|Andrey Shafarevich||Steklov Mathematical Institute of Russian Academy of Sciences|
Bio: Prof. A.I. Shafarevich is currently the Dean of the Faculty of Mechanics and Mathematics at Lomonosov Moscow State University. He is also the Corresponding Member of the Russian Academy of Sciences. The main scientific interests of A.I.Shafarevich lie in the field of mathematical physics, asymptotic and geometric theory of linear and nonlinear partial differential equations, quantum mechanics and hydrodynamics. He solved the problem posed by V.P. Maslov and widely discussed in the scientific literature on the multiphase asymptotics for the equations of hydrodynamics.
Propagation of quasi-particles on singular spaces. Relation to the behavior of geodesics and to certain problems of analytic number theory.
We study propagation of semi-classical localized solutions of Schroedinger or wave equations (Gaussian beams) on a certain class of singular spaces. These spaces are obtained by connecting of a number of smooth manifolds by several segments. Laplacians on such spaces are defined with the help of extension theory an depend on boundary conditions in the points of gluing. Statistics of a number of Gaussian packets is governed by the behavior of geodesics on manifolds and is connected with certain problems of analytic number theory - in particular, with the problem of distribution of abstract primes.
|Qiongling Li||Chern Institute of Mathematics, Nankai University|
Bio: Qiongling Li got her Ph.D. from Rice University in 2014. She is currently a research fellow at Chern Institute of Mathematics, Nankai University. Her main research fields are Higgs bundles, harmonic maps, and higher Teichmuller theory. Her recent works have been focused on understanding the non-abelian Hodge correspondence over Riemann surfaces.
Toda equations and cyclic Higgs bundles over non-compact surfaces.
For Higgs bundles over compact Kahler manifods, it is known by Hitchin and Simpson that the existence of Hermitian-Einstein metric is equivalent to the polystability of the Higgs bundle. There are some generalizations to non-compact cases. On a Riemann surface with a holomorphic r-differential, one can naturally define a Toda equation and a cyclic Higgs bundle with a grading. A solution of the Toda equation is equivalent to a Hermitian-Einstein metric of the Higgs bundle for which the grading is orthogonal. In this talk, we focus on a general non-compact Riemann surface with an r-differential which is not necessarily meromorphic at infinity. In particular, we discuss the Hermitian-Einstein metrics on the cyclic Higgs bundles determined by r-differentials. This is joint work with Takuro Mochizuki (Kyoto University).
The meeting will be held in the form of a webinar on the Zoom platform.
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Meeting ID : 827 5552 2129