# Research Areas

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My research directions are compactly explained below with the aid of presentations I have given. For more popular descriptions visit the Royal Society Exhibition section.

## Isospectrality

We developed a method which enables one to construct isospectral objects, such as quantum graphs and drums. This method is based on some basic representation theory arguments. For an explanation of the method and some neat examples, you might want to have a look at the isospectral construction method for drums (Oxford University SIAM Student Chapter Conference, February 2011) or the same construction demonstrated on quantum graphs (satellite workshop in Edinburgh belonging to the semester on Inverse Problems at the Isaac Newton Institute, October 2011). Read more…

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