arXiv subjects
Publications and source records attributed to Andrea Bianchi.
We compute the stable homology of complex braid groups of types $B(e,e,n)$ and $B(2e,e,n)$ for fixed $e\ge2$ and increasing $n$. This accounts for the stable homology of all infinite families of complex braid groups. We achieve this by explicitly computing a quillenization of their stable classifying spaces. In particular, we provide a proof of an identification of the stable homology of Artin groups of type $D$ claimed by Fuchs in the '70s.
The increasing popularity of microcontroller platforms like Arduino enables diverse end-user developers to participate in circuit prototyping. Traditionally, follow-along tutorials serve as an essential learning method for makers, and in fact, several prior toolkits leveraged this format as a way to engage new makers. However, literature and our formative study (N=12) show that makers have unique preferences regarding the construction of their circuits and idiosyncratic ways to assess and debug problems, which contrasts with the step-by-step instructional nature of tutorials and those systems leveraging this method. To address this mismatch, we present a prototyping platform that supports personalized circuit construction and debugging. Our system utilizes an augmented breadboard, which is circuit-aware and supports on-the-fly hardware reconfiguration via contextualized guidance and in-situ circuit validation through interactive tests. Through a usability study (N=12), we demonstrate how makers leverage circuit-aware guidance and debugging to support individual building patterns.
The development of user-friendly embedded prototyping systems like Arduino has made creating interactive devices more accessible. However, debugging these systems is challenging due to the intertwined nature of software and hardware issues. Existing tools often require hardware instrumentation or log visualization through serial monitors. To address this, the authors designed Inline, a programming tool that simplifies debugging by displaying hardware logs directly within the code, providing real-time execution flow tracking and an expression language for log manipulation. A study with twelve users demonstrated the tool's effectiveness in aiding debugging tasks.
Remote VR teleoperation with supernumerary robotic limbs enables distant users to operate in another's local space. While a shared first-person view aids hand-eye coordination, locking the guest's camera to the host's head can degrade comfort, embodiment, and coordination. Based on a formative study (N=10) using a virtual supernumerary robotic limbs configuration to stress-test coordination, we propose guest-driven perspective switching from a shared first-person baseline (Shared Embodied View) to two alternatives: (a) a stabilized view with guest-controlled rotation (Embedded Anchored View), and (b) a fully decoupled third-person view (Out-of-body View). We ran a user study with 24 pairs (N=48) who switched between the baseline and proposed views as task demands changed. We measured performance, embodiment, fatigue, physiological arousal, and switching behaviors. Our results reveal role-dependent trade-offs: Out-of-body View improves navigation efficiency and reduces errors, while Embedded Anchored View supports embodiment. We conclude with guidelines: use Embedded Anchored View for hand-centric adjustments, Out-of-body View for navigation and object placement, and ensure smooth transitions.
Embodiment can enhance conversational agents, such as increasing their perceived presence. This is typically achieved through visual representations of a virtual body; however, visual modalities are not always available, such as when users interact with agents using headphones or display-less glasses. In this work, we explore auditory embodiment. By introducing auditory cues of bodily presence - through spatially localized voice and situated Foley audio from environmental interactions - we investigate how audio alone can convey embodiment and influence perceptions of a conversational agent. We conducted a 2 (spatialization: monaural vs. spatialized) x 2 (Foley: none vs. Foley) within-subjects study, where participants (n=24) engaged in conversations with agents. Our results show that spatialization and Foley increase co-presence, but reduce users' perceptions of the agent's attention and other social attributes.
We exhibit the symmetric monoidal $\infty$-category $\mathrm{GrCob}$ of graph cobordisms between spaces as a full $\infty$-subcategory of the $\infty$-category $\mathrm{Psh}(\mathrm{Gr})$ of presheaves over $\mathrm{Gr}$, where $\mathrm{Gr}$ is the symmetric monoidal $\infty$-category of graph cobordisms between finite sets. We also describe a universal property for $\mathrm{GrCob}$: it is, in a suitable sense, the free symmetric monoidal extension of $\mathrm{Gr}$ endowed with the factorization homology $\int_X*$ of the universal $\mathbf{E}_\infty$-Frobenius algebra for all spaces $X$. As a corollary, we identify the space of universal natural operations on the factorization homologies, in particular the Hochschild homology, of $\mathbf{E}_\infty$-Frobenius algebras.
