Russian version of this page.

St.Petersburg Department of Steklov Institute of Mathematics


General Mathematics Seminar

Programme committee:

  • A.M.Vershik (head), doctor of sciences
  • I.A.Ibragimov, full member of Russian Academy of Sciences
  • Serguei Kisliakov, full member of Russian Academy of Sciences
  • Yu.V.Matiyasevich, full member of Russian Academy of Sciences
  • M.I.Belishev, doctor of sciences
  • N.M.Bogoliubov, doctor of sciences
  • S.V.Buyalo, doctor of sciences
  • V.I.Vasyunin, doctor of sciences
  • M.A.Vsemirnov, corresponding member of Russian Academy of Sciences
  • B.B.Lurje, doctor of sciences
  • N.D.Filonov, candidate of sciences
  • A.V.Pastor (secretary), candidate of sciences

This seminar is organized by St.Petersburg Division of Steklov Institute of Mathematics (POMI) of Russian Academy of Sciences.

The next session of the seminar.

Previous sessions of the seminar. (Also short abstracts of some talks are presented here.)

Planned talks.

Russian version of this page.


The next session(s) of the seminar.

The next (175th) session will be held on Monday, February 20, in the room no. 311 at 13.00.

Speaker: D. D. Kiselev (Russian Foreign Trade Academy, Moscow)
Title: An application of Galois theory to the optimal control.

Abstract:

Define the Zelikin-Lokutsievskiy polynomial fn(x) with integer coefficients of degree n - 1 as follows

xfn(x2) = Im (ix + 1)…(ix + 2n).

We show the irreducibility of f(q-1)/2(x) over Q for any prime q > 3. We calculate the Galois group of the polynomial fn(x), when the numbers p = n - 1, q = 2n + 1, r = 2n + 7 are prime and 889 is not a square modulo r. We also show under irreducibility hypothesis of the polynomial fp+1(x) over Q for almost all primes p that there exists an infinite sequence of natural n, for which An - 1 is embeddable into GalQ(fn(x)).

An example: for any natural k < 808 there exists an optimal control problem, the optimal control of which throws a dense winding of the k-dimensional torus in finite time.


After session tea in the marble hall will be organized.


Our address: St.Petersburg Division of
Steklov Institute of Mathematics,
27, Fontanka, St.Petersburg.


Page of St.Petersburg Department of Steklov Institute of Mathematics (POMI).

This page is maintained by Alexei Pastor, the secretary of the seminar.
All your questions and/or suggestions you may send by e-mail to: pastor@pdmi.ras.ru.

Last modified: January 27, 2017