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EOSC Beyond: advancing innovation and collaboration for research

EOSC Beyond overall objective is to advance Open Science and innovation in research in the context of the European Open Science Cloud (EOSC) by providing new EOSC Core capabilities allowing scientific applications to find, compose and access multiple Open Science resources and offer them as integrated capabilities to researchers. To do so, EOSC Beyond supports a new concept of EOSC: a federated and integrated network of Nodes operated at different levels, national, regional, international and thematic, to serve the specific scientific missions of their stakeholders. Further specific objectives of the project are to accelerate ‘time to product’ of new scientific applications with software adapters, enable Open Science with machine composability and dynamic deployment of shared resources, support innovation in EOSC with a testing and integration environment, and align the EOSC Core architecture and specifications to integrate with European dataspaces. The project extends the state of the art of the EOSC Core and adopts a co-design methodology, including requirements elicitation, software development and validation in collaboration with different use cases from EOSC national and regional initiatives (e-Infra CZ, Czechia, NFDI, Germany, and NI4OS, South East Europe region), thematic research infrastructures from Social Sciences and Humanities (CESSDA), Life Sciences (CNB-CSIC and Instruct-ERIC), Environmental Science (ENES and LifeWatch), and Health and Food (METROFood-RI). EOSC Beyond builds on the capacities of prospective EOSC Nodes and partners with multi-annual experience in developing solutions for large-scale federated digital infrastructures and aligns with the technical architecture and requirements of data spaces from different business sectors. Ultimately, EOSC Beyond supports Open Science in modern, data-intensive, and multidisciplinary research, facilitating resource discovery, access, and reuse across scientific communities, organisations, and countries. 

CULTUral heritage in RurAL remote areas for creative tourism and sustainabilITY

The main objective of the project is to contribute to the promotion of cultural and creative tourism activities, considering the different capacities, resources, and specificities (material, creative, human...) of the territories, as a mean to help with the sustainable development of peripheral rural areas, favoring job creation and population settlement. For this, the potential of its cultural heritage will be researched, taking into account both the artisan material culture (techniques, materials, patterns and decorative elements), as well as the intangible culture (music, oral knowledge and culinary traditions) as a resource.   To promote non-seasonal tourism as a form of sustainable development with a stable population settlement we are going to research the crafts linked to the territory and their implications, but we will also carry out a documentation of the productive processes. First and foremost, we are going to cater to the necessities of the local communities and pay attention to aspects related to societal groups at risk of exclusion, such as women, the elderly and the youth.  All this will be developed from a multidisciplinary perspective, for which we will count on the various teams —most of them linked to different countries— that will be part of the consortium. Each of these partners will contribute to the development, as well as to the final result of the project through input directly related to their area of ??expertise: for example, among the collaborators we have intellectual teams specialized in the digitalization of heritage, research, or communication and dissemination, as well as as various institutions that will act as a testing ground for the more practical parts of the proposal. However, if something will characterize our work, it will be the constant collaboration between all parties, as well as the exchange of advice and experiences that will help to enrich collective knowledge and guarantee optimal results.

AQUASERV – RESEARCH INFRASTRUCTURE SERVICES FOR SUSTAINABLE AQUACULTURE, FISHERIES AND THE BLUE ECONOMY

The overarching objectives of AQUASERV are to bring together, enhance, integrate and customise RI capacities (including facilities, instruments and expertise) and through the provision of transnational access (on-site or remote) and/or virtual access, to significantly further scientific advance and promote and facilitate the implementation of European Common Fisheries Policy, the Farm to Fork Strategy, the Sustainable Blue Economy and the European Green Deal.   AQUASERV will achieve these objectives by offering scientists from academia and business remote and on-site transnational (TA) and virtual (VA) access to an advanced set of European research infrastructures and its nodes related to research and management of marine and freshwater biological resources, food and biotechnology. These include the European Marine Biological Resource Centre ERIC (EMBRC), the Analysis and Experimentation on Ecosystems ERIC, The Aquaculture for Excellence for Aquaculture in Fish (Aquaexcel), and the Infrastructure for Promoting Metrology in Food and Nutrition (METROFOOD), as well as the International Council for Exploration of the Sea, both a service provider and stakeholder. It also includes the Research Infrastructure for Science and Innovation Policy Studies (RISIS) to bring contributions from the social sciences and to bring results nearer to policy makers ensuring societal impact.   To enhance, integrate and customise RI capacities, collaboration between partners and new pipelines to meet the objectives of the project will be developed during the first 3 years and will make available  to users.  To ensure these capacities will not be lost, a sustainability work package involving stakeholders will address the project legacy.    To maximize impact, AQUASERV will build a communication network among the partnership and develop a dissemination and outreach programme. Furthermore, an advanced training programme will be developed to capture future users and will be updated during the p

