singling out the structure needed in order for the proof principles of nonstandard analysis to be valid inside a `topos' --- a mathematical environment that may have a different underlying logic than what you are used to, but that is nonetheless useful and consistent.

Another facet of his work concerns the abstract theory of distributive laws. Everyone is familiar with the fact that multiplication distributes over addition --- category theorists generalised this by introducing the formalism of distributive laws between monads. These are useful because they systematically allow one to combine two different sorts of `algebraic theories' to obtain a new one in a nontrivial way. Dr Siqueira's research on this topic revolves around generalisations of this idea that allow one to merge streams of data that are not necessarily algebraic in origin.

What's on

A person holds a glowing light bulb filled with fairy lights in their cupped hands, against a dark and blurred background.

Wolfson Entrepreneurship Competition Final 2025

22/03/2025 at 10.00

Discover groundbreaking ideas and cutting-edge solutions as Cambridge’s brightest entrepreneurial minds compete for prizes over £10,000.

View more
An abstract painting dominated by vibrant blue, featuring intricate white scribbles and textured drips of green, orange, and red, creating a layered and dynamic composition.

Art Exhibition: 'Feel the Rhythm'

22/03/2025 at 10.00

Visit Wolfson's latest exhibition 'Feel the Rhythm' featuring work by emerging artist Fungai Benhura, winner of the Wolfson Royal Academy Schools Graduate Prize.

View more
A man with a shaved head, wearing a striped blazer over a patterned shirt, smiles slightly while leaning against a brick wall.

Medical Society Dinner 2025

22/03/2025 at 19.00

As Wolfson celebrates 60 years, we are excited to invite you to a special dinner in honour of this significant milestone.

View more
A photo of the choir in the College gardens.

Lent Term Concert: Myths and Legends

23/03/2025 at 18.00

As part of Wolfson’s 60th Anniversary celebrations, the College Choir and Alumni Choir, directed by Lyn Alcántara, present an evening of choral works inspired by the fantastical.

View more
Graduands wearing black gown with white shirts and bows stand together for a group photograph

Graduation Ceremony

29/03/2025 at 09.00

Graduation ceremonies are the culmination of students’ hard work and commitment, and a moment to celebrate the completion of their Cambridge degree.

View more
Show all

News

Show all