Project acronym ANPROB
Project Analytic-probabilistic methods for borderline singular integrals
Researcher (PI) Tuomas Pentinpoika Hytönen
Host Institution (HI) HELSINGIN YLIOPISTO
Call Details Starting Grant (StG), PE1, ERC-2011-StG_20101014
Summary 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.
Summary
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.
Max ERC Funding
1 100 000 €
Duration
Start date: 2011-11-01, End date: 2016-10-31
Project acronym GLUCOSE SENSING
Project Transcriptional networks in glucose sensing
Researcher (PI) Ville Ilmari Hietakangas
Host Institution (HI) HELSINGIN YLIOPISTO
Call Details Starting Grant (StG), LS4, ERC-2011-StG_20101109
Summary Glucose is key source of nutritional energy and raw material for biosynthetic processes. Maintaining glucose homeostasis requires a regulatory network that functions both in the systemic level through hormonal signaling and locally at the intracellular level. Insulin signalling is the main hormonal mechanism involved in maintaining the levels of circulating glucose through regulation of cellular glucose intake and metabolism. While the signalling pathways mediating the effects of insulin have been thoroughly studied, the transcriptional networks downstream of insulin signalling are not comprehensively understood. In addition to insulin signalling, intracellular glucose sensing mechanisms, including transcription factor complex MondoA/B-Mlx, have recently emerged as important regulators of glucose metabolism. In the proposed project we aim to take a systematic approach to characterize the transcriptional regulators involved in glucose sensing and metabolism in physiological context, using Drosophila as the main model system. We will use several complementary screening strategies, both in vivo and in cell culture, to identify transcription factors regulated by insulin and intracellular glucose. Identified transcription factors will be exposed to a panel of in vivo tests measuring parameters related to glucose and energy metabolism, aiming to identify those transcriptional regulators most essential in maintaining glucose homeostasis. With these factors, we will proceed to in-depth analysis, generating mutant alleles, analysing their metabolic profile and physiologically important target genes as well as functional conservation in mammals. Our aim is to identify and characterize several novel transcriptional regulators involved in glucose metabolism and to achieve a comprehensive overview on how these transcriptional regulators act together to achieve metabolic homeostasis in response to fluctuating dietary glucose intake.
Summary
Glucose is key source of nutritional energy and raw material for biosynthetic processes. Maintaining glucose homeostasis requires a regulatory network that functions both in the systemic level through hormonal signaling and locally at the intracellular level. Insulin signalling is the main hormonal mechanism involved in maintaining the levels of circulating glucose through regulation of cellular glucose intake and metabolism. While the signalling pathways mediating the effects of insulin have been thoroughly studied, the transcriptional networks downstream of insulin signalling are not comprehensively understood. In addition to insulin signalling, intracellular glucose sensing mechanisms, including transcription factor complex MondoA/B-Mlx, have recently emerged as important regulators of glucose metabolism. In the proposed project we aim to take a systematic approach to characterize the transcriptional regulators involved in glucose sensing and metabolism in physiological context, using Drosophila as the main model system. We will use several complementary screening strategies, both in vivo and in cell culture, to identify transcription factors regulated by insulin and intracellular glucose. Identified transcription factors will be exposed to a panel of in vivo tests measuring parameters related to glucose and energy metabolism, aiming to identify those transcriptional regulators most essential in maintaining glucose homeostasis. With these factors, we will proceed to in-depth analysis, generating mutant alleles, analysing their metabolic profile and physiologically important target genes as well as functional conservation in mammals. Our aim is to identify and characterize several novel transcriptional regulators involved in glucose metabolism and to achieve a comprehensive overview on how these transcriptional regulators act together to achieve metabolic homeostasis in response to fluctuating dietary glucose intake.
Max ERC Funding
1 496 930 €
Duration
Start date: 2012-01-01, End date: 2017-02-28
