arXiv subjects

Guillaume Douville

Publications and source records attributed to Guillaume Douville.

3 recordsLinked to original sources

arXiv2021

ABHY Associahedra and Newton polytopes of $F$-polynomials for finite type cluster algebras

A new construction of the associahedron was recently given by Arkani-Hamed, Bai, He, and Yan in connection with the physics of scattering amplitudes. We show that their construction (suitably understood) can be applied to construct generalized associahedra of any simply-laced Dynkin type. Unexpectedly, we also show that this same construction produces Newton polytopes for all the $F$-polynomials of the corresponding cluster algebras. In addition, we show that the toric variety associated to the g-vector fan has the property that its nef cone is simplicial.

math.RT↗

arXiv2019

Leading terms of $\text{SL}_3$ web invariants

We use Khovanov and Kuperberg's web growth rules to identify the minimal term in the invariant associated to an $\text{SL}_3$ web diagram, with respect to a particular term order.

math.CO↗

arXiv2018

On the combinatorics of gentle algebras

For $A$ a gentle algebra, and $X$ and $Y$ string modules, we construct a combinatorial basis for Hom($X,τY$). We use this to describe support $τ$-tilting modules for $A$. We give a combinatorial realization of maps in both directions realizing the bijection between support $τ$-tilting modules and functorially finite torsion classes. We give an explicit basis of Ext$^1(Y,X)$ as short exact sequences. We analyze several constructions given in a more restricted, combinatorial setting by McConville, showing that many but not all of them can be extended to general gentle algebras.

math.RT↗