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1. Supersymmetry and T T ¯ $$ T\overline{T} $$ deformations

   https://doi.org/10.1007/JHEP04(2019)131  

   Chang, Chih-Kai; Ferko, Christian; Sethi, Savdeep (April 2019, Journal of High Energy Physics)
2. dS/dS and T T ¯ $$ T\overline{T} $$

   https://doi.org/10.1007/JHEP03(2019)085  

   Gorbenko, Victor; Silverstein, Eva; Torroba, Gonzalo (March 2019, Journal of High Energy Physics)
3. Geometrizing $$ T\overline{T} $$

   https://doi.org/10.1007/JHEP03(2021)140  

   Caputa, Pawel; Datta, Shouvik; Jiang, Yunfeng; Kraus, Per (March 2021, Journal of High Energy Physics)

   null (Ed.)

   A bstract The $$ T\overline{T} $$ T T ¯ deformation can be formulated as a dynamical change of coordinates. We establish and generalize this relation to curved spaces by coupling the undeformed theory to 2d gravity. For curved space the dynamical change of coordinates is supplemented by a dynamical Weyl transformation. We also sharpen the holographic correspondence to cutoff AdS 3 in multiple ways. First, we show that the action of the annular region between the cutoff surface and the boundary of AdS 3 is given precisely by the $$ T\overline{T} $$ T T ¯ operator integrated over either the cutoff surface or the asymptotic boundary. Then we derive dynamical coordinate and Weyl transformations directly from the bulk. Finally, we reproduce the flow equation for the deformed stress tensor from the cutoff geometry. 

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4. q,t$q,t$‐Catalan measures

   https://doi.org/10.1112/blms.12989  

   Cavey, Ian (March 2024, Bulletin of the London Mathematical Society)

   Abstract We introduce the ‐Catalan measures, a sequence of piece‐wise polynomial measures on . These measures are defined in terms of suitable area, dinv, and bounce statistics on continuous families of paths in the plane, and have many combinatorial similarities to the ‐Catalan numbers. Our main result realizes the ‐Catalan measures as a limit of higher ‐Catalan numbers as . We also give a geometric interpretation of the ‐Catalan measures. They are the Duistermaat–Heckman measures of the punctual Hilbert schemes parametrizing subschemes of supported at the origin. 

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5. Monotone T-convex T-differential fields

   https://doi.org/10.2140/mt.2025.4.55  

   Kaplan, Elliot; Pynn-Coates, Nigel (January 2025, Model Theory)

   Let T be a complete, model complete o-minimal theory extending the theory of real closed ordered fields and assume that T is power bounded. Let K be a model of T equipped with a T-convex valuation ring O and a T-derivation ∂ such that ∂ is monotone, i.e., weakly contractive with respect to the valuation induced by O. We show that the theory of monotone T-convex T-differential fields, i.e., the common theory of such K, has a model completion, which is complete and distal. Among the axioms of this model completion, we isolate an analogue of henselianity that we call T∂-henselianity. We establish an Ax-Kochen/Ershov theorem and further results for monotone T-convex T-differential fields that are T∂-henselian. 

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