Search

The half-Heusler compound GdBiPt orders antiferromagnetically around $T_\mathrm{N}=8.5$ K which implies breaking the time reversal symmetry as well as the translational symmetry. This combination preserves the global symmetry. Here, we used rotational anisotropy of second harmonic generation (SHG) to study the symmetry changes associated with this phase transition. GdBiPt crystallizes in the space group $F\overline{4}3m$, which does not change through the phase transition. From powder neutron diffraction, the proposed magnetic point group for the magnetic unit cell is $3m$. We carried out a symmetry analysis of the SHG patterns. Above \tn, the SHG data shows a $C_2$ symmetry which excludes the point group $\overline{4}3m$, as well as the $3m$ point group which represents a $[1 1 1]$ facet of the sample. Thus, we considered the point groups $2$ and $m$, but we have to reject the first one as the associated tensor elements poorly represent the angular dependence SHG. Finally, a superposition consisting of the point groups $3m$ and $m$ fit the data correctly. Below \tn, we had to add a third contribution associated with magnetic points group $m'$ in order to properly describe the SHG signal. The SHG intensity is linearly proportional to the antiferromagnetic order parameter. This allows us to determine $T_\mathrm{N}=9.61\pm0.48$ K and a critical exponent $\beta=0.346\pm0.017$, which are in agreement with the values found in the literature., Comment: 7 pages, 3 figures

We describe the Segal $K$-theory of the symmetric monoidal category of finite-dimensional vector spaces over a perfect field $\mathbb{F}$ together with an automorphism, or, equivalently, the group-completion of the $E_\infty$-algebra of maps from $S^1$ to the disjoint union of classifying spaces $\mathrm{BGL}_d(\mathbb F)$, in terms of the $K$-theory of finite field extensions of $\mathbb{F}$. A key ingredient for this is a computation of the Segal $K$-theory of the category of finite-dimensional vector spaces with a nilpotent endomorphism, which we do over any field $\mathbb F$. We also discuss the topological cases of $\mathbb F =\mathbb C,\mathbb R$., Comment: 22 pages; accepted version

Generative AI capabilities are rapidly transforming how we perceive, interact with, and relate to machines. This one-day workshop invites HCI researchers, designers, and practitioners to imaginatively inhabit and explore the possible futures that might emerge from humans combining generative AI capabilities into everyday technologies at massive scale. Workshop participants will craft stories, visualisations, and prototypes through scenario-based design to investigate these possible futures, resulting in the production of an open-annotated scenario library and a journal or interactions article to disseminate the findings. We aim to gather the DIS community knowledge to explore, understand and shape the relations this new interaction paradigm is forging between humans, their technologies and the environment in safe, sustainable, enriching, and responsible ways.

The control of magnetization using electric fields has been extensively studied in magnetoelectric multiferroic insulator materials. Changes in magnetization in bulk metals caused by electric currents have attracted less attention. The recently discovered metallic magnet Ce$_3$TiBi$_5$ has been reported to exhibit current-induced magnetization. Here we determined the magnetic structure of Ce$_3$TiBi$_5$ using neutron diffraction, aiming to understand the microscopic origin of this magnetoelectric phenomenon in a metal. We established that the antiferromagnetic order emerging below $T_N=5$ K is a cycloid order described by $P6_3/mcm.1'(0,0,g)00sss$ with small moment sizes of $0.50(2)~\mu_B$ and propagation vector ${\bf k}=(0,0,0.386)$. Surprisingly, the symmetry of this magnetic structure is inconsistent with the presence of current-induced magnetization and potential origins of this inconsistency with previous results are discussed. Additionally, our results suggest that moments order along their hard magnetic direction in Ce$_3$TiBi$_5$, a phenomenon which has been observed in other Kondo systems., Comment: 6 pages, 3 figures, accepted for publication in Phys. Rev. B as a Letter

