Alex (Monty) Milner

I started my PhD at the University of Edinburgh in September 2024 under the supervision of Dr. Dimitra Kosta having graduated from my Masters in Mathematics in June 2024 from Durham University. I am funded by a School of Mathematics Studentship in the Algebra and Number Theory Research Group until 2028 and my office is Room 6324 in the James Clerk Maxwell Building.

My current research is in toric geometry, focusing on Markov bases. I have just finished working on a paper with Dimitra Kosta and Ollie Clarke about distance-reducing Markov bases in the context of bouquet decompositions and toric ideals of graphs. In addition, last year I wrote a Macaulay2 package with Ollie to compute every minimal Markov basis associated with a given configuration matrix. The associated paper is here.

During my time at Durham I completed a research project funded by the London Mathematical Society Research Bursary supervised by Dr Jack Shotton, into invariant factors of elliptic curves and coincidences of divison fields. As of 2026, we have now finished this project, written up here. Whilst at Durham, I also wrote my masters thesis on the Polynomial Method in Combinatorics under the supervision of Dr Dan Evans.

I spend most of my spare time either playing in orchestras or conducting them and I currently hold the position of conductor of the Edinburgh University Sinfonia. Recently, I have also conducted concerts with the Peebles Orchestra, the Herriott-Watt Orchestra and the EUMS chorus. Whilst at Durham, I conducted the Durham University Symphony Orchestra from September 2021 until June 2024 as well the Durham Choral Society, the Durham Opera Ensemble and the Durham Light Opera Group.

My government name is Alex(ander) but my nickname is Monty and I am happy to be called either!