University of Durham, United Kingdom, University of Durham, United Kingdom

Position ID: 1530-PDRA [#17056]
Position Title: Postdoctoral Research Associate
Position Type: Postdoctoral
Position Location: Durham, County Durham DH1, United Kingdom [map]
Subject Area: Pure Mathematics
Application Deadline: 2021/01/17 11:59PMhelp popup (posted 2020/12/17, listed until 2021/01/17)
Position Description:    

*** the list date or deadline for this position has passed. ***

Applications are invited for a Postdoctoral Research Associate in Pure Mathematics. The position is funded by the ERC Starting Grant of Michael Magee (the Principal Investigator) titled `The ubiquity of optimal spectral gaps’ (UBIQGAP, no. 949143). An abridged abstract of the program follows.

Spectral gap is a fundamental concept in mathematics, physics, and computer science as it governs the exponential rate at which a process converges towards its stationary state. It informs the spectral lines of hydrogen, how we shuffle cards, the behaviour of semiconductors, and web search algorithms. Moreover, some of the most prominent issues of contemporary mathematics, including the Ramanujan-Petersson conjecture and the Yang-Mills mass gap, revolve around spectral gap. This proposal seeks to investigate the nature of the spectral gap for hyperbolic surfaces and unitary representations of fundamental groups of surfaces. In the former case, the spectral gap occurs in the spectrum of the Laplace-Beltrami operator on the surface, and in the latter, it occurs in the spectrum of a Hecke operator attached to the representation. The two main motifs of the proposal are ubiquity and optimality. Is the spectral gap ubiquitous? Does it exist for random surfaces and random representations? Is it easy to construct surfaces with a large spectral gap? In what cases can one prove that the spectral gap is close to optimal? The sharpest and most ambitious questions discussed in this proposal combine these two aspects and ask whether objects with (almost) optimal spectral gap appear with high frequency.

The successful applicant will be expected to fit into one of two sub-teams of the project. One of the sub-teams will be working in `Analysis, Dynamics, and Spectral Geometry’. The other sub-team will be working on `Integration on Representation Varieties’.

The post comes with a generous allocation of travel money and opportunities to speak at international workshops that form part of the project.

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Contact: Dr Thanasis Bouganis
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