In this work, we present ab initio cavity QED methods which include interactions with a static magnetic field and nuclear spin degrees of freedom using different treatments of the quantum electromagnetic field. We derive explicit expressions for QED-HF magnetizability, nuclear shielding, and spin-spin coupling tensors. We apply this theory to explore the influence of the cavity field on the magnetizability of saturated, unsaturated, and aromatic hydrocarbons, showing the effects of different polarization orientations and coupling strengths. We also examine how the cavity affects aromaticity descriptors, such as the nucleus-independent chemical shift and magnetizability exaltation. We employ these descriptors to study the trimerization reaction of acetylene to benzene. We show how the optical cavity induces modifications in the aromatic character of the transition state leading to variations in the activation energy of the reaction. Our findings shed light on the effects induced by the cavity on magnetic properties, especially in the context of aromatic molecules, providing valuable insights into understanding the interplay between the quantum electromagnetic field and molecules., Comment: 62 pages and 10 figures

In this note we prove that two seemingly different smooth 4-manifolds arising as quotients of $S^2\times S^2$ by free actions of $\mathbb{Z}/4$ are in fact diffeomorphic, answering a question of Hambleton and Hillman., Comment: 4 pages, comments welcome

For a compact orientable surface $\Sigma_{g,1}$ of genus $g$ with one boundary component and for an odd prime number $p$, we study the homology of the unordered configuration spaces $C_\bullet(\Sigma_{g,1}):=\coprod_{n\ge0}C_n(\Sigma_{g,1})$ with coefficients in $\mathbb{F}_p$. We describe $H_*(C_\bullet(\Sigma_{g,1});\mathbb{F}_p)$ as a bigraded module over the Pontryagin ring $H_*(C_\bullet(D);\mathbb{F}_p)$, where $D$ is a disc, and compute in particular the bigraded dimension over $\mathbb{F}_p$. We also consider the action of the mapping class group $\Gamma_{g,1}$, and prove that the mod-$p$ Johnson kernel $\mathcal{K}_{g,1}(p)\subseteq\Gamma_{g,1}$ is the kernel of the action on $H_*(C_\bullet(\Sigma_{g,1};\mathbb{F}_p))$., Comment: 55 pages, 5 figures, to appear in Journal f\"ur die reine und angewandte Mathematik

Reproducibility is a crucial aspect of scientific research that involves the ability to independently replicate experimental results by analysing the same data or repeating the same experiment. Over the years, many works have been proposed to make the results of the experiments actually reproducible. However, very few address the importance of data reproducibility, defined as the ability of independent researchers to retain the same dataset used as input for experimentation. Properly addressing the problem of data reproducibility is crucial because often just providing a link to the data is not enough to make the results reproducible. In fact, also proper metadata (e.g., preprocessing instruction) must be provided to make a dataset fully reproducible. In this work, our aim is to fill this gap by proposing a decision tree to sheperd researchers through the reproducibility of their datasets. In particular, this decision tree guides researchers through identifying if the dataset is actually reproducible and if additional metadata (i.e., additional resources needed to reproduce the data) must also be provided. This decision tree will be the foundation of a future application that will automate the data reproduction process by automatically providing the necessary metadata based on the particular context (e.g., data availability, data preprocessing, and so on). It is worth noting that, in this paper, we detail the steps to make a dataset retrievable, while we will detail other crucial aspects for reproducibility (e.g., dataset documentation) in future works.

For a finite group $G$ and a conjugation-invariant subset $Q\subseteq G$, we consider the Hurwitz space $\mathrm{Hur}_n(Q)$ parametrising branched covers of the plane with $n$ branch points, monodromies in $G$ and local monodromies in $Q$. For $i\ge0$ we prove that $\bigoplus_n H_i(\mathrm{Hur}_n(Q))$ is a finitely generated module over the ring $\bigoplus_n H_0(\mathrm{Hur}_n(Q))$. As a consequence, we obtain polynomial stability of homology of Hurwitz spaces: taking homology coefficients in a field, the dimension of $H_i(\mathrm{Hur}_n(Q))$ agrees for $n$ large enough with a quasi-polynomial in $n$, whose degree is easily bounded in terms of $G$ and $Q$. Under suitable hypotheses on $G$ and $Q$, we prove classical homological stability for certain sequences of components of Hurwitz spaces. Our results generalise previous work of Ellenberg-Venkatesh-Westerland, and rely on techniques introduced by them and by Hatcher-Wahl., Comment: 24 pages, 2 figures, final version to appear in Mathematische Annalen

