Given an $m$-dimensional weight $\mathbf{r}$ and an $n$-dimensional weight $\mathbf{s}$, we prove that the set of $(\mathbf{r};\mathbf{s})$-badly approximable $m\times n$ matrices is hyperplane absolute winning on $\mathbb{R}^{m\times n}$. This fully answers a question \cite[Question 8.2 (iii)]{Kl} of D. Kleinbock in 1998.
Let $\mathrm{DY} = \mathbb{1}/(\eta, \nu) \in \mathrm{SH}(\mathbb{C})$. We construct a $w_1$-self-map of periodicity 1 $w:\Sigma^{5,3}\mathrm{DY} \to \mathrm{DY}.$ The cofiber is a realization of $DA(1)$, the double of the subalgebra $A(1)$ of the $\mathbb{C}$-motivic Steenrod algebra $A$.
Let $k=\overline{\mathbb{F}_2}$. We construct a nine-dimensional $F$-rational affine variety $X$ admitting a locally closed embedding $X\hookrightarrow \mathbb{P}_k^{19}$ together with a dense open set $U\subseteq (\mathbb{P}^{19})^\vee$ such that $X\cap H$ is not $F$-rational (or even $F$-injective) for all $H\in U$....
We study $\mathbf{E}_n$-algebras with ramification in their $\pi_0$ and in particular show that the existence of ramification places strong limitations on their chromatic behavior. In particular, we show that $\pi_0$ of nonzero $K(1)$-local $\mathbf{E}_4$-$\mathrm{KU}$-algebras cannot have a map from the ring of intege...
Let $X$ be a finite set and $\mathcal{F} \subseteq 2^X$ a non-trivial increasing property. We show that the bias-threshold $b(\mathcal{F})$ for the Picker-Chooser $\mathcal{F}$-game satisfies $b(\mathcal{F}) \ge \alpha / p_c(\mathcal{F})$, where $p_c(\mathcal{F})$ is the threshold for the property $\mathcal{F}$ and $\a...
Let $\mathcal{S}_\chi$ be a cuspidal representation of $\mathrm{GL}_2(q)$. A subset $S \subseteq \mathrm{GL}_2(q)$ is \emph{$t$-intersecting} if $\dim_{\mathbb{C}}\{v \in \mathcal{S}_\chi: g_1v = g_2v\} \geqslant t$ for any $g_1, g_2 \in S$. In this paper, we determine $\max{|S|}$ where $S$ is $t$-intersecting.
Let $X=(X_1,\dots,X_n)\in\{0,1\}^n$ have a multivariate totally positive ($\mathrm{MTP}_2$) law. We prove that $$ \sum_{i<j}\mathbb{E}\left[\left|\mathrm{Cov}(X_i,X_j \mid X_{[n]\setminus\{i,j\}})\right|\right] \le n/2, $$ and more generally a weighted MaxCut inequality for the fully conditioned covariances. As an appl...
Gleb Smirnov· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
