Oct 2015-date: Sultan Qaboos Research Fellowship/College Lectureship in Mathematics, Corpus Christi College, University of Cambridge
Dec 2014- Apr 2015: Crighton Fellowship, University of Manchester
2010-2015: Ph.D. Cambridge Centre for Analysis, Trinity College, University of Cambridge
2009-2010: Part III Mathematics, Trinity College, University of Cambridge
2006-2009: B.A. Mathematics, Trinity College, University of Cambridge
My research interest is in Partial Differential Equations (PDEs) in particulat the Wiener-Hopf method. The Wiener-Hopf method is used for a broad collection of PDEs which arise in acoustic, finance, hydrodynamic, elasticity, potential and electromagnetic theories. It is an elegant method which extends the separation of variables technique used to investigate PDEs. For the scalar Wiener-Hopf the solution can be expressed in terms of a Cauchy type integral. In more complicated scalar Wiener-Hopf equations the exact solution is difficult or slow to compute. The aim is to develop approximate methods which are easily implementable, reliable and have explicit error bounds.
Matrix Wiener–Hopf factorisation is a natural extension of the traditional scalar Wiener–Hopf factorisation. It allows to solve more advanced and realistic problems and is the field of current intensive research. Approximating matrix Wiener-Hopf equation is complex due to instabilities. Stability means that small changes in the initial Wiener–Hopf equation can only change the resulting solution by a small amount. I study the approximate Wiener-Hopf techniques and their application in acoustics. There are many interesting acoustic problems, for example, I am working on the scattering of a sound wave by an infinite periodic grating composed of rigid plates and on the silent flight of owls.
Kisil, A., Ayton, L. , 2017. Aerodynamic noise generated by finite porous extensions to rigid trailing edges. Submitted. Available at: https://www.researchgate.net/publication/315798846_Aerodynamic_noise_generated_by_finite_porous_extensions_to_rigid_trailing_edges
Kisil, A., 2017. An Iterative Wiener--Hopf method for triangular matrix functions with exponential factors. Submitted Available at: https://arxiv.org/abs/1703.08412
Kisil, A., 2015. Stability analysis of matrix Wiener--Hopf factorisation of Daniele--Khrapkov class and reliable approximate factorisation. Proc. R. Soc. A 2015 471 20150146. Available at: http://arxiv.org/abs/1504.01108
Kisil, A., 2015. The relationship between a strip Wiener--Hopf problem and a line Riemann--Hilbert problem. IMA J Appl Math (2015) doi: 10.1093/imamat/hxv007. Available at: http://arxiv.org/abs/1504.00877
Kisil, A., 2013. A Constructive method for approximate solution to scalar Wiener-Hopf Equations. Proc. R. Soc. A 469, 20120721 (2013) Available at: http://arxiv.org/abs/1302.3903
Kisil, A., 2010. Isometric action of SL2(R) on homogeneous spaces. Advances in Applied Clifford Algebras, [Online]. 20(2), 299-312. Available at: http://www.springerlink.com/content/j10l73q811625735/
Kisil, A., 2010. Gromov Conjecture on Surface Subgroups: Computational Experiments. Transactions of the Institute of Mathematics of the National Academy of Sciences of Ukraine, 11. Available at: http://arxiv.org/abs/1001.1460v1
S. D. Connell , G. Heath , P. D. Olmsted, A. Kisil, 2012. Critical point fluctuations in supported lipid membranes. Faraday Discuss. Available at: http://pubs.rsc.org/en/content/articlelanding/2013/FD/C2FD20119D
Complex Analysis IB supervisions
Topics in Analysis II supervisions
Differential Geometry II supervsions
Office: F0.13
Email: a.kisil@maths.cam.ac.uk
Address:
Cambridge Center for Analysis,
Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA
Telephone: +44 1223 339877