19 citations · 92 across the 15 of their papers we have counts for
9 papers · 1 filter
Valuative independence and cluster theta reciprocity
Man-Wai Cheung, Timothy Magee, Travis Mandel +1
We prove that theta functions constructed from positive scattering diagrams satisfy valuative independence. That is, for certain valuations , we have $\oper…
Fano mirror periods from the Frobenius structure conjecture
Travis Mandel
The Fano classification program proposed by Coates-Corti-Galkin-Golyshev-Kasprzyk is based on the mirror symmetry prediction that the regularized quantum period of a Fano should be…
Theta bases and log Gromov-Witten invariants of cluster varieties
Travis Mandel
Using heuristics from mirror symmetry, combinations of Gross, Hacking, Keel, Kontsevich, and Siebert have given combinatorial constructions of canonical bases of "theta functions"…
Tropical quantum field theory, mirror polyvector fields, and multiplicities of tropical curves
Travis Mandel, Helge Ruddat
We introduce algebraic structures on the polyvector fields of an algebraic torus that serve to compute multiplicities in tropical and log Gromov-Witten theory while also connecting…
Donaldson-Thomas invariants from tropical disks
Man-Wai Cheung, Travis Mandel
We prove that the quantum DT invariants associated to quivers with genteel potential can be expressed in terms of certain refined counts of tropical disks. This is based on a quant…
Cluster algebras are Cox rings
Travis Mandel
It was recently shown by Gross, Hacking, and Keel that, in the absence of frozen indices, a cluster A-variety with generic coefficients is the universal torsor of the corresponding…
Descendant log Gromov-Witten invariants for toric varieties and tropical curves
Travis Mandel, Helge Ruddat
Using degeneration techniques, we prove the correspondence of tropical curve counts and log Gromov-Witten invariants with general incidence and psi-class conditions in toric variet…
Classification of Rank 2 Cluster Varieties
Travis Mandel
We classify rank cluster varieties (those for which the span of the rows of the exchange matrix is -dimensional) according to the deformation type of a generic fiber of…
Tropical Theta Functions and Log Calabi-Yau Surfaces
Travis Mandel
We generalize the standard combinatorial techniques of toric geometry to the study of log Calabi-Yau surfaces. The character and cocharacter lattices are replaced by certain integr…