## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Monday, June 6, 2016 — 2:30 PM EDT

**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

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.