Alex Fink

I am a Professor of Pure Mathematics in the School of Mathematical Sciences at Queen Mary University of London.

Office: 312, Maths Building, Mile End campus (number 4 on this map)
Telephone: 020 7882 5520
Email: a.fink@qmul.ac.uk
he / him

Office hours: see my entry on the School's pages. Or email for an appointment.

Here is my CV.

Skip to: Teaching Administration Activities Group Research Publications

In Semester A of 2024/25 I taught the Professional Placement Tutorial, MTH5200A.

I am the head of the Centre for Combinatorics, Algebra and Number Theory (CeCANT). The role will be deputised to Felix Fischer for January – June 2025.

Thomas Bartsch, Madeleine Moore, Daniel Ratliff, and I are organising a one-day event The Queer Experience in Mathematics at Loughborough University on Wed 2 July 2025, centred on discussing what are the current support needs for LGBTQ+ mathematicians in the UK. 31 May is the deadline to apply for travel funding or to present a provocation.

I will be on sabbatical from January to June 2025, based at the Special Year on Algebraic and Geometric Combinatorics at the IAS and the Thematic Program in Commutative Algebra and Applications at the Fields Institute.

The weekly seminar of the Combinatorial Algebraic Geometry research group at QMUL is currently running.

Some past activities organised:

• LMS Tropical Mathematics and its Applications meeting, Nov 2024
• COW algebraic geometry seminar, Aug 2024
• Queer and Trans Mathematicians in Combinatorics 2023, Jul 2023
• Respectable recreations: combinatorics in tribute to Richard Guy, Oct 2020
• Tropical Differential Algebra Workshop, Dec 2019
• LMS Tropical Mathematics and its Applications meeting, Mar 2019
• Algebraic Geometry for Matroids minicourse, Oct–Nov 2018
• Tensors, their Decompositions, and Applications minisymposium, Aug 2016
• LMS Tropical Mathematics and its Applications meeting, Sep 2015

I have profiles at 500 Queer Scientists and LGBTQ+ STEM.

I have three current PhD students:

• Samuel-Louis Gardiner (2019–)
• Benjamin Dobres (2021–)
• Linxuan Li (2023–)

• Basile Coron (2023–).

• Amanda Cameron (PhD 2017)
• Ben Smith (PhD 2019)
• Scott Kemp (PhD 2021)

My research interests are principally in algebraic combinatorics, especially where commutative algebra or algebraic geometry apply, including matroid theory and tropical geometry.

I hold EPSRC grant EP/X001229/1 Extensions of matroid Hodge theory. I have previously held EPSRC grant EP/M01245X/1 Algebra and geometry of matroids and Horizon 2020 Marie Skłodowska-Curie grant No 792432 Tropical differential geometry.

