Mark Lyttle (He/Him)

Current Research:

Topics in Tensor-Triangular Geometry

Tensor-triangular geometry is the study of tensor-triangulated (tt-)categories, which are categories that are triangulated and have a compatible symmetric monoidal structure. This is an analogous concept to the addition and multiplication of a commutative ring, so one could therefore say that a tt-category is a categorification of a commutative ring. This analogy runs deeper, concepts like the Zariski spectrum and localisation from commutative ring theory extend to the realm of tt-categories. Some examples of tt-categories are the stable homotopy category and the derived category of a commutative ring.

Biography:

I graduated from Queen’s University Belfast in July 2024 with an MMath Mathematics degree, being awarded the A.C. Dixon and Burgess prizes for having the best marks in pure mathematics and topology respectively. For my master’s dissertation I studied commutative algebra, so I am looking forward to utilising some of the classical results from my dissertation and applying them to the new and exciting research area that is tensor-triangular geometry.

Research Interests:

• Tensor-Triangular Geometry
• Spectral Spaces
• Commutative Algebra

Pure:

https://pure.qub.ac.uk/en/persons/mark-lyttle 

Supervisor:

Dr. Scott Balchin