## Max Glick |

I am a lecturer in the mathematics department at Ohio State University. I was a postdoc at University of Connecticut last year, an NSF postdoc at University of Minnesota from 2013 to 2016 and a postdoc during the 2012-2013 year at MSRI and UC Berkeley. I completed my PhD in 2012 at University of Michigan under the supervision of Sergey Fomin.

I have a cv and a research statement.

My interests lie in the field of algebraic combinatorics, and more specifically, cluster algebras. I would like to better understand how cluster algebras relate to projective geometry and discrete integrable systems.

For a quick taste of my mathematical interests, take a look at the animation in slides 9 through 16 of this presentation. Trying to understand the incidence theorem in question leads in many surprisingly deep directions that have informed my work on the pentagram map and also that of my REU student (who proved that the green lines on slide 16 intersect at the center of mass of the eight vertices on slide 9).

- Soliton cellular automata associated with infinite reduced words, joint with Rei Inoue and Pavlo Pylyavskyy, arXiv:1712.08989.
- Gale-Robinson quivers: from representations to combinatorial formulas, joint with J. Weyman, arXiv:1710.09765.
- The limit point of the pentagram map, arXiv:1707.02320.
- The Berenstein-Kirillov group and cactus groups, joint with M. Chmutov and P. Pylyavskyy, arXiv:1609.02046.
- Discrete solitons in infinite reduced words, joint with P. Pylyavskyy, arXiv:1606.01213.
- Y-meshes and generalized pentagram maps, joint with P.
Pylyavskyy,
*Proceedings of the London Mathematical Society*,**112**(2016), 753-797. - The Devron property,
*Journal of Geometry and Physics***87**(2015), 161-189. - On singularity confinement for the pentagram map,
*Journal of Algebraic Combinatorics***38**(2013), 597-635. - The pentagram map and Y-patterns,
*Advances in Mathematics***227**(2011), 1019-1045.

- (Book Chapter) M. Glick and D. Rupel, Introduction to
cluster algebras,
*Symmetries and Integrability of Difference Equations*, Springer, Cham, (2017), 325--357.

These lecture notes are based on our presentation at the 2016 ASIDE summer school. - (Appendix) K. Baur, M. Glick, and P. Martin, The number
of `Scott permutations', appendix to K. Baur and P. Martin, The
fibers of the Scott map on polygon tilings are the flip
equivalence classes, arXiv:1601.05080.

This was my first foray into pure enumerative combinatorics. We counted the number of polygonal tilings of a convex n-gon up to flip equivalence (say a diagonal in a tiling is*flippable*if it is part of two triangles and that the corresponding*flip*replaces such a diagonal with the other diagonal of the enclosing quadrilateral).

I play bridge in my free time. An article about my team back in
Michigan was written here (thanks to
Jin for supplying the file).