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1. Gluing maps and cobordism maps for sutured monopole Floer homology.

   Li, Zhenkun (October 2018, ArXiv.org)

   In this paper we construct gluing maps and cobordism maps for sutured monopole Floer homology. 

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2. Punctured logarithmic maps

   Abramovich, Dan; Chen, Qile; Gross, Mark; Siebert, Bernd (February 2025, 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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3. Dynamics of Newton Maps of Quadratic Polynomial Maps of ℝ2 into Itself

   https://doi.org/10.1142/S021812742030027X  

   De Leo, Roberto (July 2020, International Journal of Bifurcation and Chaos)

   null (Ed.)

   We study numerically the [Formula: see text]- and [Formula: see text]-limits of the Newton maps of quadratic polynomial transformations of the plane into itself. Our results confirm the conjectures posed in a recent work about the general dynamics of real Newton maps on the plane. 

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4. Tight Stability Bounds for Entropic Brenier Maps

   https://doi.org/10.1093/imrn/rnaf078  

   Divol, Vincent; Niles-Weed, Jonathan; Pooladian, Aram-Alexandre (April 2025, International Mathematics Research Notices)

   Abstract Entropic Brenier maps are regularized analogues of Brenier maps (optimal transport maps) which converge to Brenier maps as the regularization parameter shrinks. In this work, we prove quantitative stability bounds between entropic Brenier maps under variations of the target measure. In particular, when all measures have bounded support, we establish the optimal Lipschitz constant for the mapping from probability measures to entropic Brenier maps. This provides an exponential improvement to a result of Carlier, Chizat, and Laborde (2024). As an application, we prove near-optimal bounds for the stability of semi-discrete unregularized Brenier maps for a family of discrete target measures. 

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5. Long‐diagonal pentagram maps

   https://doi.org/10.1112/blms.12792  

   Izosimov, Anton; Khesin, Boris (January 2023, Bulletin of the London Mathematical Society)

   Abstract The pentagram map on polygons in the projective plane was introduced by R. Schwartz in 1992 and is by now one of the most popular and classical discrete integrable systems. In the present paper we introduce and prove integrability of long‐diagonal pentagram maps on polygons in , by now the most universal pentagram‐type map encompassing all known integrable cases. We also establish an equivalence of long‐diagonal and bi‐diagonal maps and present a simple self‐contained construction of the Lax form for both. Finally, we prove that the continuous limit of all these maps is equivalent to the ‐KdV equation, generalizing the Boussinesq equation for . 

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