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Award ID contains: 1759514

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  1. (, International Mathematics Research Notices)
    Abstract In this paper, we prove a uniform version of Poonen’s “Mordell-Lang Plus Bogomolov” theorem [ 12], based on Vojta’s method. Our main contribution is to generalize Rèmond’s work on the large points in order to allow an extra $$\epsilon $$-neighborhood in the canonical height topology. The part on small points follows from [ 8]. 
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  2. ; ; ; (, EMS press)
    We introduce a variant of stable logarithmic maps, which we call punctured logarith- mic maps. They allow an extension of logarithmic Gromov–Witten theory in which marked points have a negative order of tangency with boundary divisors. As a main application we develop a gluing formalism which reconstructs stable logarithmic maps and their virtual cycles without expansions of the target, with trop- ical geometry providing the underlying combinatorics. Punctured Gromov–Witten invariants also play a pivotal role in the intrinsic con- struction of mirror partners by the last two authors, conjecturally relating to symplec- tic cohomology, and in the logarithmic gauged linear sigma model in work of Qile Chen, Felix Janda and Yongbin Ruan. 
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    Free, publicly-accessible full text available February 5, 2026
  3. (, International Journal of Number Theory)
    In this paper, we extend a uniformity result of Dimitrov et al. [Uniformity in Mordell-Lang for curves, Ann. of Math. (2) 194(1) (2021) 237–298] to dimension two and use it to get a uniform bound on the cardinality of the set of all quadratic points for non-hyperelliptic non-bielliptic curves which only depend on the Mordell–Weil rank, the genus of the curve and the degree of the number field. 
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  4. (, Algebraic Geometry)
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