Penn Arts & Sciences Logo

Philadelphia Area Number Theory Seminar

Wednesday, October 31, 2018 - 2:15pm

Benjamin Pollak

University of Pennsylvania

Location

Bryn Mawr College

Park Science Building, Room 328

Talk is scheduled to begin at 2:40 PM. Tea and refreshments will be served at 2:20 PM in the Math Lounge, Park Science Building, Room 361.

The inverse Galois problem asks whether every finite group appears as the Galois group of some extension of the rational numbers. In this talk I will focus on which finite groups appear as the Galois group of some extension of the rational numbers in which only a fixed set of primes may ramify. I will present results and examples in some specific cases, with an emphasis on the situation in which only one finite prime ramifies, as well as provide some insight into how the ramified primes in a Galois extension relate to generating sets of the corresponding Galois group.