We conducted a small-angle neutron scattering experiments (SANS) on the ferromagnetic semi-metal EuB$_6$, where we observed direct evidence for the presence of magnetic polarons. We carried out SANS experiments over a large range of scattering vectors $|\vec{q}|$ from 0.006 to 0.140~\AA$^{-1}$ and 2 to 60~K. Just above $T_{\mathrm{C}}$ our experiments show magnetic scattering intensity, which has a Lorentzian dependence on the wave vector, which is characteristic for the presence of magnetic polarons. Below $T_{\mathrm{C}}$ the polarons merge and most of the observed intensity is due to scattering from domain walls.We were able to extract a correlation length $\xi$ which ranges from $100$ to $300$~\AA\ for the size of the magnetic polarons. This size is much larger than one would expect for magnetic fluctuations, demonstrating the influence the magnetic polarons on the phase transition. We were able to extract a correlation length $\xi$ which ranges from $100$ to $300$~\AA\ for the size of the magnetic polarons. This size is much larger than one would expect for magnetic fluctuations, demonstrating the influence the magnetic polarons on the phase transition., Comment: 6 pages, 4 figures

We let the mapping class group $\Gamma_{g,1}$ of a genus $g$ surface $\Sigma_{g,1}$ with one boundary component act on the homology $H_*(F_{n}(\Sigma_{g,1});\mathbb{Q})$ of the $n^{th}$ ordered configuration space of the surface. We prove that the action is non-trivial when restricted to the $(n-1)^{st}$ stage of the Johnson filtration, for all $n\ge 1$ and $g\ge 2$. We deduce an analogous result for closed surfaces.

We consider for $d\geq 1$ the graded commutative $\mathbb{Q}$-algebra $\mathcal{A}(d):=H^*(\operatorname{Hilb}^d(\mathbb{C}^2);\mathbb{Q})$, which is also connected to the study of generalised Hurwitz spaces by work of the first author. These Hurwitz spaces are in turn related to the moduli spaces of Riemann surfaces with boundary. We determine two distinct, minimal sets of $\lfloor d/2\rfloor$ multiplicative generators of $\mathcal{A}(d)$. Additionally, we prove when the lowest degree generating relations occur. For small values of $d$ we also determine a minimal set of generating relations, which leads to several conjectures about the necessary generating relations for $\mathcal{A}(d)$., Comment: 25 pages; v2. Minor revisions based on referee's comments. Published version

We consider the moduli space $\mathfrak{M}_{g,n}$ of Riemann surfaces of genus $g\ge0$ with $n\ge1$ ordered and directed marked points. For $d\ge 2g+n-1$ we show that $\mathfrak{M}_{g,n}$ is homotopy equivalent to a component of the simplicial Hurwitz space $\mathrm{Hur}^{\Delta}(\mathfrak{S}_d^{\mathrm{geo}})$ associated with the partially multiplicative quandle $\mathfrak{S}_d^{\mathrm{geo}}$. As an application, we give a new proof of the Mumford conjecture on the stable rational cohomology of moduli spaces of Riemann surfaces. We also provide a combinatorial model for the infinite loop space $\Omega^{\infty-2}\mathrm{MTSO}(2)$ of Hurwitz flavour., Comment: 52 pages, 5 figures, to appear in Advances in Mathematics

For a partially multiplicative quandle (PMQ) $\mathcal{Q}$ we consider the topological monoid $\mathring{\mathrm{HM}}(\mathcal{Q})$ of Hurwitz spaces of configurations in the plane with local monodromies in $\mathcal{Q}$. We compute the group completion of $\mathring{\mathrm{HM}}(\mathcal{Q})$: it is the product of the (discrete) enveloping group $\mathcal{G}(\mathcal{Q})$ with a component of the double loop space of the relative Hurwitz space $\mathrm{Hur}_+([0,1]^2,\partial[0,1]^2;\mathcal{Q},G)_{1\!\!\,1}$; here $G$ is any group giving rise, together with $\mathcal{Q}$, to a PMQ-group pair. Assuming further that $\mathcal{Q}$ is finite and rationally Poincare and that $G$ is finite, we compute the rational cohomology ring of $\mathrm{Hur}_+([0,1]^2,\partial[0,1]^2;\mathcal{Q},G)_{1\!\!\,1}$., Comment: 67 pages, 11 figures, to appear in Compositio Mathematica

