Abstract:

סטודנטית: טל מונדרר, דוקטורנטית

מנחה: פרופ"ח דני נפטין

**Title:**

**The reducible components of the curve f(x)=g(y) for f indecomposable of large degree**

**Abstract:**Families of rational functions f,g for which the curve f(x)=g(y) is reducible give rise to interesting phenomena in number theory and complex analysis. It is known that no such indecomposable polynomials exist when deg f > 33; for rational functions little is known. We describe the possible factorizations when f is taken to be rational, indecomposable of large degree, relying on an analysis of low genus coverings with Galois closure contained in that of f.