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Award ID contains: 2037851

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  1. ; (, Nonlinearity)
    Abstract We consider the well-posedness of the surface quasi-geostrophic (SQG) front equation. Hunter–Shu–Zhang (2021Pure Appl. Anal.3403–72) established well-posedness under a small data condition as well as a convergence condition on an expansion of the equation’s nonlinearity. In the present article, we establish unconditional large data local well-posedness of the SQG front equation, while also improving the low regularity threshold for the initial data. In addition, we establish global well-posedness theory in the rough data regime by using the testing by wave packet approach of Ifrim–Tataru. 
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  2. ; ; ; (, International Mathematics Research Notices)
    Abstract We prove the sharp mixed norm $$(l^{2}, L^{q}_{t}L^{r}_{x})$$ decoupling estimate for the paraboloid in $d + 1$ dimensions. 
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  3. ; (, Journal of Fractal Geometry, Mathematics of Fractals and Related Topics)
    LetE \subseteq \mathbb{R}^{n}be a union of line segments andF \subseteq \mathbb{R}^{n}the set obtained fromEby extending each line segment inEto a full line. Keleti’sline segment extension conjectureposits that the Hausdorff dimension ofFshould equal that ofE. Working in\mathbb{R}^{2}, we use effective methods to prove a strong packing dimension variant of this conjecture. Furthermore, a key inequality in this proof readily entails the planar case of the generalized Kakeya conjecture for packing dimension. This is followed by several doubling estimates in higher dimensions and connections to related problems. 
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    Free, publicly-accessible full text available March 7, 2026
  4. (, American Mathematical Society, Contemporary Mathematics)
    The goal of this expository paper is to provide an introduction to decoupling by working in the simpler setting of decoupling for the parabola over ℚp. Over ℚp, commonly used heuristics in decoupling are significantly easier to make rigorous over ℚp than over ℝ and such decoupling theorems over ℚp are still strong enough to derive interesting number theoretic conclusions. 
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    Accepted Manuscript Full Text Available
  5. ; ; (, American Mathematical Society)
    Full Text Available 
  6. (, New York journal of mathematics)
    Let G be a random torsion-free nilpotent group generated by two random words of length l in Un(Z). Letting l grow as a function of n, we analyze the step of G, which is bounded by the step of Un(Z). We prove a conjecture of Delp, Dymarz, and Schaffer-Cohen, that the threshold function for full step is l = n2. 
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    Accepted Manuscript Full Text Available