Harmonization of Advanced Materials Ecosystems serving strategic Innovation Markets to pave the way to a Digital Materials & Product Passport

The overarching objective of DigiPass is to enhance the digital maturity of the European communities that develop materials and intermediate products. The project will develop recommendations and clear routes toward digitalized circular business models. The overarching key result of DigiPass is to create a sustainable platform which includes support for Digital Materials & Product Passport and for collaborative innovation-by-design processes in a circular economy served by advanced materials. A business model for operating such a platform completes the overarching objective. DigiPass is harmonizing and synergizing collected materials data sources and digital infrastructures. This will enable interoperability of data exchange, and standardization of advanced materials knowledge representation at all maturity levels. Accelerating the design, development, and production of advanced, safe, and sustainable chemicals and materials, as they are necessary for innovative products, calls for a collaborative approach involving different stakeholders to support durability, repair and overhaul, reuse, and recyclability of products. DigiPass project impacts all materials development communities over the whole circular value chain.  

EOSC-ENTRUST: A European Network of TRUSTed research environments

The mission of EOSC-ENTRUST is to create a European network of trusted research environments for sensitive data and to drive European interoperability by joint development of a common blueprint for federated data access and analysis.  Countries and institutions have made significant investments in secure and trusted data environments to meet the need for research and policy-driven analysis of sensitive datasets such as people's health and socio-economic status, the habitats of vulnerable species and geo-spatial locations of protected sites. There are now a large number of such secure environments in operation - linked to national centres, individual organisations or specific research communities. This fragmented landscape poses challenges for both users and providers: researchers are faced with a large number of different systems and access procedures; providers need to manage federated access across multiple, potentially incompatible, technology and governance frameworks. EOSC-ENTRUST brings together providers of operational Trusted Research Environments from 15 European countries with a shared goal to implement, validate and promote their capabilities through a common European framework using shared standards and common legal, operational and technical language. This blueprint for interoperability is anchored in the EOSC Interoperability Framework spanning the four dimensions of Legal, Organisational, Technical and Semantic interoperability. EOSC-ENTRUST has identified four driver projects covering Genomics, Clinical trials, Social science, and public-private partnerships to benchmark capabilities, inform blueprint design and demonstrate secure  data analysis using federated workflows. Targeted outreach activities will expand this open network with further providers and develop policy papers and guidelines for the full range of stakeholders to create a long-term operational TRE framework within the European Open Science Cloud. 

IMProving User experience, Long-term sustainability and Services of EU-OPENSCREEN

EU-OPENSCREEN (EU-OS), the distributed European Research Infrastructure for Chemical Biology and early drug discovery, provides world-class services in high-throughput compound screening and medicinal chemistry to users from academia and industry. As one of the largest open-access initiative globally, EU-OPENSCREEN plays an increasingly important role in facilitating early stage drug discovery in Europe. It recently integrated fragment-based drug discovery and chemoproteomics as two new services, but the increasing complexity of modern drug discovery projects requires an even more comprehensive portfolio and integration of emerging technologies. To ensure that EU-OS continues to offer a comprehensive suite of relevant services and support a growing user community to conduct forefront research, IMPULSE will develop, validate and integrate new services in AI/ML, new chemical modalities, and innovative disease-relevant cell models combined with CRISPR-Cas9/RNAi-based genetic screening. IMPULSE will work towards the implementation of common operational and data standards to increase data reproducibility and FAIRness. Bespoke outreach and training activities will raise awareness among key user groups of its new services and advance operational excellence and reproducibility in pre-clinical drug discovery. New models for pre-competitive drug discovery with industry or charities, and growing ERIC member community will reinforce the sustainability and accessibility of EU-OPENSCREEN.

