I am interested in group theoretic problems with applications to number theory and cryptography. My work concerns finite groups, algebraic groups, probabilistic group theory, Galois theory, random polynomials, monodromy groups and group-based cryptography.

• A note on groups with two minimal normal subgroups of genus at most 1 with Spencer Gerhardt and Danny Neftin, in preparation

• Applications of Finite non-Abelian Simple Groups to Cryptography in the Quantum Era with María Isabel González Vasco and Delaram Kahrobaei, Apr 2024, La Matematica: journal, arXiv

• Galois groups of random additive polynomials with Lior Bary-Soroker and Alexei Entin, Apr 2024, Transactions of the American Mathematical Society: journal, arXiv

• On the probability of generating invariably a finite simple group with Daniele Garzoni, Dec 2022, Journal of Pure and Applied Algebra: journal, arXiv

• Invariable generation of finite classical groups, June 2021, Journal of Algebra: journal, arXiv

• PhD Dissertation: Invariable generation of finite groups of Lie type. Advisor: Robert Guralnick at University of Southern California, 2020.

• MMathCompSci project: Groups of Intermediate Growth and Grigorchuk's Group supervised by Panos Papazoglou at Oxford University, 2015.

• BA project: Power graphs of finite groups supervised by Peter M. Neumann at Oxford University, 2014.

• A 20 minute talk on my research which I gave at a workshop on computational group theory in Cambridge, Jan 2020.

• A 40 minute expository lecture on random generation of groups which I gave at a young group theorists' workshop at SwissMAP, Sept 2022.

I have been an instructor at Rutgers University since Fall 2021. Click for course notes.

• Calculus I for Life and Social Sciences

• Intro Linear Algebra

• Linear Algebra

• Cryptography

• Intro Abstract Algebra

I was a teaching assistant at USC from 2016-2018. Click below for course resources.

• MATH 226 Calculus III: Fall 2018

• MATH 510a Graduate Algebra: Fall 2018

• MATH 410 Fundamental Concepts of Modern Algebra: Spring 2018

• MATH 430 Theory of Numbers: Fall 2017

• MATH 126 Calculus II: Spring 2017

• MATH 125 Calculus I: Fall 2016

• MATH 225 Linear Algebra and Linear Differential Equations: Spring 2016

The name Eilidh is of Scottish Gaelic origin and is pronounced like Hailey without the H, or איילי in Hebrew.