The Unified Transform, Medical Imaging, Asymptotics of the Riemann Zeta Function: Part I

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• Thanasis Fokas (University of Cambridge)
• Friday 15 November 2019, 11:00-12:00
• Seminar Room 2, Newton Institute.

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CAT - Complex analysis: techniques, applications and computations

Employing techniques of complex analysis, three different problems will be discussed: (i) Initial-boundary value problems via the unified
transform (also known as the Fokas method,www.wikipedia.org/wiki/Fokas_method)[1]. (ii) The evaluation of the large t-asymptotics to all orders of the Riemann zeta function², and the introduction of a new approach to the Lindelöf Hypothesis³. (iii) A novel analytical algorithm for the medical technique of SPECT and its numerical implementation [4].

[1] J. Lenells and A. S. Fokas. The Nonlinear Schrödinger Equation
with t-Periodic Data: I. Exact Results, Proc. R. Soc. A 471 , 20140925
(2015).
J. Lenells and A. S. Fokas, The Nonlinear Schrödinger Equation with
t-Periodic Data: II. Perturbative Results, Proc. R. Soc. A 471 ,
20140926 (2015).
[2] A.S. Fokas and J. Lenells, On the Asymptotics to All Orders of the
Riemann Zeta Function and of a Two-Parameter Generalization of the
Riemann Zeta Function, Mem. Amer. Math. Soc. (to appear).
[3] A.S. Fokas, A Novel Approach to the Lindelof Hypothesis,
Transactions of Mathematics and its Applications, 3(1), tnz006 (2019).
[4]N.E. Protonotarios, A.S. Fokas, K. Kostarelos and G.A. Kastis, The Attenuated Spline
Reconstruction Technique for Single Photon Emission Computed Tomography, J. R. Soc.
Interface 15, 20180509 (2018).

This talk is part of the Isaac Newton Institute Seminar Series series.

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