Семинар 24 февраля

Очередное заседание семинара кафедры высшей математики и математической физики состоится 24 февраля, начало  в 19-10. 

Докладчик: Валерий Павлович Смышляев (University College London).

Тема: Whispering gallery waves near boundary inflection: a canonical high-frequency diffraction problem

A particular problem of interest is that of a whispering gallery high-frequency asymptotic mode propagating along a concave part of a boundary and then scattering at a boundary inflection point. Like Airy ODE and associated Airy function are fundamental for describing transition from oscillatory to exponentially decaying asymptotic behaviors, the boundary inflection problem leads to an arguably equally fundamental canonical boundary-value problem for a special PDE describing transition from a “modal” to a “scattered” high-frequency asymptotic behaviors. This is a Schrödinger equation on a half-line with
a potential linear in both space and time. The latter problem was first formulated and analysed by M.M.Popov starting from 1970-s. The associated solutions have asymptotic behaviors with a discrete spectrum at one end and with a continuous spectrum at the other end, and of central interest is to find the map connecting the above two asymptotic regimes. The problem however lacks separation of variables, except in the asymptotical sense at both of the above ends.
Nevertheless, we perform a non-standard perturbation analysis at the continuous spectrum end, ultimately describing the desired map connecting the two asymptotic representations. We also show that the problem permits a re-formulation as a one-dimensional boundary integral equation, whose regularization allows its further asymptotic analysis.

Как всегда, Вы можете попасть на семинар, используя следующие данные:

Join Zoom Meeting

Meeting ID: 270 950 5573
Passcode: 779950

Обратите внимание на время начала семинара! Изменение сделано для того, чтобы все желающие могли принять участие также в семинаре по спектральной теории:
Начало семинара в 18 часов. 

Докладчик: Светлана Житомирская (University of California).

Тема: Spectral properties of the unbounded GPS model.

We discuss spectral properties of the unbounded GPS model: a family of discrete 1D Schrodinger operators with unbounded potential and exact mobility edge. Based on papers in progress joint with Xu, You (Nankai) and Zhao (UCI).
Попасть на семинар по спектральной теории можно так:
zoom channel 812-916-426. passcode: mkn
Оба семинара включены в программу ММЦ им. Эйлера по спектральной теории и математической физике https://indico.eimi.ru/event/111/
Со странички программы можно попасть на странички семинаров:
по матфизике: https://eimi.ru/math-physics-seminar/
по спектральной теории: https://eimi.ru/seminar-in-spectral-theory-and-related-topics/