Tomasz Jedrzejak

Title: The torsion part of the Mordell-Weil group of Jacobians of hyperelliptic and superelliptic curves

Abstract: 
The subject of my talk is located at the intersection of the number theory and algebraic geometry, 
it is called arithmetic algebraic geometry. First I introduce a short survey of basic notions and 
results related to arithmetic of elliptic, hyperelliptic and superelliptic curves; in particular, I present 
the Torsion Conjecture. Then I give the characterization of the torsion subgroups (over the rationals) 
of the Mordell-Weil groups of the Jacobians of hyperelliptic and superelliptic curves in certain 
infinite families. Next I present main ingredients of the proofs and some applications.