Past Talks

• Jack Heaney (University of Edinburgh) 13/04/26

Title: Monoids, Categories, and Presentability 

Abstract: A change happened in the mid 20th Century to the field of Algebraic Topology, with the advent of categorical techniques championed by Dan Quillen. And so the Model Category was born, a tool for practicing Homotopy Theory in an algebraic way, allowing for the technical gadget of the Homotopy Category to be better controlled. In the beginning of the 21st Century Jeffery Smith refined Quillen's definition (to a Combinatorial Model Category) with the main addition being a size controlling property, local presentability. In this talk I will speak about ideas from my master's thesis, 'Differential Graded Algebras and their Model Structure', my focus will be to elucidate a very useful theorem which allows us to deduce local presentability of one category from another by leveraging 2-categorical limits.  I will deliver motivation and background to Symmetric Monoidal Categories, with the main example of chain complexes of vector spaces, as well as their categories of monoid objects and how this is related to algebras for an endofunctor.

• Susanna Terron (University of Glasgow) 16/03/26

Title: Constructing Thompson representatives 

Abstract: In 2017 Vaughan Jones introduced a construction associating links to elements of Thompson’s group F and its generalisation F3. He then proved that all links can be obtained in such a way, opening the way to new possible connections between these objects. In this talk I will present Jones’ construction and extend it to obtain a surjective map into the set of pointed links. I’ll then define a new algebraic structure by endowing F3 with a monoid operation, which turns our map into a surjective monoid homomorphism. As a consequence, we obtain a standard form for connected sum representatives, which can then be extended to obtain representatives for a certain family of links that we will refer to as tree links.  

• Ludovico Dziecielski (University of Aberdeen) 16/02/26

Title: Categorification of the Adams spectral sequence  

Abstract: The Adams spectral sequence is a fundamental tool in stable homotopy groups. Many of the most famous computations of stable homotopy groups of spectra rely on this technical machinery. In this talk I will give an introduction to the Adams spectral sequence following a new \infty- categorical approach developed by Piotr Pstragowski and Irakli Patchkoria. This approach allows us to study the Adams spectral sequences in a categorically rich environment. Furthermore, we will see that, in this context, the spectral sequence naturally arises as a generalisation of injective resolutions to stable categories.

• Jakub Hampl (University of Aberdeen) 02/02/2026

Title: Vanishing homology of the Temperley-Lieb algebra on an odd number of strands.

Abstract: This talk closely follows a paper of Robin J. Sroka on the homology of a Temperley-Lieb algebra on an odd number of strands. The key is to construct a certain nice chain complex, called the cellular Davis complex of a Temperley-Lieb algebra, and to then study spectral sequences attached to it. This approach has been generalised and further developed in a recent preprint by Boyd - Boyde - Randal-Williams - Sroka, which studies the even Temperley-Lieb algebras. I will introduce the Temperley-Lieb algebras and define homology for augmented algebras, and then I'll move on to proving the main result. If I have time at the end, I will deduce that Temperley-Lieb algebras satisfy homological stability. 

• Daniel Sölch (University of Aberdeen) 09/12/2025

Title: Representation cohomology of a small category 

Abstract: I will present current research of Ran Levi, Markus Klemetti, Henri Riihimäki, and I establishing a framework for differential calculus on modules over small categories.