ERC FUNDED PROJECTS

The proposal consists of an extensive research program to advance the understanding of singular integral operators of Harmonic Analysis in various situations on the borderline of the existing theory. This is to be achieved by a creative combination of techniques from Analysis and Probability. On top of the standard arsenal of modern Harmonic Analysis, the main probabilistic tools are the martingale transform inequalities of Burkholder, and random geometric constructions in the spirit of the random dyadic cubes introduced to Nonhomogeneous Analysis by Nazarov, Treil and Volberg. The problems to be addressed fall under the following subtitles, with many interconnections and overlap: (i) sharp weighted inequalities; (ii) nonhomogeneous singular integrals on metric spaces; (iii) local Tb theorems with borderline assumptions; (iv) functional calculus of rough differential operators; and (v) vector-valued singular integrals. Topic (i) is a part of Classical Analysis, where new methods have led to substantial recent progress, culminating in my solution in July 2010 of a celebrated problem on the linear dependence of the weighted operator norm on the Muckenhoupt norm of the weight. The proof should be extendible to several related questions, and the aim is to also address some outstanding open problems in the area. Topics (ii) and (v) deal with extensions of the theory of singular integrals to functions with more general domain and range spaces, allowing them to be abstract metric and Banach spaces, respectively. In case (ii), I have recently been able to relax the requirements on the space compared to the established theories, opening a new research direction here. Topics (iii) and (iv) are concerned with weakening the assumptions on singular integrals in the usual Euclidean space, to allow certain applications in the theory of Partial Differential Equations. The goal is to maintain a close contact and exchange of ideas between such abstract and concrete questions.

1 100 000 €

Start date: 2011-11-01, End date: 2016-10-31

This project has the potential to radically change current understanding of cultic and social transformation in the post-exilic temple community of Jerusalem (c. 6th-4th centuries BCE), an important formative phase of ancient Judaism. “BABYLON” draws on recent, ground-breaking advances in the study of cuneiform texts to illuminate the Babylonian environment of the Judean exile, the socio-historical context which gave rise to the transformative era in Second Temple Judaism. In particular, these new data show that the parallels between Babylonian and post-exilic forms of cultic and social organization were substantially more far-reaching than presently recognized in Biblical scholarship. “BABYLON” will study the extent of these similarities and explore the question how Babylonian models could have influenced the restoration effort in Jerusalem. This goal will be achieved through four sub-projects. P1 will study the social dynamics and intellectual universe of the Babylonian priesthood. P2 will finalize the publication of cuneiform archives of Babylonian priests living in the time of the exile. P3 will identify the exact areas of change in the post-exilic temple community of Jerusalem. P4, the synthesis, will draw from each of these sub-projects to present a comparative study of the Second Temple and contemporary Babylonian models of cultic and social organization, and to propose a strategy of research into the possible routes of transmission between Babylonia and Jerusalem. The research will be carried out by three team members: the PI (P1 and P4), a PhD in Assyriology (P2) and a post-doctoral researcher in Biblical Studies specialized in the Second Temple period (P3 and P4). The participation of the wider academic community will be invited at two moments in the course of the project, in the form of a workshop and an international conference. “BABYLON” will adopt an interdisciplinary approach by bringing together Assyriologists and Biblical scholars for a much-needed dialogue, thereby exploding the artificial boundaries that currently exist in the academic landscape between these two fields.

1 200 000 €

Start date: 2009-09-01, End date: 2015-08-31

This project revisits a major question in world history: how can we explain the continuity of the Chinese Empire. Moving beyond the comparison of early world empires (China and Rome) to explain the different courses Chinese and European history have taken, this project aims to assess the importance of political communication in the maintenance of empire in the last millennium. The core questions are twofold: 1) How can the continuity of empire in the Chinese case be best explained? 2) Does the nature and extent of political communication networks, measured through the frequency and multiplexity of information exchange ties, play a critical role in the reconstitution and maintenance of empire? Its methodology is based on the conviction that an investigation of the nature and extent of political communication in imperial Chinese society should include a systematic quantitative and qualitative analysis of the rich commentary on current affairs in correspondence and notebooks. By combining multi-faceted digital analyses of relatively large corpora of texts with an intellectually ambitious research agenda, this project will both radically transform our understanding of the history of Chinese political culture and inspire wide-ranging methodological innovation across the humanities.

1 432 797 €

Start date: 2012-04-01, End date: 2017-08-31

Our primary motivation stems from queueing theory, the branch of applied probability that deals with congestion phenomena. Congestion levels are typically nonnegative, which is why reflected stochastic processes arise naturally in queueing theory. Other applications of reflected stochastic processes are in the fields of branching processes and random graphs. We are particularly interested in critically-loaded queueing systems (close to 100% utilization), also referred to as queues in heavy traffic. Heavy-traffic analysis typically reduces complicated queueing processes to much simpler (reflected) limit processes or scaling limits. This makes the analysis of complex systems tractable, and from a mathematical point of view, these results are appealing since they can be made rigorous. Within the large body of literature on heavy-traffic theory and critical stochastic processes, we launch two new research lines: (i) Time-dependent analysis through scaling limits. (ii) Dimensioning stochastic systems via refined scaling limits and optimization. Both research lines involve mathematical techniques that combine stochastic theory with asymptotic theory, complex analysis, functional analysis, and modern probabilistic methods. It will provide a platform enabling collaborations between researchers in pure and applied probability and researchers in performance analysis of queueing systems. This will particularly be the case at TU/e, the host institution, and at the affiliated institution EURANDOM.

970 800 €

Start date: 2010-08-01, End date: 2016-07-31