Journal articles, conference papers, preprints

• Alex Fink and Luis Ferroni, The polytope of all matroids, arXiv:2502.20157 (pdf).
• Andrew Berget and Alex Fink, The external activity complex of a pair of matroids, arXiv:2412.11759 (pdf).
• Alex Fink, Kris Shaw and David E Speyer, The omega invariant of a matroid, arXiv:2411.19521 (pdf).
• Alex Fink, Jeffrey Giansiracusa and Noah Giansiracusa, with an appendix by Joshua Mundinger, Projective hypersurfaces in tropical scheme theory I: the Macaulay ideal, Research in the Mathematical Sciences 12 (2025), article number 30. arXiv:2405.16338 (pdf).
• Alex Fink and Jorge Alberto Olarte, Extensions of transversal valuated matroids, European Journal of Combinatorics 127 (2025), 104153. arXiv:2308.05556 (pdf).
• Christopher Eur, Alex Fink, Matt Larson and Hunter Spink, Signed permutohedra, delta-matroids, and beyond, Proceedings of the London Mathematical Society 128 no. 3 (2024), e12592. arXiv:2209.06752 (pdf).
• Javier Elizondo, Alex Fink and Cristhian Garay López, Matroids and the space of torus-invariant subvarieties of the Grassmannian with given homology class, Journal of Pure and Applied Algebra 229 no. 6 (2025), 107930. doi:10.1016/j.jpaa.2025.107930. arXiv:2112.15334 (pdf).
• Laura Escobar, Alex Fink, Jenna Rajchgot and Alexander Woo, Gröbner bases, symmetric matrices, and type C Kazhdan–Lusztig varieties, Journal of the London Mathematical Society 109 no. 2 (2024), e12856. doi:10.1112/jlms.12856. arXiv:2104.09589 (pdf).
• Alex Fink and Zeinab Toghani, Initial forms and a notion of basis for tropical differential equations, Pacific Journal of Mathematics 318 no. 2 (2022), 453–468. doi:10.2140/pjm.2022.318.453. arXiv:2004.08258 (pdf).
• Andrew Berget and Alex Fink, Equivariant K-theory classes of matrix orbit closures, International Mathematics Research Notices 2022 no. 18 (2022), 14105–14133. arXiv:1904.10047 (pdf).
• Alex Fink, Karola Mészáros and Avery St. Dizier, Zero-one Schubert polynomials, Mathematische Zeitschrift 297 no. 3 (2020), 1023–1042. doi:10.1007/s00209-020-02544-2. arXiv:1903.10332 (pdf).
• Alex Fink and Jorge Alberto Olarte, Presentations of transversal valuated matroids, Journal of the London Mathematical Society 105 no. 1 (2022), 24–62, published online. arXiv:1903.08288 (pdf).
• Amanda Cameron and Alex Fink, The Tutte polynomial via lattice point counting, Journal of Combinatorial Theory, Series A 188 (2022), 105584. arXiv:1802.09859 (pdf). See also the FPSAC 2016 extended abstract.
• Clément Dupont, Alex Fink and Luca Moci, Universal Tutte characters via combinatorial coalgebras, Algebraic Combinatorics 1 no. 5 (2018), 603–651. arXiv:1711.09028 (pdf). Luca's notes from his minicourse at Dobbiaco 2018.
• Alex Fink and Luca Moci, Polytopes and parameter spaces for matroids over valuation rings, Advances in Mathematics 343 (2019), 449–494. doi:10.1016/j.aim.2018.11.009. arXiv:1707.01026 (pdf). Slides.
• Alex Fink, Karola Mészáros and Avery St. Dizier, Schubert polynomials as integer point transforms of generalized permutahedra, Advances in Mathematics 332 (2018), 465–475. arXiv:1706.04935 (pdf).
• Alex Fink, David E Speyer and Alexander Woo, A Gröbner basis for the graph of the reciprocal plane, Journal of Commutative Algebra 12 no. 1 (2020), 77–86. arXiv:1703.05967 (pdf).
• Alex Fink, Jenna Rajchgot and Seth Sullivant, Matrix Schubert varieties and Gaussian conditional independence models, arXiv:1510.04124 (pdf). Journal of Algebraic Combinatorics 44 no. 4 (2016), 1009–1046.
• Andrew Berget and Alex Fink, Equivariant Chow classes of matrix orbit closures, Transformation Groups 22 no. 3 (2016), published online. doi:10.1007/s00031-016-9406-5. arXiv:1507.05054 (pdf).
• Andrew Berget and Alex Fink, Matrix orbit closures, Beiträge zur Algebra und Geometrie 59 no. 3 (2018), 1–34, published online. doi:10.1007/s13366-018-0402-x. arXiv:1306.1810 (pdf).