We introduce a symmetric monoidal $\infty$-category $\mathrm{GrCob}$ of graph cobordisms between spaces, and use the homology of its morphism spaces to define string operations. Precisely, for an $E_\infty$-ring spectrum $R$ and an oriented $d$-dimensional $R$-Poincaré duality space $M$, we construct a "graph field theory" $\mathrm{GFT}_M$, i.e. a symmetric monoidal functor from a suitable $R$-linearisation of $\mathrm{GrCob}^\mathrm{op}$ to the category $\mathrm{Mod}_R$ of $R$-modules in spectra; the graph field theory takes an object $X\in\mathrm{GrCob}^\mathrm{op}$, i.e. a space, to the $R$-module $Σ_+^\infty\mathrm{map}(X,M)\otimes R$ of $R$-chains on the mapping space from $X$ to $M$; by selecting suitable graph cobordisms we recover the basic string operations given by restriction, cross product with the fundamental class, and the Chas-Sullivan operations. The construction is natural with respect to oriented homotopy equivalences of $R$-Poincaré duality spaces; in particular, restricting to the endomorphisms of $\emptyset\in\mathrm{GrCob}^\mathrm{op}$, we obtain characteristic classes of $R$-oriented $M$-fibrations parametrised by the suitably twisted homology of $\mathbf{B}\mathrm{Out}(F_n)$, recovering results of Berglund and Barkan-Steinebrunner. Finally, we describe explicitly the morphism spaces in $\mathrm{GrCob}$, answering along the way a question by Hatcher. This allows us to construct a symmetric monoidal functor from the open-closed cobordism $\infty$-category $\mathcal{OC}$ to $\mathrm{GrCob}$. Composing with $\mathrm{GFT}_M$, we obtain an open-closed field theory with values in $\mathrm{Mod}_R$, attaining values $Σ^\infty_+LM\otimes R$ and $Σ^\infty_+M\otimes R$ at the circle and at the interval, respectively. We expect this to recover and extend constructions of Cohen, Godin and others.
The eT program is an open-source electronic structure program with emphasis on performance and modularity. As its name suggests, the program features extensive coupled cluster capabilities, performing well compared to other electronic structure programs, and, in some cases, outperforming commercial alternatives. However, eT is more than a coupled cluster program; other models based on wave function theory (such as full and reduced space configuration interaction and a variety of self-consistent field models) and density functional theory are supported. The second major release of the program, eT 2.0, has specialized functionality for strong light-matter coupling conditions. In addition, it includes a wide range of optimizations and algorithmic improvements, as well as new capabilities for exploring potential energy surfaces and for modeling experiments in the UV and X-ray regimes. Molecular gradients are now available at the coupled cluster level, and high-accuracy spectroscopic simulations are available at reduced computational cost within the multilevel coupled cluster and multiscale frameworks. We present the modifications to the program since its first major release, eT 1.0, highlighting some notable new features and demonstrating the performance of the new version relative to the first release and to other established electronic structure programs.
We introduce a notion of Poincaré duality for pairs of $\infty$-categories, extending Poincaré-Lefschetz duality for pairs of spaces. This categorical extension yields an efficient book-keeping device that affords, among other things, a uniform treatment of Wall's Poincaré ads of spaces, iterated Poincaré cobordisms, and in general, diagrams of spaces parametrised by the face poset of a combinatorial manifold. In each of these cases, the theory reduces them to studying a single pair of $\infty$-categories and the properties of a single functor, the relative cohomology functor. Using this formalism, we prove a very general fibration theorem which, in particular, specialises to a generalisation of Klein-Qin-Su's fibration theorem for Poincaré triads to all ads. This theory also lays the foundation for future work by the authors on Poincaré cobordism categories, isovariant Poincaré spaces and string topology.