Strengthening resilience and mental wellbeing through the Support4Resilience toolbox for leaders in elderly care

European elderly care experiences labor shortages, lack of qualified workers and a mismatch between capacity and demands, causing stress, burnout, and reduced mental wellbeing among healthcare workers and informal caregivers. Leaders are crucial in promoting supportive working conditions but lack research-based measures to act upon these challenges.  Support4Resilience (S4R) will develop, implement, and evaluate a research-based Toolbox to support healthcare leaders in improving healthcare workers’ and informal caregivers’ resilience and mental wellbeing in elderly care. S4R will identify resilience and mental wellbeing factors among healthcare workers and informal caregivers; explore their perspectives and needs; develop new theory on the relationship between individual and organizational resilience, and mental wellbeing; and develop recommendations and cost-effective interventions. The Toolbox with tailormade resources for policy and practical use will be available through an open access S4R Resource Bank.  The S4R Toolbox includes three main tools: 1) Mapping and identification, 2) Reflection and education, and 3) Reorganization. Measures are initiated at the organizational level and effects on mental wellbeing and resilience transpire at the frontline of elderly care. The Toolbox covers different situational contexts, types of healthcare providers and health system levels. Elderly care settings in six European countries will implement and evaluate the Toolbox through a process evaluation, effectiveness evaluation, and cost-effectiveness evaluation.   S4R provides policymakers, decisions-makers and leaders with solutions for taking action to solve specific risks for healthcare workers’ and informal caregivers’ resilience and mental wellbeing. Thus, pertinent to the work programme, S4R will support the development of resilient health systems in European elderly care through improved leadership capabilities, governance structures, and adaptive capacities.

UNIVERSAL SENSOR BASED ON ELECTRICALLY-PUMPED MID-INFRARED SPECTROMETER ON SILICON CHIPS

High resolution optical spectroscopy in the mid-infrared (mid-IR) spectral range (3-12 µm wavelength) is an unambiguous way to detect and quantify small traces of greenhouse and toxic gases down to sensitivities of parts-per-billion. Such sensitivities are a prerequisite to safeguard low-pollution and toxic-free environment defined by the EU Action Plan: "Towards a Zero Pollution for Air, Water and Soil.” However, size, cost, and general complexity of the commercially available instruments limits their use to a small number of highly specialized applications, and prevents their deployment with sufficient coverage e.g. in networks, wearable electronics, etc. Particularly in the context of Internet of Things (IoT) devices, on chip integration of spectroscopic systems would constitute a game changer for mid-IR high-precision and portable sensors. The objective of UNISON is to address this challenge and demonstrate a highly scalable platform for infra-red spectroscopy that has both high-end performance and is compact. UNISON sensing scheme relies on dual comb spectrometers obtained by leveraging on electrically pumped cascade lasers (QCL and ICL) and on silicon-germanium (SiGe) mid-IR photonic circuits to surpass current spectroscopic systems in terms of detection bandwidth, point spacing and system compactness. UNISON is organized around 3 main cornerstones each of them relying on ambitious physical and technological challenges: (i) tunable large bandwidth frequency combs will be generated on SiGe photonics circuits  by combining electro-optical comb generation, non-linear effects and dispersion engineering ; (ii) the comb sources will be pumped by novel electrically-driven cascade laser sources integrated with the SiGe photonics circuits ; (iii) compact, broadband, and sensitive interaction region for trace gas detection, designed and optimized for the SiGe platform, will be integrated with the dual comb source to showcase the sensing capability of the spectrometer. 

