About me

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Hi! My name is Aahana, and I am currently a first year PhD student in mathematics at the University of Warwick. My supervisor is Dr. Gareth Tracey, and I am working on some bounds of the Chebotarev invariant of (finite) almost simple groups. I am generally interested in all things related to groups, but I tend to lean (haha!) towards the finite side.

I did my bachelor's in maths from IISER Bhopal and my master's from Imperial College London.

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Projects

• Master's Thesis: On the Orbital Diameter of the action of PSL_2(q) on the cosets of its maximal dihedral subgroups

  2026

  The aim of the project is to bound the orbital diameter of this action. The techniques differ for the even and odd characteristic case, and the diameter has been succesfully calculated for the even one. The idea is to identify the coset actions with equivalent ones described by quadratic and bilinear forms to better understand what the orbitals actually look like, thus simplifying the computations.

• Lean codes

  2026

  At some point I will add my Lean codes here. These were three simple projects for my coursework, respectively on the generators of SL_2(Z), binary quadratic forms, and some preliminaries of my master's thesis. I intend to polish them up a bit before leaving them here.

• Amalgams of p-groups

  2024

  The study of automorphism groups heavily uses first order logic and model theory as they provide tools that can work with an infinite class of structures. One such tool is the Fraissé limit, which, from a class of finite structures, gives a unique countable homogeneous structure whose finite substructures are exactly that class, provided they satisfy certain properties. The most interesting of these properties is the amalgamation property. When looking at various classes of groups, a question arose: fixing p, does the class of p-groups satisfy the amalgamation property? The answer is no as we can construct a counterexample for every p.

  This was done at TU Wien as part of a summer study visit at the FB1 Algebra group.

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