Departmental PhD Thesis Exam – Bin Xu

Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam.

Wednesday, March 19, 2014
2:00 p.m.
BA6183, 40 St George St.

PhD Candidate: Bin Xu

Supervisor: Jim Arthur

Thesis title: Endoscopic Classification of Representations of GSp(2n) and GSO(2n)

In 1989 Arthur conjectured a very precise description about the structure of automorphic representations of reductive groups using Arthur packets and endoscopy theory.  And in his recent monograph [Art13], he proved this conjecture for symplectic groups and orthogonal groups G upon the stabilization of twisted trace formula, which is a project in progress under Moeglin and Waldspurger (see [MW13] [Wal13a], [Wal13b] and [Wal13c]). Our goal is to extend Arthur’s result to general symplectic groups and general even orthogonal groups $\tilde{G}$, by studying the restriction of representations from $\tilde{G}$ to $G$.  This idea goes back to Labesse and Langlands [LL79], where they considered $G$ to be $SL(2)$ and $\tilde{G}$ to be $GL(2)$.

To extend Arthur’s result, there are two main problems that we have solved in this thesis, one is local and the other is global. Locally, we have determined the tempered Arthur packets for $\tilde{G}$, and shown they satisfy certain character relations under the endoscopic transfer. Globally, we have proven the functoriality of endoscopic transfer for a large family of automorphic representations of $\tilde{G}$, which includes the tempered cohomological automorphic representations.

A copy of the thesis is available in this link:  http://www.math.toronto.edu/binxu/Thesis.pdf