Providing research infrastructure services to support Next Generation EU

This four-year project will harness outputs from key social science RIs in Europe and other reliable sources to support the aims of the ‘Next Generation EU’ programme and to inform EU youth policy. Virtual access will be provided to the outputs through special installations (portals) developed during the project. The core of the proposal is a set of existing research ‘services’, which will be re-purposed and customised to focus directly on the five themes: Make it Green; Make it Digital; Make it Healthy; Make it Strong; and Make it Equal.   For each area, the consortium will work collaboratively to produce seven sets of resources:  i)	A searchable inventory of relevant variables drawn from multiple cross-national datasets;   ii)	Analytical summaries, suitable for policy makers and analysts new to the field, as well as interactive resources available through the project portal;  iii)	Harmonised and merged extracts from these datasets that reduce the burden on analysts and increase sample sizes;  iv)	New data collected through the ESS’s established CRONOS web panel infrastructure. Eleven countries will field five waves of the panel, each one dedicated to a NextGenEU theme. Free and rapid access to the data will be available through the CRONOS portal alongside analytical summaries;  v)	In-person and virtual deliberative forums with young people (aged 18-34) in four countries covering the five Next Generation EU’ themes;  vi)	An educational tool (E-NextGen) channelling our data for use in classrooms and by the general public;  vii)	Comprehensive training materials related to all project outputs. 

Cooperation and AgReements enhancing Global interOperability for Aerosol, Cloud and Trace gas research infrastructures

The goal of CARGO-ACT is to deliver a clear roadmap for sustainable global cooperation between key ground-based aerosol, cloud and trace gas research infrastructures, each having invested in infrastructure and services to support their observing networks with a long-term perspective, with a view to consolidating into a sustainable global research infrastructure in the future. There is a strong desire for global integration from the research community, including weather, climate, and air quality monitoring and modelling,  and in particular from space agencies, since global networks of ground-based observations are an essential component complementing Earth Observation from space, providing calibration and validation of the remote sensing information collected by current and future satellite missions. The integration of the current ground-based networks, which may have different interests and priorities, requires cooperation and agreements at the global level, including engagement with relevant stakeholders. Their service provision is not limited to data services, but includes access to the measurement facilities, reference instruments, reference standards and laboratories, all of which are topics to be assessed in CARGO-ACT.    The specific objectives of CARGO-ACT are to, develop sustainable partnerships and decision making processes with relevant partners, demonstrate the benefits of converging interoperability and standards to stakeholders and the global research community, establish the mechanisms for providing  international access to distributed research infrastructures and develop a roadmap for upscaling towards an integrated global research infrastructure for aerosol, cloud and trace gases. 

Midlene fra FINANSMARK-Finansmarkedet fordelt på år

Midlene fra FINANSMARK-Finansmarkedet fordelt på fylker

Midlene fra FINANSMARK-Finansmarkedet fordelt på fagområde

Regulatorisk sandkasse for fintech - anbefalinger for implementering i Norge

Dette prosjektet er sentrert rundt Riemanns zeta-funksjon som bærer i seg informasjon om hvordan primtallene er fordelt, det vil si de positive heltallene 2, 3, 5, 7, 11 osv. som bare er delelige med 1 og seg selv. Slike tall spiller en viktig rolle i sikre systemer for asymmetrisk kryptering. Den berømte Riemann-hypotesen forutsier hvor de såkalt ikke-trivielle nullpunktene til zeta-funksjonen ligger. Hvis vi visste at Riemann-hypotesen var sann, ville vi ha en presis asymptotisk formel for hvordan primtallene er fordelt. 

Dette prosjektet utforsker forbindelser mellom de ikke-trivielle nullpunktene til zeta-funksjonen og usikkerhetsprinsippet fra fysikk og signalbehandling. Prosjektet undersøker også hvordan sammenhengen mellom primtallene og de ikke-trivielle nullpunktene til zeta-funksjonen kan forstås i lys av teorien for kvasikrystaller, som er strukturer med en bestemt orden men uten noen form for periodisitet.

