From Weyl type asymptotics to Lieb-Thirring inequalities

2 November 2007
15:30
Prof Ari Laptev
Abstract
We shall begin with simple Weyl type asymptotic formulae for the spectrum of Dirichlet Laplacians and eventually prove a new result which I have recently obtained, jointly with J. Dolbeault and M. Loss. Following Eden and Foias, we derive a matrix version of a generalised Sobolev inequality in one dimension. This allows us to improve on the known estimates of best constants in Lieb-Thirring inequalities for the sum of the negative eigenvalues for multi-dimensional Schrödinger operators. Bio: Ari Laptev received his PhD in Mathematics from Leningrad University (LU) in 1978, under the supervision of Michael Solomyak. He is well known for his contributions to the Spectral Theory of Differential Operators. Between 1972 - 77 and 1977- 82 he was employed as a junior researcher and as Assistant Professor at the Mathematics & Mechanics Department of LU. In 1981- 82 he held a post-doc position at the University of Stockholm and in 1982 he lost his position at LU due to his marriage to a British subject. Up until his emigration to England in 1987 he was working as a builder, constructing houses in small villages in the Novgorod district of Russia. In 1987 he was employed in Sweden, first as a lecturer at Linköping University and then from 1992 at the Royal Institute of Technology (KTH). In 1999 he became a professor at KTH and also Vice Chairman of its Mathematics Department. In 1992 he was granted Swedish citizenship. Ari Laptev was the President of the Swedish Mathematical Society from 2001 to 2003 and the President of the Organizing Committee of the Fourth European Congress of Mathematics in Stockholm in 2004. From January 2007 he has been employed by Imperial College London. Ari Laptev has supervised twelve PhD students. From January 2007 until the end of 2010 he is President of the European Mathematical Society.