Liam Riordan

I am a PhD student at the University of Bath under the supervision of Xiuping Su. My research is centred around cluster algebras on Grassmannians, their quantum counterparts and the role of quiver Grassmannians in this picture. In fact any bit of maths containing the word Grassmannian is probably of great interest to me. Once I have some papers to display I will add a section for these below. If you are interested in any of the following topics then let me know:

• Coefficients of cluster characters and quantum cluster characters,
• the geometry of quiver Grassmannians (related to the above topic),
• cluster algebras and quantum cluster algebras in (homogeneous) coordinate rings of Lie-theoretic varieties.

Teaching

Currently teaching: Cryptography (CM30173).

In previous semesters I tutored either the first or second year algebra module in some various combinations. These modules are Algebra 1A, Algebra 1B, Algebra 2A and Algebra 2B. I am now tutoring Cryptography. For my cryptography students, here is the link to the code/notes from our tutorials. These will probably contain errors but could be helpful for you to look back over. I will try to update before each tutorial but given I often write them the evening before this may not always be true.

Miscellaneous

This page will probably collect some random odds and ends. For the moment, here is my github. Some of the projects in here are:

• KWIVAH is a python file which I have added to at various point so that it performs quiver/cluster computations for me. I will probably try to clean it up a bit at some point.
• XGvsNN is a python script which I wrote for a presentation to the Heilbronn summer school in 2022. It allows the user to plug in a function depending on two variables and then uses XGBoost and a Neural network to learn this function and plots the outcomes with corresponding errors.
• CM30173 is for my cryptography students but contains many related scripts. For example it contains an implementation of linear and differential cryptanalysis against SPN ciphers.
• Leclerc_Tilting is an algorithm described in section 4.8 of Leclerc's paper Cluster structures on strata of flag varieties which gives a cluster tilting object in his categorification of a postroid variety. Our code implements this algorithm for positroids in the Grassmannian by producing the two modules needed for the construction. See the read me for more details.