Given a couple of subspaces $\mathcal{Y}\subset\mathcal{X}$ of the complex plane $\mathbb{C}$ satisfying some mild conditions (a ``nice couple''), and given a PMQ-pair $(\mathcal{Q},G)$, consisting of a partially multiplicative quandle (PMQ) $\mathcal{Q}$ and a group $G$, we introduce a ``Hurwitz-Ran'' space $\mathrm{Hur}(\mathcal{X},\mathcal{Y};\mathcal{Q},G)$, containing configurations of points in $\mathcal{X}\setminus\mathcal{Y}$ and in $\mathcal{Y}$ with monodromies in $\mathcal{Q}$ and in $G$, respectively. We further introduce a notion of morphisms between nice couples, and prove that Hurwitz-Ran spaces are functorial both in the nice couple and in the PMQ-group pair. For a locally finite PMQ $\mathcal{Q}$ we prove a homeomorphism between $\mathrm{Hur}((0,1)^2;\mathcal{Q}_+)$ and the simplicial Hurwitz space $\mathrm{Hur}^{\Delta}(\mathcal{Q})$, introduced in previous work of the author: this provides in particular $\mathrm{Hur}((0,1)^2;\mathcal{Q}_+)$ with a cell stratification in the spirit of Fox-Neuwirth and Fuchs., Comment: 52 pages, 9 figures, the title has been changed according to the suggestion of the referee. To appear in Geometriae Dedicata

We introduce the notion of partially multiplicative quandle (PMQ), generalising both classical notions of partial monoid and of quandle. We set up the basic theory of PMQs, in analogy with classical group theory. For a complete PMQ $\hat{\mathcal{Q}}$, and for a braided closed monoidal category $\mathbf{A}$, we introduce a braided monoidal category of $\hat{\mathcal{Q}}$-crossed object in $\mathbf{A}$, in analogy with the classical notion of $G$-crossed objects, depending on a discrete group $G$. We use the previous to give a definition of Hurwitz spaces $\mathrm{Hur}^{\Delta}(\mathcal{Q})$ of configurations of points in the plane with monodromies in a PMQ: the definition has a simplicial flavour, and gives rise to topological spaces with a natural cell stratification; it recovers the classical definition of Hurwitz spaces in the case of a discrete group $G$ considered as a PMQ with trivial multiplication. We give a criterion to detect whether a PMQ $\mathcal{Q}$ is Poincare, i.e. whether all connected components of $\mathrm{Hur}^{\Delta}(\mathcal{Q})$ are topological manifolds. Finally, we analyse thoroughly the PMQ $\mathfrak{S}_d^{\mathrm{geo}}$, for $d\ge2$, and we compute its enveloping group and its completion as PMQ., Comment: 53 pages, 1 figure; the introduction has been changed

We study the $E_2$-algebra $\Lambda\mathfrak{M}_{*,1}=\coprod_{g\geqslant 0}\Lambda\mathfrak{M}_{g,1}$ consisting of free loop spaces of moduli spaces of Riemann surfaces with one parametrised boundary component, and compute the homotopy type of the group completion $\Omega B\Lambda\mathfrak{M}_{*,1}$: it is the product of $\Omega^\infty\mathbf{MTSO}(2)$ with a certain free $\Omega^\infty$-space depending on the family of all boundary-irreducible mapping classes in all mapping class groups $\Gamma_{g,n}$ with $g\geqslant 0$ and $n\geqslant 1$., Comment: 59 pages, 11 figures; accepted version (Forum of Mathematics, Sigma)