Studiet av fordelingen av primtallene dreier seg i stor grad om å forstå samspillet mellom additive og multiplikative strukturer. Prosjektet utvikler en gren av matematisk analyse som kalles multiplikativ analyse, der man studerer denne typen samspill innenfor rammen av funksjonalanalyse.

The proposal consists of three topics: (A) Analysis on the Riemann zeta function, (B) multiplicative analysis, and (C) Fourier interpolation and quasicrystals. Parts (B) and (C) represent emerging fields of analysis and are interconnected via their link to part (A). The proposed research aims at shaping the new fields (B) and (C) and at the same time advancing related analytic methods pertaining to part (A). 

Part (A) aims at developing analytic techniques and viewpoints that are of specific interest to the Riemann zeta function and other L-functions. The project will in particular pursue possible number theoretic applications of Fourier interpolation and quasicrystals in this context. 

Part (B) will develop the theory of Hardy spaces of Dirichlet series and specifically study composition operators acting on such spaces and spectral resolution of Mellin type operators. The project aims at solving embedding problems, with special emphasis on clarifying the scope of contractive embeddings and describing suitable classes of Carleson measures. An additional goal of part (B) is to describe curves and measures for which Fourier restriction is admitted. 

Part (C) will develop the general theory of Fourier interpolation and quasicrystals. The proposed research aims at clarifying the scope of Fourier interpolation and at unifying this emerging theory with classical time–frequency analysis. This involves obtaining a better understanding of the link between Fourier interpolation and crystalline measures, as well as determining whether the full structure inherent in a quasicrystal is indeed needed for universal sampling.

The project will support 9 man-years of research carried out by three PhD students.

Fourier Methods and Multiplicative Analysis

[Hentet fra abstraktet]: The proposal will develop areas of analysis related to the Riemann zeta function. The proposed research aims at advancing analytic methods and viewpoints that will enhance our understanding of the zeta function and other objects of number theoretic interest.

Analysis around the Riemann zeta function

Analyse er en gren av matematikken der man studerer ulike egenskaper til funksjoner, alt fra polynomer og elementære funksjoner av én variabel til løsninger av partielle differensialligninger eller kompliserte funksjoner i analytisk tallteori.  Den grunnleggende ideen i harmonisk analyse er å finne hensiktsmessige måter å representere funksjoner på. Eksempler inkluderer harmoniske svingninger i signalbehandling og wavelet-dekomposisjoner i bildehandling.

Vi har nylig hatt betydelig fremgang i vårt arbeid med geometrisk analyse av partielle differensialligninger og analytisk tallteori, noe som har ledet oss til å formulere et ambisiøst program for COMAN. Prosjektet er delt opp i fire retninger. Vi studerer kvantitative egenskaper til løsninger av elliptiske partielle differensialligninger som beskriver vibrasjoner i membraner. Oppførselen til Schrödinger-evolusjonen utgjør et annet tema; vi studerer evolusjon på diskrete strukturer som web-lignende grafer. Vi studerer Dirichlet-rekker og Riemanns zeta-funksjon, som forbinder tallteori og kompleks analyse. Det siste temaet i prosjektet er ikkeharmoniske Fourier-rekker og Meyer-kvasikrystaller. Fellesnevneren i vårt arbeid innenfor disse fire områdene er vår søken etter distinkte kombinatoriske strukturer og enkle byggeklosser som verktøy for å forstå det foreliggende problem. 

I vårt studium av elliptiske partielle differensialligninger som beskriver vibrasjoner i tynne metallplater, er hovedmålet å forstå ulike geometriske objekter gjennom noen tydelige karakteristiske trekk eller ved å tilnærme disse objektene ved hjelp av enklere størrelser. Vi arbeider med å etablere en formodning om at mønstre som forekommer i disse vibrasjonene, er av lignende art som de mye enklere mønstrene som fremkommer i studiet av algebraiske polynomer.

