WEEKLY ACTIVITIES

Time: 9h00, Thursday, October 16, 2015
Location: Room 6, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: Let f(x,y) be a polynomial. We show that if f is degenerate in some sense then the volume of the sublevel sets of f is finite and computed explicitly in terms of the Newton polygon of f at infinity. Also, for a more generalized degenerate condition of f, the cardinal of lattice points in the sublevel sets of f can be controlled by the cardinal of lattice points in these sets which is contained in a some bounded set K_f; and the asymptotic formula of this quantity is determined explicitly in terms of the complete Newton polygon of f at infinity.