19 citations · 92 across the 15 of their papers we have counts for
6 papers · 1 filter
Strong positivity for quantum theta bases of quantum cluster algebras
Ben Davison, Travis Mandel
We construct "quantum theta bases," extending the set of quantum cluster monomials, for various versions of skew-symmetric quantum cluster algebras. These bases consist precisely o…
Let's Keep It Safe: Designing User Interfaces that Allow Everyone to Contribute to AI Safety
Travis Mandel, Jahnu Best, Randall H. Tanaka +4
When AI systems are granted the agency to take impactful actions in the real world, there is an inherent risk that these systems behave in ways that are harmful. Typically, humans…
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…