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Authors:
Uri Andrews; Julia Knight Abstract: Uri Andrews, Julia KnightWe give effectiveness conditions on a strongly minimal theory $T$ guaranteeing that all countable models have computable copies. In particular, we show that if $T$ is strongly minimal and for all $n\geq 1$, $T\cap\exists_{n+2}$ is $\Delta^0_n$, uniformly in $n$, then every countable model has a computable copy. A longstanding question of computable model theory (...) PubDate: Tue, 22 May 2018 23:30:02 +020

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Authors:
Stephen Lester; Kaisa Matomäki, Maksym Radziwiłł Abstract: Stephen Lester, Kaisa Matomäki, Maksym RadziwiłłWe study the behavior of zeros and mass of holomorphic Hecke cusp forms on SL$_2(\mathbb Z) \backslash \mathbb H$ at small scales. In particular, we examine the distribution of the zeros within hyperbolic balls whose radii shrink sufficiently slowly as $k \rightarrow \infty$. We show that the zeros equidistribute within such balls as $k (...) PubDate: Tue, 22 May 2018 23:30:02 +020

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Authors:
Jørgen Vold Rennemo
Abstract: Jørgen Vold RennemoLet $C$ be a proper, integral, locally planar curve, and consider its Hilbert schemes of points $C^[n]$. We define four creation/annihilation operators acting on the rational homology groups of these Hilbert schemes and show that the operators satisfy the relations of a Weyl algebra. The action of this algebra is similar to that defined by Grojnowski and Nakajima for a (...) PubDate: Tue, 22 May 2018 23:30:02 +020

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Authors:
Terry Lyons; Weijun Xu Abstract: Terry Lyons, Weijun XuThe aim of this article is to develop an explicit procedure that enables one to reconstruct any $\mathcal C^1$ path (at natural parametrization) from its signature. We also explicitly quantify the distance between the reconstructed path and the original path in terms of the number of terms in the signature that are used for the construction and the modulus of (...) PubDate: Tue, 22 May 2018 23:30:02 +020

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Authors:
John Lewis; Kaj Nyström Abstract: John Lewis, Kaj NyströmIn this paper we establish new results concerning boundary Harnack inequalities and the Martin boundary problem, for non-negative solutions to equations of $p$-Laplace type with variable coefficients. The key novelty is that we consider solutions which vanish only on a low-dimensional set $\Sigma$ in $\mathbb R^n$ and this is different compared to the more (...) PubDate: Tue, 22 May 2018 23:30:02 +020

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Authors:
Boris Bukh; David Conlon Abstract: Boris Bukh, David ConlonGiven a family of graphs $\mathcal{H}$, the extremal number ex$(n, \mathcal{H})$ is the largest $m$ for which there exists a graph with $n$ vertices and $m$ edges containing no graph from the family $\mathcal{H}$ as a subgraph. We show that for every rational number $r$ between 1 and 2, there is a family of graphs $\mathcal{H}_r$ such that ex$(n, \mathcal{H}_r) = (...) PubDate: Tue, 22 May 2018 23:30:02 +020

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Authors:
Jonathan Bober; Leo Goldmakher, Andrew Granville, Dimitris Koukoulopoulos Abstract: Jonathan Bober, Leo Goldmakher, Andrew Granville, Dimitris KoukoulopoulosLet $M(\chi)$ denote the maximum of $ \sum_{n\le N}\chi(n) $ for a given non-principal Dirichlet character $\chi$ modulo $q$, and let $N_\chi$ denote a point at which the maximum is attained. In this article we study the distribution of $M(\chi)/\sqrt{q}$ as one varies over characters modulo $q$, where $q$ is prime, (...) PubDate: Tue, 22 May 2018 23:30:02 +020

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Authors:
Nicolas Lerner; Toan Nguyen, Benjamin Texier Abstract: Nicolas Lerner, Toan Nguyen, Benjamin TexierWe study the Cauchy problem for first-order quasi-linear systems of partial differential equations. When the spectrum of the initial principal symbol is not included in the real line, i.e., hyperbolicity is violated at initial time, the Cauchy problem is strongly unstable in the sense of Hadamard. This phenomenon, which extends the linear (...) PubDate: Mon, 07 May 2018 23:30:02 +020

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Authors:
Diego Armentano; Carlos Beltrán, Peter Bürgisser, Felipe Cucker, Michael Shub Abstract: Diego Armentano, Carlos Beltrán, Peter Bürgisser, Felipe Cucker, Michael ShubWe describe algorithms for computing eigenpairs (eigenvalue-eigenvector pairs) of a complex $n \times n$ matrix $A$. These algorithms are numerically stable, strongly accurate, and theoretically efficient (i.e., polynomial-time). We do not believe they outperform in practice the algorithms currently used for this (...) PubDate: Mon, 07 May 2018 23:30:02 +020

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Authors:
Libor Barto
Abstract: Libor BartoWe show that every finite algebra which is finitely related and lies in a congruence modular variety has few subpowers. This result, combined with other theorems, has interesting consequences for the complexity of several computational problems associated to finite relational structures: the constraint satisfaction problem, the primitive positive formula comparison problem, and (...) PubDate: Mon, 07 May 2018 23:30:02 +020

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Authors:
Tobias Dyckerhoff; Mikhail Kapranov Abstract: Tobias Dyckerhoff, Mikhail KapranovFor a triangulated category $\mathcal A$ with a 2-periodic dg-enhancement and a triangulated oriented marked surface $S$, we introduce a dg-category $F(S,\mathcal A)$ parametrizing systems of exact triangles in $\mathcal A$ labelled by triangles of $S$. Our main result is that $\mathcal F(S,\mathcal A)$ is independent of the choice of a triangulation of (...) PubDate: Mon, 07 May 2018 23:30:02 +020

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Authors:
Tuna Altınel; Joshua Wiscons Abstract: Tuna Altınel, Joshua WisconsWe show that the only transitive and generically 4-transitive action of a group of finite Morley rank on a set of Morley rank 2 is the natural action of PGL$_3$ on the projective plane. PubDate: Mon, 07 May 2018 23:30:02 +020