The agenda of next meetings of Krasil'shchik's seminar on geometry of
differential equations at the Independent University of Moscow.

On 13 December seminar will be held online only.

Speaker: Yagub Aliyev
Title: Apollonius problem and caustics of an ellipsoid
Language: English
Zoom:
https://us06web.zoom.us/j/8817121842?pwd=0Xk64SsrOOWPdmlOuJMW2cSLNHrgRt.1&omn=84267555918
Zoom Passcode: 1312

Abstract:

In the talk we discuss Apollonius Problem on the number of normals of an
ellipse passing through a given point. It is known that the number is
dependent on the position of the given point with respect to a certain
astroida. The intersection points of the astroida and the ellipse are
used to study the case when the given point is on the ellipse. The
problem is then generalized for 3-dimensional space, namely for
Ellipsoids. The number of concurrent normals in this case is known to be
dependent on the position of the given point with respect to caustics of
the ellipsoid. If the given point is on the ellipsoid then the number of
normals is dependent on position of the point with respect to the
intersections of the ellipsoid with its caustics. The main motivation of
this talk is to find parametrizations and classify all possible cases of
these intersections.


The seminar meets on Wednesday evenings at 19:20 MSK in Zoom,
Meeting ID: 88 17 12 1842
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FROM 202.120.11.*