The (almost) integral Chow ring of M‾3\overline{\mathcal{M}}_3

This paper is the fourth in a series of four papers aiming to describe the (almost integral) Chow ring of $\overline{\mathcal{M}}_3$, the moduli stack of stable curves of genus $3$. In this paper, we finally compute the Chow ring of $\overline{\mathcal{M}}_3$ with $\mathbb{Z}[1/6]$-coefficients.Comment: The paper is the last of four papers that compose the author's PhD thesis. In particular, it contains the entire Chapter 3 of arXiv:2211.09793. Some results have been corrected and the notation has been improved. 37 pages; comments are very welcom

The derived Brauer map via twisted sheaves

Let $X$ be a quasicompact quasiseparated scheme. The collection of derived Azumaya algebras in the sense of To\"en forms a group, which contains the classical Brauer group of $X$ and which we call $Br^\dagger(X)$ following Lurie. To\"en introduced a map $\phi:Br^\dagger(X)\to H^2_{et}(X,\mathbb G_m)$ which extends the classical Brauer map, but instead of being injective, it is surjective. In this paper we study the restriction of $\phi$ to a subgroup $Br(X)\subset Br^\dagger(X)$, which we call the "derived Brauer group", on which $\phi$ becomes an isomorphism $Br(X)\simeq H^2_{et}(X,\mathbb G_m)$. This map may be interpreted as a derived version of the classical Brauer map which offers a way to "fill the gap" between the classical Brauer group and the cohomogical Brauer group. The group $Br(X)$ was introduced by Lurie by making use of the theory of prestable $\infty$-categories. There, the mentioned isomorphism of abelian groups was deduced from an equivalence of $\infty$-categories between the "Brauer space" of invertible presentable prestable $\mathcal O_X$-linear categories, and the space $Map(X,K(\mathbb G_m,2))$. We offer an alternative proof of this equivalence of $\infty$-categories, characterizing the functor from the left to the right via gerbes of connective trivializations, and its inverse via connective twisted sheaves. We also prove that this equivalence carries a symmetric monoidal structure, thus proving a conjecture of Binda an Porta.Comment: 23 page

Stable cuspidal curves and the integral Chow ring of M‾2,1\overline{\mathscr{M}}_{2,1}

In this paper we introduce the moduli stack $\widetilde{\mathscr{M}}_{g,n}$ of $n$-marked stable at most cuspidal curves of genus $g$ and we use it to determine the integral Chow ring of $\overline{\mathscr{M}}_{2,1}$. Along the way, we also determine the integral Chow ring of $\overline{\mathscr{M}}_{1,2}$.Comment: 47 pages, comments welcome! V2: some mistakes corrected, some new figures added. To appear on Geometry & Topolog

Good Moduli Spaces in Derived Algebraic Geometry

We develop a theory of good moduli spaces for derived Artin stacks, which naturally generalizes the classical theory of good moduli spaces introduced by Alper. As such, many of the fundamental results and properties regarding good moduli spaces for classical Artin stacks carry over to the derived context. In fact, under natural assumptions, often satisfied in practice, we show that the derived theory essentially reduces to the classical theory. As applications, we establish derived versions of the \'{e}tale slice theorem for good moduli spaces and the partial desingularization procedure of good moduli spaces.Comment: 38 pages. Comments welcome

A criterion for smooth weighted blow-downs

We establish a criterion for determining when a smooth Deligne-Mumford stack is a weighted blow-up. More precisely, given a smooth Deligne-Mumford stack $\mathcal{X}$ and a Cartier divisor $\mathcal{E} \subset \mathcal{X}$ such that (1) $\mathcal{E}$ is a weighted projective bundle over a smooth Deligne-Mumford stack $\mathcal{Y}$ and (2) for every $y\in\mathcal{Y}$ we have $\mathcal{O}_{\mathcal{X}}(\mathcal{E})|_{\mathcal{E}_y}\simeq \mathcal{O}_{\mathcal{E}_y}(-1)$, then there exists a contraction $\mathcal{X}\to\mathcal{Z}$ to a smooth Deligne-Mumford stack $\mathcal{Z}$. Moreover, $\mathcal{X}$ can be recovered as a weighted blow-up along $\mathcal{Y}\subset \mathcal{Z}$ with exceptional divisor $\mathcal{E}$. As an application, we show that the moduli stack $\overline{\mathscr{M}}_{1,n}$ of stable $n$-pointed genus one curves is a weighted blow-up of the stack of pseudo-stable curves. Along the way we also prove a reconstruction result for smooth Deligne-Mumford stacks that is of independent interest.Comment: 27 pages, comments welcome

