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- publication . Preprint . 2016Open Access EnglishAuthors:Carlotto, Alessandro; Mondino, Andrea;doi: 10.1112/jlms.12012Project: NSF | Mathematical Sciences Res... (1440140)
We show that asymptotically Schwarzschildean 3-manifolds cannot contain minimal surfaces obtained by perturbative deformations of a Euclidean catenoid, no matter how small the ADM mass of the ambient space and how large the neck of the catenoid itself. Such an obstructi...

- publication . Preprint . 2016Open Access EnglishAuthors:Bejenaru, Ioan;Project: NSF | Mathematical Sciences Res... (1440140)
We provide an alternative and self contained proof of the main result of Bennett, Carbery, Tao regarding the multilinear restriction estimate. The approach is inspired by the recent result of Guth about the Kakeya version of multilinear restriction estimate. At lower le...

- publication . Preprint . 2018Open Access EnglishAuthors:Brandes, Julia; Dietmann, Rainer;Project: NSF | Mathematical Sciences Res... (1440140)
We show that any smooth projective cubic hypersurface of dimension at least $29$ over the rationals contains a rational line. A variation of our methods provides a similar result over p-adic fields. In both cases, we improve on previous results due to the second author ...

- publication . Preprint . 2018Open Access EnglishAuthors:Barcelo, Helene; Greene, Curtis; Jarrah, Abdul Salam; Welker, Volkmar;Project: NSF | Mathematical Sciences Res... (1440140)
Toward defining commutative cubes in all dimensions, Brown and Spencer introduced the notion of "connection" as a new kind of degeneracy. In this paper, for a cubical set with connections, we show that the connections generate an acyclic subcomplex of the chain complex ...

- publication . Preprint . 2018Open Access EnglishAuthors:Stovall, Betsy;Project: NSF | Mathematical Sciences Res... (1440140)
In this article, we prove that all global, nonendpoint Fourier restriction inequalities for the paraboloid in $\mathbb R^{1+d}$ have extremizers and that $L^p$-normalized extremizing sequences are precompact modulo symmetries. This result had previously been established...

- publication . Preprint . 2019Open Access EnglishAuthors:Benedetti, Gabriele; Kang, Jungsoo;Project: NSF | Mathematical Sciences Res... (1440140)
Let $\alpha$ be a contact form on a connected closed three-manifold $\Sigma$. The systolic ratio of $\alpha$ is defined as $\rho_{\mathrm{sys}}(\alpha):=\tfrac{1}{\mathrm{Vol}(\alpha)}T_{\min}(\alpha)^2$, where $T_{\min}(\alpha)$ and $\mathrm{Vol}(\alpha)$ denote the mi...

- publication . Preprint . 2017Open Access EnglishAuthors:Hickman, Jonathan; Wright, James;Project: NSF | Mathematical Sciences Res... (1440140)
A sharp bound is obtained for the number of ways to express the monomial $X^n$ as a product of linear factors over $\mathbb{Z}/p^{\alpha}\mathbb{Z}$. The proof relies on an induction-on-scale procedure which is used to estimate the number of solutions to a certain syste...

- publication . Preprint . 2018Open Access EnglishAuthors:Braddell, Roisin; Kiesenhofer, Anna; Miranda, Eva;Project: NSF | Mathematical Sciences Res... (1440140)
In this article we give a normal form of a $b$-symplectic form in the neighborhood of a compact orbit of a Lie group action on a $b$-symplectic manifold. We establish cotangent models for Poisson actions on $b$-Poisson manifolds and a $b$-symplectic slice theorem. We ex...

- publication . Preprint . 2017Open Access EnglishAuthors:Oberlin, Richard;Project: NSF | Mathematical Sciences Res... (1440140)
We use a variant of the technique in [Lac17a] to give sparse L^p(log(L))^4 bounds for a class of model singular and maximal Radon transforms

- publication . Preprint . 2018Open Access EnglishAuthors:Benson, David; Kessar, Radha; Linckelmann, Markus;Project: NSF | Mathematical Sciences Res... (1440140)
Let $k$ be an algebraically closed field of characteristic $p$, and let $\mathcal{O}$ be either $k$ or its ring of Witt vectors $W(k)$. Let $G$ a finite group and $B$ a block of $\mathcal{O}G$ with normal abelian defect group and abelian $p'$ inertial quotient. We show ...