Graduate Student

Event Information First Steps in the Langlands Program
18:00 on Thursday March 28, 2013
19:00 on Thursday March 28, 2013
BA6183, Bahen Center, 40 St. George St.
Patrick Walls

University of Toronto

The Langlands program is a series of conjectures which aim to build a bridge between two worlds: the arithmetic world of algebraic number fields and their Galois groups, and the spectral world of infinite dimensional representations. To merely state the conjectures requires plenty of heavy machinery: algebraic number theory, class field theory, Galois representations, algebraic geometry, the structure theory of algebraic groups and root systems, and the representation theory of Lie groups and p-adic groups. The initiation process is daunting to say the least. So where does a graduate student even start? I will try to present a simplified picture of the Langlands program by exploring some of its more accessible features and where they fit in the general program. This naive picture is far from complete and inevitably leads to inaccuracies... but we have to start somewhere.