• Alex Fink and Felipe Rincón, Stiefel tropical linear spaces, Journal of Combinatorial Theory, Series A 135 (2015), 291–331. arXiv:1305.6329 (pdf).
• Alex Fink and Luca Moci, Matroids over a ring, Journal of the European Mathematical Society 18 issue 4 (2016), 681–731. arXiv:1209.6571 (pdf). Slides: motivation, some details.
• Alex Fink, Boij-Söderberg expansions of matroid Stanley-Reisner rings, unpublished note.
• Alex Fink, Aviezri Fraenkel, Carlos Santos, Lim is not slim, International Journal of Game Theory 43 issue 2 (2014), 269–281. doi:10.1007/s00182-013-0380-z. Online at IJGT.
• Alex Fink, Lattice games without rational strategies, Journal of Combinatorial Theory, Series A 119 (2012), 450–459. doi:10.1016/j.jcta.2011.10.005. arXiv:1106.1883 (pdf). Slides.
• Alex Fink and David E Speyer, K-classes of matroids and equivariant localization, Duke Math. J. 161 no. 14 (2012), 2699–2723. arXiv:1004.2403 (pdf). Slides.
• Alex Fink, Tropical cycles and Chow polytopes, Beiträge zur Algebra und Geometrie 54 no. 1 (2013), 13–40. Online at Beiträge. arXiv:1001.4784 (pdf). Slides. Video of the talk, MSRI, 16 October 2009.
• Harm Derksen and Alex Fink, Valuative invariants for polymatroids, Advances in Mathematics 225 no. 4 (2010), 1840–1892. doi:10.1016/j.aim.2010.04.016. arXiv:0908.2988 (pdf). Slides.
• Alex Fink, The binomial ideal of the intersection axiom for conditional probabilities, J. of Algebraic Combinatorics 33 issue 3 (2011), 455–463. doi:10.1007/s10801-010-0253-5. arXiv:0902.1495 (pdf). Slides.
• Alex Fink, Richard Nowakowski, Aaron Siegel, David Wolfe, Toppling conjectures, Games of No Chance 4, MSRI Publications volume 63, 65–76.
• Alex Fink and Benjamin Iriarte Giraldo, Bijections between noncrossing and nonnesting partitions for classical reflection groups, Portugaliae Mathematicae 67 fasc. 3 (2010), 369–401. arXiv:0810.2613 (pdf).
• Alex Fink and Richard K Guy, The outercoarseness of the n-cube, Contributions to Discrete Math. 12 no. 2 (2017), #582.
• Alex Fink, Richard Guy and Mark Krusemeyer, Partitions with parts appearing at most thrice, Contributions to Discrete Math. 3 (2008), #79.
• Federico Ardila, Alex Fink and Felipe Rincón, Valuations for matroid polytope subdivisions, Canadian Journal of Mathematics, published electronically on July 29, 2010. doi:10.4153/CJM-2010-064-9. arXiv:0710.4424 (pdf).
• Alex Fink, Jörg Denzinger, and John Aycock, Extracting NPC behavior from Computer Games using Computer Vision and Machine Learning Techniques, IEEE Symposium on Computational Intelligence and Games, 2007, 24–31.
• Alex Fink and Richard Guy, The number-pad game, Coll. Math. J. 38 (2007), 260–264.
• Alex Fink, A generalization of an IMO problem, Integers, Electronic Journal of Combinatorial Number Theory 6 (2006), #A17.
• Alex Fink and Bill Sands, Rationals whose sum equals the reciprocal of their product, Crux Math. 30 (2004), 292–295.

Doctoral thesis

My thesis was titled Matroid polytope subdivisions and valuations. Aside from an introduction all its content appears in the papers above.

Expository writing, manuscripts

• Matroid subdivisions, and a computational appendix. Written for Jack Edmonds' 2015 summer courses on Polyhedral Combinatorics and Exponential Polytime, of which I gave a segment.
• Alex Fink and Richard Guy, Rick's Tricky Six Puzzle: S₅ sits specially in S₆, Math. Magazine 82 no. 2 (April, 2009). See also Doug Ensley's interactive supplement with implementations of the puzzle.
• If two were three, what would Hex be?, 2008, for Gathering for Gardner 8. See also my other page on this game, with an implementation.
• Patulous pegboard polygons, with Derek Kisman and Richard Guy, 2006, for Gathering for Gardner 7, in Mathematical wizardry for a Gardner, AK Peters, 2009.

Diversions

• A tool for guessing the hidden card in Fitch Cheney's five card trick