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Creators/Authors contains: "Ross, Dustin"

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  1. ; ; (, Discrete & Computational Geometry)
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  2. (, International Mathematics Research Notices)
    Abstract We introduce the notion of Lorentzian fans, which form a special class of tropical fans that are particularly well-suited for proving Alexandrov–Fenchel-type inequalities. To demonstrate the utility of Lorentzian fans, we prove a practical characterization of them in terms of their two-dimensional star fans. We also show that Lorentzian fans are closed under many common tropical fan operations, and we discuss how the Lorentzian property descends to the underlying tropical variety, allowing us to deduce Alexandrov–Fenchel-type inequalities in the general setting of tropical intersection theory on tropical fan varieties. 
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  3. ; (, Advances in Mathematics)
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  4. ; (, Selecta Mathematica)
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  5. ; (, Canadian Journal of Mathematics)
    Abstract We study the number of ways of factoring elements in the complex reflection groups $G(r,s,n)$ as products of reflections. We prove a result that compares factorization numbers in $G(r,s,n)$ to those in the symmetric group $$S_n$$ , and we use this comparison, along with the Ekedahl, Lando, Shapiro, and Vainshtein (ELSV) formula, to deduce a polynomial structure for factorizations in $G(r,s,n)$ . 
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  6. ; (, Advances in Geometry)
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    Abstract The hybrid model is the Landau–Ginzburg-type theory that is expected, via the Landau–Ginzburg/ Calabi–Yau correspondence, to match the Gromov–Witten theory of a complete intersection in weighted projective space. We prove a wall-crossing formula exhibiting the dependence of the genus-zero hybrid model on its stability parameter, generalizing the work of [21] for quantum singularity theory and paralleling the work of Ciocan-Fontanine–Kim [7] for quasimaps. This completes the proof of the genus-zero Landau– Ginzburg/Calabi–Yau correspondence for complete intersections of hypersurfaces of the same degree, as well as the proof of the all-genus hybrid wall-crossing [11]. 
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