Research

My research interests are in algebra and combinatorics, primarily in the representation theory of the symmetric groups and related algebras. My current research is studying the submodule structure of Specht modules for the symmetric groups in characteristic 2.

Works

• Kapadia, Zain Ahmed. “On the Submodule Structure of Hook Specht Modules in Characteristic 2 II” arXiv preprint arXiv:2410.19441 (2024)

• Kapadia, Zain Ahmed. “On the Submodule Structure of Hook Specht Modules in Characteristic 2” arXiv preprint arXiv:2405.02039 (2024)

• 4th Year Research Project "McKay Graphs and Representations of Finite Groups", Supervised by Prof. Martin Liebeck

Talks and Presentations

• "Some Uniserial Specht Modules"

  • • Junior Algebra and Combinatorics Seminar, University of Bristol, Jan 2025

    • Spring Term Seminar, Royal Holloway, University of London, Jan 2025

    • Junior Algebra and Representation Theory Seminar, University of Oxford, Dec 2024

• "On the Submodule Structure of Hook Specht Modules for the Symmetric Groups in Characteristic 2"

  • • 75th British Mathematical Colloquium, University of Manchester, Jun 2024

    • Symmetric Groups & Lie-theoretic friends, University of Birmingham, May 2024

    • PGR Day, Queen Mary University of London, May 2024

• "Algebra is Hard, Combinatorics is Simple(r)"

  • • Junior Algebra Seminar, University of Oxford, Mar 2024

    • QuIPS, Queen Mary University of London, Feb 2024

• "Introduction to Representation Theory of the Symmetric Groups"

  • • Junior Algebra and Number Theory Seminar, University of Cambridge, Mar 2023

    • QuIPS, Queen Mary University of London, Oct 2022

• "A gentle introduction to Category Theory." 

  • • QuIPS, Queen Mary University of London, Nov 2021

• A number of talks at Imperial College London’s Mathematics Undergraduate Colloquium, and WIMP (Warwick Imperial Mathematics Conference) on a variety of topics relating to algebra and pure mathematics (Sep 2014 - Aug 2019).

Teaching

Spring 2024:

• MTH4104 - Introduction to Algebra (TA)

Autumn 2023:

• MTH4113/MTH4213 - Numbers, Sets and Functions (TA)

Spring 2023:

• MTH4104 - Introduction to Algebra (TA)

• MTH6150 - Numerical Computing with C and C++ (Demonstrator)

Autumn 2022:

• MTH4114 - Computing and Data Analysis with Excel (TA)

Spring 2022:

• MTH4104 - Introduction to Algebra (TA)