Reading Seminar on the Trace Formula for SL₂

Spring 2025

The main references for this seminar are The Invariant Trace Formula for SL₂ by A. Parab and Lectures on the Stable Trace Formula with Emphasis on SL₂ by T. Kaletha.

Talk Schedule

• February 2: Zhaolin Li
  • [Par24] Section 3: Notation.
  • [Par24] Section 4: The kernel and its truncation.
  • [Par24] Section 5: Proof of absolute convergence of the truncated kernel for SL₂ — the geometric part.
• February 16: Guodong Xi
  • [Par24] Section 5: Proof of absolute convergence of the truncated kernel for SL₂ — the analytic part.
  • [Par24] Section 6: The geometric expansion.
• February 23: Yuxuan Ge
  • [Par24] Section 7: The spectral expansion.
• March 2: Junyi Zhai
  • [Par24] Section 8: The invariant trace formula.
  • [Par24] Section 9: Absolute convergence and relation with Beyond Endoscopy.
• March 23: Zhaolin Li
  • [Kal24] Section 2: Stabilization of the elliptic regular part of the trace formula for SL₂.
• April 6: Junyi Zhai
  • [Kal24] Section 3.1: Stable conjugacy.
  • [Kal24] Section 3.2: The Langlands dual group.
  • [Kal24] Section 3.3: Endoscopic data.
• April 13: Junyi Zhai
  • [Kal24] Section 3.4: Admissible isomorphisms.
  • [Kal24] Section 3.5: Transfer factors.
  • [Kal24] Section 3.6: Local transfer.
• April 16: 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 joint work in progress with Cheng Chen.
• April 20: Yuxuan Ge
  • [Kal24] Section 5: Stabilization of the elliptic regular part of the trace formula for general reductive groups.
• April 27: Guodong Xi
  • [Kal24] Section 6: Stabilization of the full trace formula for the group SL₂.