KK-theoretic counterexamples to Ravenel's telescope conjecture

At each prime $p$ and height $n+1 \ge 2$, we prove that the telescopic and chromatic localizations of spectra differ. Specifically, for $\mathbb{Z}$ acting by Adams operations on $\mathrm{BP}\langle n \rangle$, we prove that the $T(n+1)$-localized algebraic $K$-theory of $\mathrm{BP}\langle n \rangle^{h\mathbb{Z}}$ is not $K(n+1)$-local. We also show that Galois hyperdescent, $\mathbb{A}^1$-invariance, and nil-invariance fail for the $K(n+1)$-localized algebraic $K$-theory of $K(n)$-local $\mathbb{E}_{\infty}$-rings. In the case $n=1$ and $p \ge 7$ we make complete computations of $T(2)_*\mathrm{K}(R)$, for $R$ certain finite Galois extensions of the $K(1)$-local sphere. We show for $p\geq 5$ that the algebraic $K$-theory of the $K(1)$-local sphere is asymptotically $L_2^{f}$-local.Comment: 100 pages. Comments very welcom

Giant conductivity switching of LaAlO3/SrTiO3 heterointerfaces governed by surface protonation

Complex-oxide interfaces host a diversity of phenomena not present in traditional semiconductor heterostructures. Despite intense interest, many basic questions remain about the mechanisms that give rise to interfacial conductivity and the role of surface chemistry in dictating these properties. Here we demonstrate a fully reversible >4 order of magnitude conductance change at LaAlO3/SrTiO3 (LAO/STO) interfaces, regulated by LAO surface protonation. Nominally conductive interfaces are rendered insulating by solvent immersion, which deprotonates the hydroxylated LAO surface; interface conductivity is restored by exposure to light, which induces reprotonation via photocatalytic oxidation of adsorbed water. The proposed mechanisms are supported by a coordinated series of electrical measurements, optical/solvent exposures, and X-ray photoelectron spectroscopy. This intimate connection between LAO surface chemistry and LAO/STO interface physics bears far-reaching implications for reconfigurable oxide nanoelectronics and raises the possibility of novel applications in which electronic properties of these materials can be locally tuned using synthetic chemistry

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements

Eilenberg Mac Lane spectra as p-cyclonic Thom spectra

Hopkins and Mahowald gave a simple description of the mod $p$ Eilenberg Mac Lane spectrum $\mathbb{F}_p$ as the free $\mathbb{E}_2$-algebra with an equivalence of $p$ and $0$. We show for each faithful $2$-dimensional representation $\lambda$ of a $p$-group $G$ that the $G$-equivariant Eilenberg Mac Lane spectrum $\underline{\mathbb{F}}_p$ is the free $\mathbb{E}_{\lambda}$-algebra with an equivalence of $p$ and $0$. This unifies and simplifies recent work of Behrens, Hahn, and Wilson, and extends it to include the dihedral $2$-subgroups of O(2). The main new idea is that $\underline{\mathbb{F}}_p$ has a simple description as a $p$-cyclonic module over $\rm{THH}(\mathbb{F}_p)$. We show our result is the best possible one in that it gives all groups $G$ and representations $V$ such that $\underline{\mathbb{F}}_p$ is the free $\mathbb{E}_V$-algebra with an equivalence of $p$ and $0$.Comment: Revised in response to referee feedback. 19 page

S3-pairs and Dehn surgery on knots

Two general ways are explained to produce pairs of knots K, K′ in S3 and a γ ∈ Q such that the γ surgery of K coincides with the ±γ surgery of K′. They are similar in that the key ingredient in the construction is an S3-pair, a pair of framed knots whose surgery yields S3. They generalize some techniques in the literature, and give plenty of flexibility on choosing both the knots and their framings. Examples are given with a focus on a special case that works for 0 surgeries of many ribbon knots

Topological Hochschild homology of the image of j

We compute the mod $(p,v_1)$ and mod $(2,\eta,v_1)$ $\mathrm{THH}$ of many variants of the image-of-$J$ spectrum. In particular, we do this for $j_{\zeta}$, whose $\mathrm{TC}$ is closely related to the $K$-theory of the $K(1)$-local sphere. We find in particular that the failure for $\mathrm{THH}$ to satisfy $\mathbb{Z}_p$-Galois descent for the extension $j_{\zeta} \to \ell_p$ corresponds to the failure of the $p$-adic circle to be its own free loop space. For $p>2$, we also prove the Segal conjecture for $j_{\zeta}$, and we compute the $K$-theory of the $K(1)$-local sphere in degrees $\leq 4p-6$.Comment: 42 pages, 4 figures, comments welcome