Alex Fink

I am a postdoctoral research assistant in mathematics at North Carolina State, working with Seth Sullivant. In the fall of 2013 I will begin as a Lecturer in Pure Mathematics at Queen Mary, University of London.

My research interests are principally in algebraic combinatorics, especially where commutative algebra or algebraic geometry apply; matroid theory and tropical geometry have been recent themes. Here are my CV and a research statement.

Office: 3250 SAS Hall
Phone: (919) 513-2300
Email: arfink@ncsu.edu

In Spring 2013 I am teaching MA231-003, Calculus for Life and Management Sciences B.

Previously I have taught:

• Applied Differential Equations I (MA341): spring 2012, spring 2011, fall 2010
• Calculus III (MA242): fall 2011

I remain an organiser, with Bojko Bakalov, of the NCSU algebra / combinatorics seminar.

Journal articles, conference papers, preprints

• Alex Fink and Luca Moci, Matroids over a ring, arXiv:1209.6571 (pdf). Slides: motivation, some details.
• Alex Fink, Aviezri Fraenkel, Carlos Santos, Lim is not slim, to appear in International Journal of Game Theory, 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, to appear in Games of No Chance 4, Cambridge University Press.
• 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, 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

• 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.