Let $F_n(\Sigma_{g,1})$ denote the configuration space of $n$ ordered points on the surface $\Sigma_{g,1}$ and let $\Gamma_{g,1}$ denote the mapping class group of $\Sigma_{g,1}$. We prove that the action of $\Gamma_{g,1}$ on $H_i(F_n(\Sigma_{g,1});\mathbb{Z})$ is trivial when restricted to the $i^{th}$ stage of the Johnson filtration $\mathcal{J}(i)\subset \Gamma_{g,1}$. We give examples showing that $\mathcal{J}(2)$ acts nontrivially on $H_3(F_3(\Sigma_{g,1}))$ for $g\ge 2$, and provide two new conceptual reinterpretations of a certain group introduced by Moriyama., Comment: 30 pages, 14 figures, to appear in Transactions of the American Mathematical Society

We introduce ordered and unordered configuration spaces of 'clusters' of points in an Euclidean space $\mathbb{R}^d$, where points in each cluster satisfy a 'verticality' condition, depending on a decomposition $d=p+q$. We compute the homology in the ordered case and prove homological stability in the unordered case., Comment: 29 pages, 9 figures; accepted version

We give an upper bound on the topological complexity of varieties $\mathcal{V}$ obtained as complements in $\mathbb{C}^m$ of the zero locus of a polynomial. As an application, we determine the topological complexity of unordered configuration spaces of the plane., Comment: 15 pages

EuB6 has for a long time captured the attention of the physics community, as it shows a ferromagnetic phase transition leading to a insulator the metal transition together with colossal magnetoresistance (CMR). EuB6 has a very low carrier density, which is known to drastically change the interaction between the localized Eu moments and the conduction electrons. One of early triumphs of the quantum theory in condensed matter was the presence of Fermi surface, which is intimately linked to the symmetry of the underlying crystal lattice. This symmetry can be probed by angle resolved magnetoresistance (AMRO) measurements. Here, we present angle resolved magnetoresistance (AMRO) measurements that show a that in EuB6 this symmetry is broken, possibly indicating the presence of a quantum nematic phase. We identify the region in the temperature-magnetic field phase diagram where the magnetoresistance shows two-fold oscillations instead of the expected fourfold pattern. Quantum nematic phases are analogous to classical liquid crystals. Like liquid crystals, which break the rotational symmetry of space, their quantum analogs break the point-group symmetry of the crystal due to strong electron-electron interactions, as in quantum Hall states, Sr3Ru2O7, and high temperature superconductors. This is the same region where magnetic polarons were previously observed, suggesting that they drive the nematicity in EuB6. This is also the region of the phase diagram where EuB6 shows a colossal magnetoresistance (CMR). This novel interplay between magnetic and electronic properties could thus be harnessed for spintronic applications., Comment: 6+5 pages. v2: added demagnetization analysis

We study the homology of $[P_n,P_n]$, the commutator subgroup of the pure braid group on $n$ strands, and show that $H_l([P_n,P_n])$ contains a free abelian group of infinite rank for all $1\leq l\leq n-2$. As a consequence we determine the cohomological dimension of $[P_n,P_n]$: for $n\geq 2$ we have $\mathrm{cd}([P_n,P_n])=n-2$., Comment: 21 pages

Let $\Gamma_{g,1}^m$ be the mapping class group of the orientable surface $\Sigma_{g,1}^m$ of genus $g$ with one parametrised boundary curve and $m$ permutable punctures; when $m=0$ we omit it from the notation. Let $\beta_{m}(\Sigma_{g,1})$ be the braid group on $m$ strands of the surface $\Sigma_{g,1}$. We prove that $H_*(\Gamma_{g,1}^m;\mathbb{Z}_2)\cong H_*(\Gamma_{g,1};H_*(\beta_{m}(\Sigma_{g,1});\mathbb{Z}_2))$. The main ingredient is the computation of $H_*(\beta_{m}(\Sigma_{g,1});\mathbb{Z}_2)$ as a symplectic representation of $\Gamma_{g,1}$., Comment: 32 pages, 16 figures. Accepted for publication in Journal of Topology