Monday, October 24
Milner 216, 12:30 PM
Title: Dihedral groups: Comparing cusps on modular curves to their MT generalization
Abstract: A Regular Inverse Galois Problem (RIGP) analogy: Modular curve towers are to MT's as dihedral groups (not of 2-power order) are to all non-nilpotent finite groups. RIGP asks if for each finite group G some Galois extension L/Q(z) has group G and L intersected with the complex numbers equals the rational numbers. Such a Q-realization has r branch points with associated branch cycle conjugacy classes C of G. The branch cycle lemma constrains what C can define a rational regular realization and has links with diophantine problems.