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We show that under mild assumptions, the Fano surfaces of lines on smooth cubic threefolds are the only smooth subvarieties of abelian varieties whose Tannaka group for the convolution of perverse sheaves is an exceptional simple group. This in particular leads to a considerable strengthening of our previous work on the Shafarevich conjecture. A key idea is to control the Hodge decomposition on cohomology by a cocharacter of the Tannaka group of Hodge modules, and to play this off against an improvement of the Hodge number estimates for irregular varieties by Lazarsfeld-Popa and Lombardi.

We prove the Shafarevich conjecture for very irregular varieties of dimension less than half the dimension of their Albanese variety, subject to some mild numerical conditions. Our proof relies on the Lawrence-Venkatesh method as in the work of Lawrence-Sawin, together with the big monodromy criterion from our work with Javanpeykar and Lehn., Comment: The main results now hold also for varieties without rational points and under weaker numerical assumptions

Motivated by recent work of Lawrence-Venkatesh and Lawrence-Sawin, we show that non-isotrivial families of subvarieties in abelian varieties have big monodromy when twisted by generic rank one local systems. While Lawrence-Sawin discuss the case of subvarieties of codimension one, our results hold for subvarieties of codimension at least half the dimension of the ambient abelian variety. For the proof, we use a combination of geometric arguments and representation theory to show that the Tannaka groups of intersection complexes on such subvarieties are big., Comment: 68 pages, v2: substantial improvement of the main results

In this demo paper, we present ConSTR, a novel Contextual Search Term Recommender that utilises the user's interaction context for search term recommendation and literature retrieval. ConSTR integrates a two-layered recommendation interface: the first layer suggests terms with respect to a user's current search term, and the second layer suggests terms based on the users' previous search activities (interaction context). For the demonstration, ConSTR is built on the arXiv, an academic repository consisting of 1.8 million documents., Comment: 2 pages, 2 figures, accepted demo paper at JCDL 2021

We show that the degree of Gauss maps on abelian varieties is semicontinuous in families, and we study its jump loci. As an application we obtain that in the case of theta divisors this degree answers the Schottky problem. Our proof computes the degree of Gauss maps by specialization of Lagrangian cycles on the cotangent bundle. We also get similar results for the intersection cohomology of varieties with a finite morphism to an abelian variety; it follows that many components of Andreotti-Mayer loci, including the Schottky locus, are part of the stratification of the moduli space of ppav's defined by the topological type of the theta divisor., Comment: Final version, to appear in Math. Annalen

We show that the only summands of theta divisors on Jacobians of curves and on intermediate Jacobians of cubic threefolds are the obvious powers of the curve and the Fano surface of lines on the threefold. The proof uses the decomposition theorem for perverse sheaves, a bit of representation theory and a computation of characteristic cycles for Brill-Noether sheaves., Comment: references updated, background on fiber functors and lambda rings added, proof of 2.5 made self-contained

We show that for the reductive Tannaka groups of semisimple holonomic $\mathscr{D}$-modules on abelian varieties, every Weyl group orbit of weights of their universal cover is realized by a conic Lagrangian cycle on the cotangent bundle. Applications include a weak solution to the Schottky problem in genus five, an obstruction for the existence of summands of subvarieties on abelian varieties and a criterion for the simplicity of the arising Lie algebras., Comment: 38 pages, comments welcome

Reduction of heat and friction losses is a proven approach to increase the engine efficiency. Therefore, and due to a stabilized, robust combustion, a specific adjustment of component temperatures is desirable in highly transient conditions. In this paper, a turbocharged SI engine is investigated numerically concerning the potential regulation of temperatures, including heat fluxes, only by controlling the water mass flow rate. Using two independent models, a simplified lumped capacity model and a detailed three-dimensional CFD-CHT simulation, an efficient, two-stage calculation method is suggested for an optimized determination of control strategies and their parameters. This complements existing published works which usually control more than one parameter, but use one model. Different control strategies, like feed forward or feedback controllers, are proposed and compared. In addition, a more holistic approach is presented performing a Monte Carlo simulation which evaluates temperatures, as well as hydraulic pumping losses. Using expedient control strategies and parameters, it could be shown that the engine temperatures can be effectively regulated within a wide range. The two different models show partly similar results, and the efficient, two-stage optimization method has proven its worth. However, there are some significant differences between simplified and detailed modelling which are worth mentioning.

A calculation method for engine temperatures is presented. Special focus is placed on the transient and scattering boundary conditions within the combustion chamber, including fired and coasting conditions, as well as the dynamic heat transfer of the water jacket. Model reduction is achieved with dimensional analysis and the application of probability density functions, which allows for a timescale separation. Stationary in-cylinder pressure measurements are used as input values and, according to the transient behavior, modified with an own part-load model. A turbocharged SI race engine is equipped with 70 thermocouples at various positions in proximity to the combustion chamber. Differentiating from already published works, the method deals with the transient engine behavior during a race lap, which undergoes a frequency range of 0.1-1 Hz. This includes engine speed build-ups under gear changes, torque variations, or the transition from fired to coasting conditions. Different thermal behaviors of various measuring positions can be simulated successfully. Additionally, cylinder individual temperature effects resulting from an unsymmetrical ignition sequence and different volumetric efficiencies with unequal residual gas can be predicted. Up to a few percent, the energy balance of the water jacket is fulfilled and variations of water inlet temperatures can be simulated accurately enough.