Strong coupling with circularly polarized vacuum fluctuations offers a viable route to manipulate molecular chirality. While experiments are advancing toward the realization of chiral cavities, a mean-field theoretical framework for describing electron-photon interaction in this platform has been missing. Here, we present a mean-field theory that can be systematically improved to capture the chiral correlation effects responsible for the enantioselective power of chiral light. We use strong coupling Møller-Plesset perturbation theory for accessing the excitation manifold of electrons and chiral virtual photons. We apply the developed methods to selected chiral systems and show that the mean-field theory captures cavity frequency dispersion, but fails to describe the chiral discrimination arising from coupled electron-photon excitations.
Given a symmetric monoidal $(\infty,n)$-category $\mathcal{C}$ and a space $X$, we address the problem of explicitly describing the symmetric monoidal $(\infty,n)$-category freely obtained from $\mathcal{C}$ by adjoining $X$ new $n$-morphisms with prescribed sources and targets. We develop an apparatus of tools that allow one to detect in concrete situations such a free symmetric monoidal extension. As motivating application, we introduce a symmetric monoidal $(\infty,2)$-category ${\mathbb{G}\mathrm{r}}$ of graph cobordisms between finite sets, following classical constructions of Gersten, Culler--Vogtmann and Hatcher--Vogtmann, and we exhibit it as an extension of the symmetric monoidal $(\infty,1)$-category $\mathrm{Fin}$ of finite sets, obtained by freely adjoining a specific list of new 1-morphisms and 2-morphisms. We recover results of Barkan--Steinebrunner and of Galatius.
In this work, we present the analytical derivation and implementation of the quantum electrodynamics Hartree-Fock Hessian. We investigate how electronic strong coupling influences molecular vibrational properties, applying this framework to formaldehyde, p-nitroaniline, and adamantane. Our analysis reveals cavity-induced changes in vibrational frequencies and intensities. Additionally, we show how the quantum electromagnetic field breaks molecular symmetry, activating previously forbidden infrared transitions. Our findings highlight the potential of strong coupling as a method for controlling and modulating molecular vibrational properties.
We introduce partially multiplicative quandles (PMQ), a generalisation of both partial monoids and quandles. We set up the basic theory of PMQs, focusing on the properties of free PMQs and complete PMQs. For a PMQ $\mathcal{Q}$ with completion $\hat{\mathcal{Q}}$, we introduce the category of $\hat{\mathcal{Q}}$-crossed topological spaces, and define the Hurwitz space $\mathrm{Hur}^Δ(\mathcal{Q})$: it is a $\hat{\mathcal{Q}}$-crossed space, and it parametrises $\mathcal{Q}$-branched coverings of the plane. The definition recovers classical Hurwitz spaces when $\mathcal{Q}$ is a discrete group $G$. Finally, we analyse the class of PMQs $\mathfrak{S}_d^{\mathrm{geo}}$ arising from the symmetric groups $\mathfrak{S}_d$, and we compute their enveloping groups and their PMQ completions.
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.
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 $\mathbb F =\mathbb C,\mathbb R$.
For a compact orientable surface $Σ_{g,1}$ of genus $g$ with one boundary component and for an odd prime number $p$, we study the homology of the unordered configuration spaces $C_\bullet(Σ_{g,1}):=\coprod_{n\ge0}C_n(Σ_{g,1})$ with coefficients in $\mathbb{F}_p$. We describe $H_*(C_\bullet(Σ_{g,1});\mathbb{F}_p)$ 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 $Γ_{g,1}$, and prove that the mod-$p$ Johnson kernel $\mathcal{K}_{g,1}(p)\subseteqΓ_{g,1}$ is the kernel of the action on $H_*(C_\bullet(Σ_{g,1};\mathbb{F}_p))$.
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 $\mathrm{Hur}_+([0,1]^2,\partial[0,1]^2;\mathcal{Q},G)_{1\!\!\,1}$.
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.