This seminar will focus on the invariant trace formula and the stable trace formula for SL_2. The main references for this seminar are The Invariant Trace Formula for SL_2 by A. Parab and Lectures on the Stable Trace Formula with Emphasis on SL_2 by T. Kaletha.
Notes for the invariant trace formula and the stable trace formula will be updated here.
Feb. 2nd: Zhaolin Li
[Par24] Section 3: Notations.
[Par24] Section 4: The kernel and its truncation.
[Par24] Section 5: Proof of absolute convergence of the truncated kernel for SL_2 - the geometric part.
Feb. 16th: Guodong Xi
[Par24] Section 5: Proof of absolute convergence of the truncated kernel for SL_2 - the analytic part.
[Par24] Section 6: The geometric expansion.
Feb. 23rd: Yuxuan Ge
[Par24] Section7: The Spectrum expansion
Mar. 2th: Junyi Zhai
[Par24] Section 8: The invariant trace formula.
[Par24] Section 9: Absolute convergence and relation with Beyond Endoscopy.
Mar. 23rd: Zhaolin li
[Kal24] Section 2: Stabilization of the elliptic regular part of the trace formula for SL_2.
Apr. 6th: Junyi Zhai
[Kal24] Section 3.1: Stable conjugacy.
[Kal24] Section 3.2: The Langlands dual group.
[Kal24] Section 3.3: Endoscopic data.
Apr. 13rd: Junyi Zhai
[Kal24] Section 3.4: Admissible isomorphisms.
[Kal24] Section 3.5: Transfer factors.
[Kal24] Section 3.6: Local transfer
Apr. 16th: Zhilin Luo (University of Chicago)
Title: Fourier transform and endoscopic transfer on real Lie algebras
Abstract: We show that the endoscopic transfer commutes with the Fourier transform on real Lie algebras using purely local methods. This is based on my joint work in progress with Cheng Chen.
Apr. 20th: Yuxuan Ge
[Kal24] Section 5: Stabilization of the elliptic regular part of the trace formula for general reductive groups.
Apr. 27th: Guodong Xi
[Kal 24] Section 6: Stabilization of the full trace formula for the group SL_2.