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UID:1454
SUMMARY:50th Anniversary Special Lectures: E. Brian Davies
DESCRIPTION:Non-self-adjoint spectral problems\n\nNon-self-adjoint spectral theory is not yet a coherent subject, in the sense that there is no analogue of the spectral theorem that can act as a basis for further research. The very high instability of eigenvalues under small perturbations often affects the analysis of particular models. The number of these understood is expanding rapidly and will continue to do so into the foreseeable future.\n\n\nWe describe joint work with Michael Levitin on the N → ∞ asymptotic spectral behaviour of a particular family of large non-self-adjoint matrices Ac,N associated with a self-adjoint linear pencil. Crucial insights were obtained by numerical experiments, even though the final analysis does not use rely on numerics. The problem is a matrix analogue of an indefinite self-adjoint linear pencil that concerns a Dirac operator with an indefinite potential. In some sense it is the simplest matrix example of its type, but its behaviour is still far more complex than one might expect. The eigenvalues of the matrix Ac,N converge to the real axis as N → ∞, but the details of the convergence depend strongly on the choice of the real parameter c, in a way that presently defies understanding, even at a numerical level.\n\nAbout the speaker\n\nProfessor Brian Davies has a post-retirement, part time position at King's College, London. He was the President of the London Mathematical Society from 2007 to 2009; honours include a Fellowship of the Royal Society since 1995.\n\nHe is the author of more than 200 mathematical papers, mostly devoted to analysis, heat equations and non-self-adjoint spectral theory, and he has written 7 books, including 'Linear Operators and their Spectra'; his interests encompass the philosophy of mathematics - as seen in 'Science in the Looking Glass' and 'Why Beliefs Matter'. He is also well known in the quantum physics community for work that he did in the 1970s on quantum measurement and open quantum systems.
DTSTART:20140926T150000
DTEND:20140926T160000
LOCATION:Frankland Lecture Theatre, Faraday Building
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UID:1453
SUMMARY:50th Anniversary Special Lectures
DESCRIPTION:This year Lancaster University celebrates the 50th anniversary of its foundation. In honour of this event the Department has organised two Special Lectures. They will take place on Friday 26th September in the Frankland Lecture Theatre; all are welcome. \n\nThe programme is as follows:\n\n\n15:00 Welcome from Professor Amanda Cheywynd\n15:00 - 16:00 Professor E. Brian Davies FRS, King's College, LondonNon-self-adjoint spectral problems abstract\n16:30 - 17:30 Professor W. Hugh Woodin, Harvard UniversityA half-century of independence abstract\n\n\nInformation on travelling to Lancaster and accommodation may be found on the central University pages. The Frankland Lecture Theatre is in the Faraday complex, number 27a on the campus map.\n\nThere will be a dinner in the evening of Friday 26th September. If you wish to attend or for any further information, please contact H.G. Dales at g.dales@lancaster.ac.uk.\n\nThe Special Lectures will be preceded by a meeting of the QOP Network.
DTSTART:20140926T150000
DTEND:20140926T173000
LOCATION:Frankland Lecture Theatre, Faraday Building
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UID:1455
SUMMARY:50th Anniversary Special Lectures: W. Hugh Woodin
DESCRIPTION:A half-century of independence\n\nJust over 50 years ago, Paul Cohen announced the unsolvability of Cantor’s Continuum Hypothesis on the basis of the basic principles of Set Theory, these are the ZFC axioms.\n\nBut does this mean that the question of the Continuum Hypothesis has no answer? Any "solution" must involve the adoption of new principles but which principles should one adopt? Alternatively, perhaps the correct assessment of Cohen's discovery is that the entire enterprise of the mathematical study of Infinity is ultimately doomed because the entire subject is simply a human fiction without any true foundation. In this case, any "solution" to the Continuum Hypothesis is just an arbitrary (human) choice.\n\nOver the last few years a scenario has emerged by which with the addition of a single new principle not only can the problem of the Continuum Hypothesis be resolved, but so can all of the other problems which Cohen's method has been used to show are also unsolvable (and there have been many such problems). Moreover the extension of the basic (ZFC) principles by this new principle would be seen as a compelling option based on the fundamental intuitions on which the entire mathematical conception of Infinity is founded.\n\nHowever, this scenario critically depends upon the outcome of a single conjecture. If this conjecture is false then the entire approach, which itself is the culmination of nearly 50 years of research, fails or at the very least has to be significantly revised.\n\nThus the mathematical study of Infinity has arguably reached a critical point and interesting times are ahead.\n\nAbout the speaker\n\nProfessor W. H. Woodin holds a joint position in the Departments of Mathematics and of Philosophy at Harvard University; he was previously Professor at the University of California, Berkeley, from 1989 to 2014. In 1985 Professor Woodin was awarded the `Presidential Young Investigator Award', and he received the `Hausdorff Medal' of the European Set Theory Society in 2013. He was a plenary lecturer at the International Congress of Mathematicians in 2010, and a section lecturer in 1986 and 2002. He featured in the BBC Horizon programme `To Infinity and Beyond' in 2010.\n \nProfessor Woodin is one of the leaders in our era in the quest to understand the fundamental nature of sets and the real numbers, taking forward the journey of Godel and Tarski into the far reaches of `higher cardinals'.
DTSTART:20140926T163000
DTEND:20140926T173000
LOCATION:Frankland Lecture Theatre, Faraday Building
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BEGIN:VEVENT
UID:1449
SUMMARY:Pure Mathematics Seminar: Mahya Ghandehari
DESCRIPTION:
DTSTART:20141022T150000
DTEND:20141022T160000
LOCATION:A54, Postgraduate Statistics Centre Lecture Theatre
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