General Mathematics SeminarProgramme committee:

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.)
The next (175^{th}) 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. 
Define the ZelikinLokutsievskiy polynomial f_{n}(x) with integer coefficients of degree n  1 as follows
We show the irreducibility of f_{(q1)/2}(x) over Q for any prime q > 3. We calculate the Galois group of the polynomial f_{n}(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 f_{p+1}(x) over Q for almost all primes p that there exists an infinite sequence of natural n, for which A_{n}  1 is embeddable into Gal_{Q}(f_{n}(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 kdimensional torus in finite time.
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 email to: pastor@pdmi.ras.ru. 