On the Hilbert scheme of curves in higher-dimensional projective space

In this paper we prove that, for any $n\ge 3$, there exist infinitely many $r\in \N$ and for each of them a smooth, connected curve $C_r$ in $\P^r$ such that $C_r$ lies on exactly $n$ irreducible components of the Hilbert scheme \hilb(\P^r). This is proven by reducing the problem to an analogous statement for the moduli of surfaces of general type.Comment: latex, 12 pages, no figure

Integrating Multimedia: Demonstrations of Student-Generated Multimedia Products Made within Regular Content-Driven Courses

Education doctoral students in five different courses demonstrated their understanding of key concepts though creating multimedia learning products. This demonstration looks at the use of student-generated multimedia products as a pedagogical strategy to encourage learners to think more deeply about academic content. This demonstration shares over 20 different multimedia products from these different courses. The products are encouraging since students demonstrated a deeper level of academic understanding and a higher level of student engagement

Overconvergent Eichler-Shimura isomorphisms for quaternionic modular forms over Q

In this work we construct overconvergent Eichler-Shimura isomorphisms over Shimura curves over Q. More precisely, for a prime p > 3 and a wide open disk U in the weight space, we construct a Hecke-Galois-equivariant morphism from the space of families of overconvergent modular symbols over U to the space of families of overconvergent modular forms over U . In addition, for all but finitely many weights λ ∈ U , this morphism provides a description of the finite slope part of the space of overconvergent modular symbols of weight λ in terms of the finite slope part of the space of overconvergent modular forms of weight λ + 2. Moreover, for classical weights these overconvergent isomorphisms are compatible with the classical Eichler-Shimura isomorphism.Postprint (author's final draft

On a Conjecture of Rapoport and Zink

In their book Rapoport and Zink constructed rigid analytic period spaces $F^{wa}$ for Fontaine's filtered isocrystals, and period morphisms from PEL moduli spaces of $p$-divisible groups to some of these period spaces. They conjectured the existence of an \'etale bijective morphism $F^a \to F^{wa}$ of rigid analytic spaces and of a universal local system of $Q_p$-vector spaces on $F^a$. For Hodge-Tate weights $n-1$ and $n$ we construct in this article an intrinsic Berkovich open subspace $F^0$ of $F^{wa}$ and the universal local system on $F^0$. We conjecture that the rigid-analytic space associated with $F^0$ is the maximal possible $F^a$, and that $F^0$ is connected. We give evidence for these conjectures and we show that for those period spaces possessing PEL period morphisms, $F^0$ equals the image of the period morphism. Then our local system is the rational Tate module of the universal $p$-divisible group and enjoys additional functoriality properties. We show that only in exceptional cases $F^0$ equals all of $F^{wa}$ and when the Shimura group is $GL_n$ we determine all these cases.Comment: v2: 48 pages; many new results added, v3: final version that will appear in Inventiones Mathematica

Detection of Listeria monocytogenes in foods with a textile organic electrochemical transistor biosensor

Abstract: Foods contaminated by pathogens are responsible for foodborne diseases which have socioeconomic impacts. Many approaches have been extensively investigated to obtain specific and sensitive methods to detect pathogens in food, but they are often not easy to perform and require trained personnel. This work aims to propose a textile organic electrochemical transistor-based (OECT) biosensor to detect L. monocytogenes in food samples. The analyses were performed with culture-based methods, Listeria Precis™ method, PCR, and our textile OECT biosensor which used poly(3,4-ethylenedioxythiophene) (PEDOT):polystyrene sulfonate (PSS) (PEDOT:PSS) for doping the organic channel. Atomic force microscopy (AFM) was used to obtain topographic maps of the gold gate. The electrochemical activity on gate electrodes was measured and related to the concentration of DNA extracted from samples and hybridized to the specific capture probe immobilized onto the gold surface of the gate. This assay reached a limit of detection of 1.05 ng/μL, corresponding to 0.56 pM of L. monocytogenes ATCC 7644, and allowed the specific and rapid detection of L. monocytogenes in the analyzed samples. Keypoints: • Textile organic electrochemical transistors functionalized with a specific DNA probe • AFM topographic and surface potential maps of a functionalized gold gate surface • Comparison between the Listeria monocytogenes Precis™ method and an OECT biosenso