Reading Seminar on the Jacquet-Rallis Trace Formula

Fall 2025

This seminar focuses on the Jacquet-Rallis trace formula and its applications to the Gan-Gross-Prasad conjecture for unitary groups. The primary references for the seminar are:

• [Jac86] H. Jacquet, Sur un résultat de Waldspurger .
• [JR11] H. Jacquet and S. Rallis, On the Gross-Prasad Conjecture for Unitary Groups .
• [Yun11] Z. Yun, The Fundamental Lemma of Jacquet and Rallis .
• [Zha14] W. Zhang, Fourier Transform and the Global Gan-Gross-Prasad Conjecture for Unitary Groups .
• [BP21] R. Beuzart-Plessis, A New Proof of the Jacquet-Rallis Fundamental Lemma .
• [BPLZZ21] R. Beuzart-Plessis, Y. Liu, W. Zhang and X. Zhu, Isolation of Cuspidal Spectrum, with Application to the Gan-Gross-Prasad Conjecture .
• [BPCZ22] R. Beuzart-Plessis, P.-H. Chaudouard and M. Zydor, The Global Gan-Gross-Prasad Conjecture for Unitary Groups: the Endoscopic Case .
• [Zyd22] M. Zydor, Periods of Automorphic Forms over Reductive Subgroups .

We meet every Friday from 2:00 to 4:00 pm at Vincent Hall 364.

Talk Schedule

• September 5: Zhaolin Li
  • Orbits of strongly regular elements.
• September 12: Zhaolin Li
  • Smooth matching and the fundamental lemma.
  • The global comparison for n = 2.
• September 19: Zhaolin Li
  • Smooth matching: reduction to Lie algebras.
• September 26: Zhaolin Li
  • Smooth matching: reduction to local transfer around zero.
• October 3: Sagnik Mukherjee
  • Explicit étale Luna slices.
• October 10: Zhaolin Li
  • Smooth transfer for Lie algebras.
• October 17: Canceled
• October 24: Zhaolin Li
  • Compatibility of smooth transfer with Fourier transforms.
  • The infinitesimal version of the fundamental lemma.
• October 31: Halloween
• November 7: Zhaolin Li
  • Relative truncation.
• November 14: Canceled
• November 21: Sagnik Mukherjee
  • Symplectic periods of general linear groups.
• November 28: Thanksgiving