**
Anton
Mosunov,
Department
of
Pure
Mathematics,
University
of
Waterloo**

“The
number
of
solutions
of
a
Thue
equation”

Let F be an irreducible binary form of degree d > 2 and m be a positive integer. In 1909, Thue famously proved that the number of solutions to |F(x,y)| = m is finite. In the 1980’s Evertse demonstrated that the number of solutions to |F (x, y)| = m with coprime x and y is bounded above by some effective constant C, which depends only on d and m. In this talk, we will present the technique of Bombieri and Schmidt for showing that one can take C = c′dt, where c′ is a positive absolute constant and t is the number of prime divisors of m. We will also discuss various refinements of this result due to Stewart, Akhtari, Thunder, Sharma and Saradha.

MC 5403