Mathematical Colloquium 
Beyond Fermat's Last Theorem 

By  David ZureickBrown 
From  Department of Mathematics Emory University 
When  Monday, February 12, 2018 4:00 pm 
Where  Weber 223 
Abstract  What do we (number theorists) do with ourselves now that Fermat's last theorem (FLT) has fallen? I'll discuss lots of generalizations of FLT (and some underlying intuitions)  for instance, for integers a,b,c >= 2 satisfying 1/a + 1/b + 1/c < 1, Darmon and Granville proved the single generalized Fermat equation x^a + y^b = z^c has only finitely many coprime integer solutions; conjecturally something stronger is true: for a,b,c \geq 3 there are no nontrivial solutions and for (a,b,c) = (2,3,n) with n >= 10 the only solutions are the trivial solutions and (+ 3,2,1) $ (or (+3,2,+1) $ when n is even). 
Further Information 
Rachel Pries 