As digital collections of scientific literature are widespread and used frequently in knowledge-intense working environments, it has become a challenge to identify author names correctly. The treatment of homonyms is crucial for the reliable resolution of author names. Apart from varying handling of first, middle and last names, vendors as well as the digital library community created tools to address the problem of author name disambiguation. This technical report focuses on two widespread collections of scientific literature, Web of Science (WoS) and Scopus, and the coverage with author identification information such as Researcher ID, ORCID and Scopus Author Identifier in the period 1996 - 2014. The goal of this study is to describe the significant differences of the two collections with respect to overall distribution of author identifiers and its use across different subject domains. We found that the STM disciplines show the best coverage of author identifiers in our dataset of 6,032,000 publications which are both covered by WoS and Scopus. In our dataset we found 184,823 distinct ResearcherIDs and 70,043 distinct ORCIDs. In the appendix of this report we list a complete overview of all WoS subject areas and the amount of author identifiers in these subject areas., Comment: 23 pages, 1 figure, technical report

We propose two new approaches to the Tannakian Galois groups of holonomic D-modules on abelian varieties. The first is an interpretation in terms of principal bundles given by the Fourier-Mukai transform, which shows that they are almost connected. The second constructs a microlocalization functor relating characteristic cycles to Weyl group orbits of weights. This explains the ubiquity of minuscule representations, and we illustrate it with a Torelli theorem and with a bound for decompositions of a given subvariety as a sum of subvarieties. The appendix sketches a twistor variant that may be useful for D-modules not coming from Hodge theory., Comment: Many suggestions by the referees incorporated, exposition largely expanded. To appear in Ann. Sci. ENS

The Tannakian formalism allows to attach to any subvariety of an abelian variety an algebraic group in a natural way. The arising groups are closely related to moduli questions such as the Schottky problem, but their geometric interpretation is still mysterious. We show that for the theta divisor on the intermediate Jacobian of a cubic threefold, the Tannaka group is an exceptional group of type E_6. This is the first known exceptional case, and it suggests a connection with the monodromy of the Gauss map., Comment: Some typos corrected, references updated

The convolution powers of a perverse sheaf on an abelian variety define an interesting family of branched local systems whose geometry is still poorly understood. We show that the generating series for their generic rank is a rational function of a very simple shape and that a similar result holds for the symmetric convolution powers. We also give formulae for other Schur functors in terms of characteristic classes on the dual abelian variety, and as an example we discuss the case of Prym-Tjurin varieties., Comment: Some typos removed, references updated

We consider semisimple super Tannakian categories generated by an object whose symmetric or alternating tensor square is simple up to trivial summands. Using representation theory, we provide a criterion to identify the corresponding Tannaka super groups that applies in many situations. As an example we discuss the tensor category generated by the convolution powers of an algebraic curve inside its Jacobian variety.

We give a Tannakian description for categories of l-adic perverse sheaves on semiabelian varieties which combines a construction of Gabber and Loeser for algebraic tori with a generic vanishing theorem for the cohomology of constructible sheaves on abelian varieties. As an application we explain how the arising Tannaka groups on abelian varieties can be studied in terms of semiabelian degenerations via the functor of nearby cycles., Comment: 14 pages

We study a family of surfaces of general type that arises from the intersections of two translates of the theta divisor on a principally polarized complex abelian fourfold. In particular we determine the N\'eron-Severi lattices of these surfaces and show that for a general abelian fourfold the monodromy group of the associated variation of Hodge structures is a subgroup of index at most two in the Weyl group W(E_6), whereas for a Jacobian variety it degenerates to a subgroup of the symmetric group S_6., Comment: 29 pages

To any closed subvariety $Y$ of a complex abelian variety one can attach a reductive algebraic group $G$ which is determined by the decomposition of the convolution powers of $Y$ via a certain Tannakian formalism. For a theta divisor $Y$ on a principally polarized abelian variety, this group $G$ provides a new invariant that naturally endows the moduli space $A_g$ of principally polarized abelian varieties of dimension $g$ with a finite constructible stratification. We determine $G$ for a generic principally polarized abelian variety, and for $g=4$ we show that the stratification detects the locus of Jacobian varieties inside the moduli space of abelian varieties.

We show that the hypercohomology of most character twists of perverse sheaves on a complex abelian variety vanishes in all non-zero degrees. As a consequence we obtain a vanishing theorem for constructible sheaves and a relative vanishing theorem for a homomorphism between abelian varieties. Our proof relies on a Tannakian description for convolution products of perverse sheaves, and with future applications in mind we discuss the basic properties of the arising Tannaka groups.