Related papers: Effective methods for plane quartics, their theta …
We discuss the principle tools and results and state a few open problems concerning the classification and topology of plane sextics and trigonal curves in ruled surfaces.
We provide explicit equations of some smooth complex quartic surfaces with many lines, including all 10 quartics with more than 52 lines. We study the relation between linear automorphisms and some configurations of lines such as twin lines…
This is a survey paper on algebraic surfaces in positive characteristic based on a series of lectures that the author gave at the University of Edinburgh in March 2023. It is focused on certain positive characteristic phenomena like…
This manuscript collects three independent works: arXiv:1902.03805, arXiv:1906.04444, with Antonio Lerario and arXiv:2103.10853, together with some additional results, observations, examples and comments, some of which were taken up in the…
Aronhold's classical result states that a plane quartic can be recovered by the configuration of any Aronhold systems of bitangents, i.e. special 7-tuples of bitangents such that the six points at which any subtriple of bitangents touches…
We give examples of smooth plane quartics over $\mathbb{Q}$ with complex multiplication over $\overline{\mathbb{Q}}$ by a maximal order with primitive CM type. We describe the required algorithms as we go, these involve the reduction of…
Four parallel workshops were organized at the 1996 Girona Conference, "Blazars, Black Holes, and Jets", with conference attendees free to choose which session they would like to attend. The chosen topics were ``Jet Models'',…
This volume contains the papers presented at LINEARITY 2016, the Fourth International Workshop on Linearity, held on June 26, 2016 in Porto, Portugal. The workshop was a one-day satellite event of FSCD 2016, the first International…
Prior research in computational argumentation has mainly focused on scoring the quality of arguments, with less attention on explicating logical errors. In this work, we introduce four sets of explainable templates for common informal…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
These notes are an extension of the rough notes provided for my four lecture graduate level course on "Quadratic Forms and Automorphic Forms" at the March 2009 Arizona Winter School on Quadratic Forms. They are meant to give a survey of…
Strongly lensed quadruply imaged quasars (quads) are extraordinary objects. They are very rare in the sky -- only a few tens are known to date -- and yet they provide unique information about a wide range of topics, including the expansion…
Plane quartics containing the ten vertices of a complete pentalateral and limits of them are called L\"uroth quartics. The locus of singular L\"uroth quartics has two irreducible components, both of codimension two in $\P^{14}$. We compute…
In this report we review recent theoretical progress and the latest experimental results in jet substructure from the Tevatron and the LHC. We review the status of and outlook for calculation and simulation tools for studying jet…
We construct 9-parameter and 13-parameter dynamical systems of the plane which map bi-quadratic curves to other bi-quadratic curves and return to the original curve after two iterations. These generalize the QRT maps which map each such…
Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. We give an introduction focusing on the example of unitary groups and highlight…
Teaching the software engineers of the future to write high-quality code with good style and structure is important. This systematic literature review identifies existing instructional approaches, their objectives, and the strategies used…
There are many methods for projecting spherical maps onto the plane. Interactive versions of these projections allow the user to centre the region of interest. However, the effects of such interaction have not previously been evaluated. In…
Let $(\Sigma,p)$ be a pointed Riemann surface of genus $g\geq 1$. For any integer $k\geq 1$, we parametrize the space of meromorphic quadratic differentials on $\Sigma$ with a pole of order $(k+2)$ at $p$, having a connected critical graph…
A plane quartic curve is called L\"uroth if it contains the ten vertices of a complete pentalateral. White and Miller constructed in 1909 a covariant quartic 4-fold, associated to any plane quartic. We review their construction and we show…