Speciality:
01.01.06 (Mathematical logic, algebra, and number theory)
Birth date:
8.10.1972
E-mail: Website: https://logic.pdmi.ras.ru/~vsemir Keywords: Diophantine equations,
algorithms in number theory,
combinatorial group theory,
combinatorics.
Subject:
It was proved that there exists an infinite set of primes which coincides with the set of positive values of a polynomial in 8 integer-valued variables. Simple Diophantine representations of recurrent sequences of order 3 and 4 wee found. It was found for which $k$'s the triangle group $T(2,3,k)$ coincides with the projective image of the special unitary group $SU(2,R)$ over some ring $R$ of algebraic integers.
Main publications:
Vsemirnov M., “The Woods–Erdős conjecture for polynomial rings”, Annals of Pure and Applied Logic, 113:1-3 (2002), 331–344
Vsemirnov M., Mysovskikh V., Tamburini M. C., “Triangle groups as subgroups of unitary groups”, J. Algebra, 245:2 (2001), 562–583
Vsemirnov M. A., “Beskonechnye mnozhestva prostykh chisel, dopuskayuschie diofantovy predstavleniya s vosemyu peremennymi”, Zapiski nauchnykh seminarov POMI, 220, 1995, 36–48
Vsemirnov M. A., “Diofantovy predstavleniya lineinykh rekurrentnykh posledovatelnostei, I”, Zapiski nauchnykh seminarov POMI, 227, 1995, 52–60
Vsemirnov M. A., “Diofantovy predstavleniya lineinykh rekurrentnykh posledovatelnostei, II”, Zapiski nauchnykh seminarov POMI, 241, 1997, 5–29
