As Buzz mentioned in comments, the fact that your own PhD student reported you for plagiarism is deeply troubling. It indicates that your PhD student is very unhappy with you as an academic supervisor. But you do not even mention why your PhD student reported you to the University, as if their motivation does not matter. I would expect a PhD supervisor to be better involved in academic life of their student to be able at least spot the problem before it hits you in the back.
The way how you describe the alleged misconduct is also deeply troubling to me. The methods are clearly potent enough to help you win a significant piece of funding, yet you did not care to research them properly and establish attribution in three years. Your attempts to explain the situation sound rather weak to me.
I had no clue that these papers are published and are available on
In academia, when we do not "have a clue" about things, we research them. You had three years to find out and many ways to do so: to contact the author of the poster and ask her for references, to search online, to ask a colleague in your department or from a maths department for help. I expect a PhD student to be persistent enough to find proper references for their paper; I am shocked that an established academic attempts to brush it off with a simple "I dunno" comment.
To answer your questions:
Can I call the granting body for correction and refining the proposal and updating the citations?
Please read the definition of plagiarism or ask people from the ethical committee at your university to explain them to you. Plagiarism is an act of passing someone else's intellectual work as your own. By default, a funding panel assumes that all ideas put in your proposal are your own, unless specified otherwise. The funding you received is a recognition of the strength and value of these ideas – and these ideas are not your own! You can amend the document, but it does not wipe the fact that your proposal have likely misled the awarding panel. And obviously you cannot return the funding because it is already spent on hiring the PhD students and staff for the project.
Can they sack me for just not citing the methods that I have used?
It depends on the policies and practices of your university, and frankly on how much support your head of department is willing to offer you. If this information is passed on to the funder – which your university is probably obligated to do – it is likely that you may be banned from making further applications for several years at least. Your university may not be pleased with it.
I am shocked, however, that you are concerned with your own safety rather with making things right. The real problem is not that your PhD student reported you, but that you clearly do not understand the ethical standards of the environment you chose to work in. Your real concern should be not to fix the proposal, but to fix your own misunderstanding of how academic research works.