Vi har arbeidet videre med analyse av punktmengder i enhetskuben som har en spesiell type jevn fordeling og studerer anvendelser av disse i signalbehandling. Punktmengder med såkalt lav diskrepans har vært mye brukt i kvasi-Monte Carlo-metoder, og i den senere tid er det blitt erkjent at slike mengder også kan være nyttige i signalbehandling. Det er velkjent at om man forskyver heltallene ved hjelp av en Kronecker-følge, får man en følge med interessante sampling-egenskaper; dette følger av det berømte sampling-teoremet til Matei og Meyer for kvasikrystaller. Vårt mål er å avgjøre om et lignende resultat kan oppnås om man i stedet gjør en forskyvning ved hjelp av en Halton-følge. Et slikt resultat vil kunne være av betydelig interesse fordi Halton-følger er mye enklere å håndtere numerisk.
 
Arbeidet med å utvikle teorien for funksjonsrom av Dirichlet-rekker og samspillet med tallteori og teorien for Riemanns zeta-funksjon står sentralt i prosjektet. Vi hadde nylig et gjennombrudd som har som konsekvens at den klassiske Riemann-Weil-formelen for Riemanns zeta-funksjon kan betraktes som et spesialtilfelle av en større klasse av tid-frekvens-representasjoner av funksjoner. Vi undersøker for tiden de analytiske egenskapene til slike representasjoner og mulige tallteoretiske anvendelser av dette arbeidet. Vi har også videreutviklet vår metode for deteksjon av ekstremverdier av L-funksjoner og oppnådd en dikotomi som antyder at zeta-funksjonen kan oppnå vesentlig større verdier enn det vi tidligere har vært i stand til å påvise.

En nøkkelresultat, nært knyttet til usikkerhetsprinsippet, etablerer en fundamental lokaliseringsegenskap for reproduserende kjerner i Hardy-og Bergman-rom. Slike kjerner er sentrale i kvantemekanikk der de kalles koherente tilstander. Vårt resultat verifiserer en formodning om en viss type entropi som studeres innen matematisk fysikk.

Schrödinger-evolusjonen studeres i kvantemekanikk og er nært forbundet med Heisenbergs usikkerhetsprinsipp. Et av våre mål er å forstå og beskrive konsentrasjonsegenskapene til løsninger til Schrödinger-ligningen, kjent som bølgefunksjoner. Vi har lykkes med å besvare et spørsmål som har stått åpent i lang tid innenfor dette feltet, angående hvordan stasjonære plane bølger avtar. Nylig har vi også funnet et nytt bevis for Hardys klassiske usikkerhetsprinsipp ved bruk av Schrödinger-evolusjoner med kompleksifisert tid. Beviset er mer elementært enn det klassiske man finner i lærebøker. I et annet arbeid om usikkerhetsrelasjoner har vi oppnådd nye resultater om konsentrasjon av signaler i porøse mengder; dette bidrar til å videreutvikle og utvide et forskningsfelt med dype klassiske røtter som har ulike anvendelser innen tid-frekvens-analyse og spektralgeometri.

COMAN is a 5-year FRIPRO Toppforsk project in mathematics at the Norwegian University of Science and Technology (NTNU). Its focus is basic research in analysis and its interaction with mathematical physics, PDEs, and number theory. 

The applicants are Eugenia Malinnikova (principal investigator),
Andriy Bondarenko, Sigrid Grepstad, Yurii Lyubarskii, and Kristian Seip. Funding is sought for 3 PhD students, 3 postdoctoral fellows, and operating expenses. Collaboration with world-leading mathematicians is included.

A perpetual trend in classical analysis is that major breakthroughs tend to rely on constructions or decompositions that are of a distinct combinatorial nature. The crux of the matter is often to identify
and analyze certain discrete structures or simple building blocks that are instrumental in understanding and controlling the branching complexity of the problem at hand. In harmonic analysis, prominent
examples stretch from the classical Calderón-Zygmund theory and Carleson's corona construction to wavelets, compressed sensing, and applications of Meyer quasicrystals.
 
The recent significant progress in our work on geometric analysis of PDEs and analytic number theory has led us to formulate an ambitious program for COMAN, aiming to tackle several hard problems in classical analysis and related fields. The choice of topics rests on the
scientific interests of our team members; the common thread in our scientific approach is to investigate in depth concrete and fundamental problems, in search for the basic underlying principles that are likely to be of a combinatorial nature and to arise from geometric, probabilistic, or number theoretic insight.

