We are pleased to announce the research visit of PhD Deepika Kumari from Guru Gobind Singh Indraprastha University between 01.07.2017 and 09.07.2017 for a seminar at the Romanian Institute of Science and Technology. Deepika’s research area of specialization is Differential Geometry and she has worked extensively on the validity of Chen’s conjecture of Biharmonic Submanifolds in various ambient spaces such as Euclidean space, pseudo-Euclidean space and space forms. Her research interests have strong correlation with the topics of the DeepRiemann project – Riemannian Optimization Methods for Deep Learning (2016-2020), supported by the POC 2014-2020 grant – ANCSI Competitiveness Operational Program 2014-2020, and led by PhD Luigi Malagò, head of the Machine Learning and Optimization Group at RIST. The DeepRiemann project aims at the design and analysis of novel training algorithms for Neural Networks in Deep Learning, by applying notions of Riemannian optimization and Differential Geometry.
During her visit, Deepika will hold the seminar entitled “Geometry of Biharmonic Submanifolds” on 04.07.2017 at 3 pm local time. You can find below the abstract of this seminar:
During the last two decades, the study of biharmonic submanifolds has been an active area of research. It is well-known that the conjecture made by Chen in 1991 that “the only biharmonic submanifolds of Euclidean spaces are the minimal ones” is still an open problem. Deepika has proven some important results to validate and generalize the Chen’s conjecture in different ambient spaces such as Euclidean space, pseudo-Euclidean space and space form. In her presentation, she will give a brief introduction to biharmonic submanifold. Also, she will introduce the Chen’s conjecture of biharmonic submanifold and present some recent developments of conjecture.
Key Words: Biharmonic submanifolds, Pseudo-Euclidean space, Space form, Null 2-type hypersurfaces, Mean curvature vector.
Deepika Kumari has recently completed her Ph.D. from University School of Basic & Applied Sciences, Guru Gobind Singh Indraprastha University, New Delhi, India under the supervision of Dr. Ram Shankar Gupta, on the topic of “Geometry of Submanifolds and Biharmonic Maps”. She has been awarded Indraprastha research fellowship (2012-2016) for pursuing her research. Her area of specialization is Differential Geometry and has worked extensively on the validity of Chen’s conjecture of Biharmonic Submanifolds in various ambient spaces such as Euclidean space, pseudo-Euclidean space and space forms. Additionally, her research interests include real analysis and algebra. She has worked as senior lecturer (2007-2012) in Gurgaon Institute of Technology and Management, Gurgaon, India and taught Engineering Mathematics to engineering graduate students. Previously, she has worked as lecturer (2006-2007) in S. A. Jain College, Ambala city, India, teaching undergraduate students. She has obtained her Master of philosophy (2005) and masters in pure mathematics (2003) from Kurukshetra University, Haryana, India.