Abstract: In this talk, I give a brief overview of connections between cluster algebras and polytopes, focusing on the ABHY construction and generalizations thereof. I first give a brief review on cluster algebras from the perspective of total positivity, focusing on A_{N} as a motivating example. I then shift focus to cluster polytopes, reviewing the connection between finite cluster algebras and polytopes. I conclude with some explicit constructions of associahedra from cluster algebras, the ABHY construction, and my own research into "open associahedra," a type of unbounded cluster polytope. Although physics is not the primary motivation for this talk, connections to physics will be emphasized throughout.

Some relevant papers are:
1. Arkani-Hamed, Nima et al. "Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet." Journal of High Energy Physics 2018.5 (2018): n. pag. Crossref. Web.
2. Bazier-Matte, V'eronique et al. "ABHY Associahedra and Newton polytopes of $F$-polynomials for finite type cluster algebras." (2018).
3. Chapoton, Fr\'ed\'eric, Sergey Fomin, and Andrei Zelevinsky. "Polytopal Realizations of Generalized Associahedra." Canadian Mathematical Bulletin 45.4 (2002): 537-566. Crossref. Web. Speaker(s): Aidan Herderschee (UM)