Methyl Jasmonate and Methyl-β-Cyclodextrin Individually Boost Triterpenoid Biosynthesis in <i>Chlamydomonas Reinhardtii</i> UVM4

The commercialisation of valuable plant triterpenoids faces major challenges, including low abundance in natural hosts and costly downstream purification procedures. Endeavours to produce these compounds at industrial scale using microbial systems are gaining attention. Here, we report on a strategy to enrich the biomass of the biotechnologically-relevant Chlamydomonas reinhardtii strain UVM4 with valuable triterpenes, such as squalene and (S)-2,3-epoxysqualene. C. reinhardtii UVM4 was subjected to the elicitor compounds methyl jasmonate (MeJA) and methyl-β-cyclodextrine (MβCD) to increase triterpene yields. MeJA treatment triggered oxidative stress, arrested growth, and altered the photosynthetic activity of the cells, while increasing squalene, (S)-2,3-epoxysqualene, and cycloartenol contents. Applying MβCD to cultures of C. reinhardtii lead to the sequestration of the two main sterols (ergosterol and 7-dehydroporiferasterol) into the growth medium and the intracellular accumulation of the intermediate cycloartenol, without compromising cell growth. When MβCD was applied in combination with MeJA, it counteracted the negative effects of MeJA on cell growth and physiology, but no synergistic effect on triterpene yield was observed. Together, our findings provide strategies for the triterpene enrichment of microalgal biomass and medium

Advanced workstations and collaborative robots : exploiting eye-tracking and cardiac activity indices to unveil senior workers’ mental workload in assembly tasks

Introduction: As a result of Industry 5.0’s technological advancements, collaborative robots (cobots) have emerged as pivotal enablers for refining manufacturing processes while re-focusing on humans. However, the successful integration of these cutting-edge tools hinges on a better understanding of human factors when interacting with such new technologies, eventually fostering workers’ trust and acceptance and promoting low-fatigue work. This study thus delves into the intricate dynamics of human-cobot interactions by adopting a human-centric view. Methods: With this intent, we targeted senior workers, who often contend with diminishing work capabilities, and we explored the nexus between various human factors and task outcomes during a joint assembly operation with a cobot on an ergonomic workstation. Exploiting a dual-task manipulation to increase the task demand, we measured performance, subjective perceptions, eye-tracking indices and cardiac activity during the task. Firstly, we provided an overview of the senior workers’ perceptions regarding their shared work with the cobot, by measuring technology acceptance, perceived wellbeing, work experience, and the estimated social impact of this technology in the industrial sector. Secondly, we asked whether the considered human factors varied significantly under dual-tasking, thus responding to a higher mental load while working alongside the cobot. Finally, we explored the predictive power of the collected measurements over the number of errors committed at the work task and the participants’ perceived workload. Results: The present findings demonstrated how senior workers exhibited strong acceptance and positive experiences with our advanced workstation and the cobot, even under higher mental strain. Besides, their task performance suffered increased errors and duration during dual-tasking, while the eye behavior partially reflected the increased mental demand. Some interesting outcomes were also gained about the predictive power of some of the collected indices over the number of errors committed at the assembly task, even though the same did not apply to predicting perceived workload levels. Discussion: Overall, the paper discusses possible applications of these results in the 5.0 manufacturing sector, emphasizing the importance of adopting a holistic human-centered approach to understand the human-cobot complex better.Peer reviewe