Hyperbolic 3-manifolds of bounded volume and trace field degree

Bogwang Jeon (Columbia)

n the study of hyperbolic 3-manifolds, the following question is natural: Are there only finitely many hyperbolic three manifolds of bounded volume and trace field degree ? By Thurston's hyperbolic Dehn filling theorem, to answer to the above question, it is enough to answer the following question: For an n-cusped manifold M and a constant D>0, are there only finitely many Dehn fillings of M whose trace fields have degree< D Although it is commonly believed that the answer is yes and Hodgson proved it for the 1-cusped case, little was previously known in general. In the talk, I will present some further results and related questions for the 2-cusped case. No further background will be necessary but it will be good to know about Thurston's Dehn filling theorem.