Combinatorial Methods in Analysis

Prosjektet har utviklet et forskningsområde som spenner over analytisk tallteori, operatorteori og 
kompleks og harmonisk analyse. Det sentrale problemet som ligger til grunn for denne forskningen, dreier seg om å oppnå en bedre forståelse av hvordan primtallene er fordelt. I 2014 løste medarbeidere i prosjektet et nesten 30 år gammelt problem angående såkalte GCD-matriser, nært forbundet
med veksten til Riemanns zeta-funksjon på den kritiske linjen. Dette arbeidet ledet til et nytt nedre estimat for veksten av Riemanns zeta-funksjon, som er første vesentlige forbedring siden 1977. Senere i perioden ble en lignende teknikk brukt til å gi forbedrede estimat for argumentet til zeta-funksjonen, hvilket er relatert til fordelingen av de ikke-trivielle nullpunktene og, via en klassisk dualitet, til fordelingen av primtallene.  Arbeidet med å bedre forståelsen av Riemanns zeta-funksjon pågår fremdeles, noe som gir forhåpninger om ytterligere forbedringer i fremtidige prosjekter. Andre resultater dreier seg om forståelsen av grunnleggende operatorer som virker på rom av Dirichlet-rekker. Et eksempel på en slik operator er en multiplikativ versjon av Hilberts klassiske matrise. Den fremkommer på en naturlig måte som matrisen til en integraloperator som involverer Riemanns zeta-funksjon. I 2016 ferdigstilte prosjektet et første studium av en annen type grunnleggende operatorer, nemlig såkalte Volterra-operatorer, som fremviser et nytt og ukonvensjonelt samspill mellom rom av holomorfe funksjoner og tallteori. Prosjektet har i den senere tid studert kontraktive ulikheter og anvendelser av disse med sikte på å oppnå forbedrede estimat for pseudomomenter til Riemanns zeta-funksjon.

The proposal addresses major problems concerning Hardy spaces of Dirichlet series, boundary limits of Dirichlet series, the interplay between complex analytic methods, probabilistic techniques, and analytic number theory in the study of Dirichlet series a nd Dirichlet polynomials, function theory in polydiscs, and harmonic analysis and operator theory on the infinite-dimensional torus. The proposal will
-	search for novel concepts and methods required to solve some of the basic problems of operator-related  function theory and harmonic analysis on the infinite-dimensional torus
-	direct efforts to significantly strengthen the interplay between the different research directions involved in the project.

Dirichlet Series and Analysis on Polydiscs

The project aims to strengthen and further develop basic research within the group of researchers in classical analysis and differential equations at NTNU. Situated at Norway's premier engineering school, the research team of this project has as its visio n to  
- operate in the two-way street between mathematical and technological sciences
- develop basic research of high quality and contemporary interest.
A common feature of the basic research of this group of analysts is that
- problems often have their  origin in physical or technological applications
- problems are inherently nonlinear
- harmonic and complex analysis often enter the analysis, in addition to tools from PDEs and functional analysis
The project will 
- support interaction within the group 
- strengthen recruitment to the field in terms of new PhDs and postdoctoral fellows
- strengthen collaboration between junior and senior faculty
- support scientific development of the two junior faculty members Malinnikova (female) and Selberg
- strengt hen collaboration with relevant groups within Norway
- strengthen and develop international collaboration.
The core of the project will be the training of 4 PhDs (projects are specified) and 2 postdoctoral fellows (projects are specified). These young res earchers will join an active group of researchers consisting of a blend of senior and junior faculty, postdoctoral fellows (currently 3) and fellow PhD students (currently 8 of whom 3 are women). The group has extensive international collaboration, and gu est researchers will frequently visit the group. The group run two weekly seminars; during the project period, two international workshops will be organised at NTNU. The project will support high quality research closely related to the core activity of th e project. 
The research team aims to continue its successful recruitment of female PhD students.

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