Symmetries in real and complex geometry. This project concerns an important area of abstract modern geometry. The results and techniques of the project will lead to significant progress in this area. It will benefit the national scientific reputation, strengthen the research profile of the home institutions, and provide training to young researchers.
Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds. This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on
Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form ....Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds. This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on
Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form for multicodimensional Levi-nondegenerate CR-manifolds and extension of CR-mappings between them are major goals in complex analysis. Identification of Chern-Moser chains and equivariant linearisation of isotropy automorphisms are major goals in geometry.Read moreRead less
Estimating genotype-environment interaction using genomic information. This project aims to develop statistical methods that can explore genotype–environment interaction at the genomic level using genome-wide single nucleotide polymorphisms or sequence data. It plans to estimate how the effects of genetic variants change with changing environmental conditions and how overall genetic variance changes due to changing effects in specific gene regions. It plans to deliver statistical models and meth ....Estimating genotype-environment interaction using genomic information. This project aims to develop statistical methods that can explore genotype–environment interaction at the genomic level using genome-wide single nucleotide polymorphisms or sequence data. It plans to estimate how the effects of genetic variants change with changing environmental conditions and how overall genetic variance changes due to changing effects in specific gene regions. It plans to deliver statistical models and methods and an efficient algorithm implemented in software, which would broadly benefit the field of complex trait genetics. Methods to estimate genotype–environment interaction effects at the genomic level would help elucidate complex biological systems, including human genetic response to changing environmental factors and the potential adaptation of animals to changing environmental conditions.Read moreRead less
Whole-genome multivariate reaction norm model for complex traits. This project aims to develop a multivariate whole-genome genotype-covariate correlation and interaction model that can be applied to a wide range of existing genome-wide association study (GWAS) datasets. Genotype-covariate correlation and interaction (GCCI) are fundamental in biology but there is no standard approach to disentangle interaction from correlation in the whole-genome analyses. This project will address the key featur ....Whole-genome multivariate reaction norm model for complex traits. This project aims to develop a multivariate whole-genome genotype-covariate correlation and interaction model that can be applied to a wide range of existing genome-wide association study (GWAS) datasets. Genotype-covariate correlation and interaction (GCCI) are fundamental in biology but there is no standard approach to disentangle interaction from correlation in the whole-genome analyses. This project will address the key feature in biology, which relates to dissecting the complex mechanism of association and interaction. The proposed statistical model implemented in a context of a novel design based on multiple GWAS data sets is a paradigm shifting-tool with applications to multiple industries.Read moreRead less