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Analysis

Research Highlights

Professor Adrian Constantin's research interests are in analysis interpreted in a broad sense (with emphasis on Partial Differential Equations and Dynamical Systems) and in Fluid Mechanics. He was a plenary speaker at the 6th European Congress of Mathematics, Krakow, Poland (2012). In 2011, he was awarded the ERC Advanced Grant "Nonlinear studies of water flows with vorticity". Professor Constantin is a member of the scientific board of the "Erwin Schrödinger International Institute for Mathematical Physics", Vienna, Austria (since 2011). In 2007 he was awarded the "F. W. Bessel'' prize in Mathematics of the Humboldt Foundation, Germany and in 2005 the "G. Gustafsson'' prize in Mathematics of the Royal Swedish Academy of Sciences. He was elected Fellow of Trinity College, Dublin, Ireland in 2005 and elected to the Royal Physiographical Society, Sweden in 2001.  He has been Professor of Mathematics at the University of Vienna (Austria) since 2008, and is the current holder of the Chair in Analysis at King's College London. 

Professor Brian Davies has made seminal contributions to the quantum theory of open systems, Gaussian bounds for the heat kernels associated with parabolic equations, and most recently the spectral theory of non-self-adjoint operators. In each of these he has written an important monograph that laid or lays out the route for future researchers to follow. In recognition of his lifetime achievements he has been elected a Fellow of the Royal Society and a Fellow of King's College London and awarded the Senior Berwick Prize by the London Mathematical Society (see this link for further details). He has also written two books on the philosophy of mathematics and science that have both received excellent reviews. In 2011 he won the London Mathematical Society Polya Prize.

Dr. Alexander Pushnitski's research interests are in the area of spectral and scattering theory for self-adjoint operators with applications to mathematical physics. The focus of his research for many years has been M.G.Krein's spectral shift function; he is regarded as one of the world leading authorities in this subject. Dr.Pushnitski was awarded a Leverhulme Research Fellowship in 2005 and has been working as an invited researcher at numerous Universities around the world. He is one of the most active members of the group, with collaborations involving scientists from the U.S., France, Germany, Sweden, Russia, Japan and Chile. He is one of the organisers of a major annual conference in Spectral Theory which takes place every summer in St.Petersburg, Russia. In 2011 Dr. Pushnitski was awarded the London Mathematical Society Whitehead prize.

Professor Yuri Safarov's mathematical interests lie between spectral theory and geometry. In particular, he obtained a general formula for the second term in the asymptotic formula for eigenvalues of partial differential operators, thus resolving the famous Weyl conjecture. A rough idea of the subject can be obtained from his book The Asymptotic Distribution of Eigenvalues of Partial Differential Operators. His recent research is concentrated on spectral properties of differential operators in relation to the geometry of the underlying manifold or domain, the abstract theory of operators and convex analysis. He has been awarded the Whitehead Prize by the London Mathematical Society, has been an invited speaker at numerous national and international conferences, and has worked as an invited scientist at more than 10 universities all over the world.

Professor Eugene Shargorodsky is an expert in the area of partial differential and integral equations, spectral theory, functional analysis, complex variables, microlocal analysis, global analysis, and their applications in fluid dynamics and elasticity theory. Recently, he solved several long-standing problems related to the definition of pseudospectra and to the spectra of Toeplitz operators with arbitrary bounded measurable coefficients, and together with J.F. Toland started a new area of research in the theory of free-boundary problems.

Professor Simon Scott obtained his DPhil under the supervision of Prof Graeme Segal FRS during an extraordinary period of intense create mathematical activity in the mathematics department in Oxford, with the presence there of Michael Atiyah, Simon Donaldson, Dan Quillen (all Fields medalists), Roger Penrose, and others, and a constant flow of very high profile international experts in topology, geometry, mathematical physics and analysis. This diverse mix of mathematics and international collaboration has been a formative background for Professor Scott's research interests and activities. A more detailed account of his work, which uses differential operators to compute invariants of space and straddles a mixture of geometric analysis and  topological quantum field theory, may be found in his recent book in the prestigious OUP Mathematical Monograph series. He is a frequent invited speaker at international conferences and meetings and has been a visiting professor at a number of universities.

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