Tasha Montgomery

Current research project

My research is primarily focused on fully generalising a classical result in algebraic K-theory. Namely that the K-theory of the projective line over an arbitrary commutative ring splits into two copies of the K-theory of the ground ring. This was generalised to noncommutative rings, by Bass ('68) and Quillen ('73)

Dade ('80) then introduced the concept of strong gradings, in order to capture properties of group rings, but this strong grading is what controls the splitting behaviour of algebraic K-theory.

As such, I am currently looking to generalise the splitting result further by proving that the K-theoretical splitting result still holds for projective spaces associated to strongly graded rings.

Biography

After completing my MSci Mathematics in 2016 I was accepted for a PhD studentship under the same supervisor. I have also been a teaching assistant for PMA1020, now MTH1002. Alongside my studies I have been an active member of clubs & societies in the Students’ Union:

• President of Dragonslayers 2016-2019
• Director of Q-Con 2017-2019
• Women’s Epee Captain for QUB Fencing (2013-present)
• I am a QUB Sports Honours holder, having been awarded my Blues in 2018

I also am a qualified fencing coach and run a fencing club at my old school, Hunterhouse College.

Research interests

• Algebraic topology

• K-theory

• Algebraic geometry

• Homological algebra