19 citations · 92 across the 15 of their papers we have counts for
16 papers
A Statistically Reliable Optimization Framework for Bandit Experiments in Scientific Discovery
Tong Li, Travis Mandel, Goldie Phillips +4
Scientific experimentation is largely driven by statistical hypothesis testing to determine significant differences in interventions. Traditionally, experimenters allocate samples…
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…
Stability scattering diagrams and quiver coverings
Qiyue Chen, Travis Mandel, Fan Qin
Given a covering of a quiver (with potential), we show that the associated Bridgeland stability scattering diagrams are related by a restriction operation under the assumption of a…
Bracelets bases are theta bases
Travis Mandel, Fan Qin
The skein algebra of a marked surface, possibly with punctures, admits the basis of (tagged) bracelet elements constructed by Fock-Goncharov and Musiker-Schiffler-Williams. As a cl…
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…
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…
Theta bases are atomic
Travis Mandel
Fock and Goncharov conjectured that the indecomposable universally positive (i.e., atomic) elements of a cluster algebra should form a basis for the algebra. This was shown to be f…
Scattering diagrams, theta functions, and refined tropical curve counts
Travis Mandel
Working over various graded Lie algebras and in arbitrary dimension, we express scattering diagrams and theta functions in terms of counts of tropical curves/disks, weighted by mul…
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…