Beijing-Saint Petersburg Mathematics Colloquium (online) | FTiMS - Politechnika Gdańska

• Wykład 1: Symmetry Results in Two-Dimensional Inequalities for Aharonov–Bohm Magnetic Fields.
  Prelegent: Prof. Ari Laptev, Czas: 13:00-14:00

 

Abstrakty oraz sylwetki prelegentów:

 

Abstract: We study functional and spectral properties of perturbations of a magnetic second order differential operator on a circle. This operator appears when considering the restriction to the unit circle of a two dimensional Schrödinger operator with the Bohm-Aharonov vector potential. We prove some Hardy’s and sharp Keller-Lieb-Thirring inequalities.
Bio: Prof. Ari Laptev is Professor at both KTH in Stockholm and Imperial College of London an Researcher at the Faculty of Mathematics and Computer Science at Saint Petersburg State University. Also, he is a member of the Council of Sirius Mathematical Center. He is a worldwide famous expert in Spectral Theory of Partial Differential Equations, in particular, Schrödinger operators; Polya conjecture; Lieb-Thirring inequalities; Trace formulae; Inverse problems; Global solutions of Wave Equations; Generalized Szegö Problems, Pseudodifferential Operators. Ari Laptev graduated from Leningrad State University and obtained in 1978 his PhD under the supervision of Michael Solomyak.  In 2001-2003 Prof. Laptev was the President of the Swedish Mathematical Society. In 2007 he received the Royal Society Wolfson Research Merit Award.  From 2007 to 2011 Prof Laptev served as the President of European Mathematical Society. He was the Director of Institut Mittag-Leffler between 2011 and 2018. He is Editor-in-Chief of Acta Mathematica, Editor-in-Chief of Arkiv för Matematik, Deputy Chief Editor of the Journal of Spectral Theory, Editor of the Bulletin of Mathematical Sciences, Editor of Problems in Mathematical Analysis, and Editor of Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika.

 

Abstract: Using the perturbation determinant introduced by B. Simon, we show the microscopic conservation laws for the Schwarz solutions of the derivative nonlinear Schrodinger equation (DNLS) with small mass, which can be used to show uniformly boundedness and local smoothing estimate of DNLS in the lower regularity space. This is joint work with Xingdong Tang. Lastly, we will show some progresses about DNLS. 
Bio: Guixiang Xu got Ph. D from the Institute of Applied Physics and Computational Mathematics in China on 2006, and now is a full professor at School of Mathematical Sciences of Beijing Normal Universiity. His research fields are harmonic analysis and partial differential equations, in particular, global well-posedness and scattering theory, stability theory and blow-up dynamics of nonlinear dispersive equations.

 

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