University of California-Irvine and Montana State-Billings

**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.