Johns Hopkins Number Theory Seminar

Talk Schedule

• September 2: Chun-Hsien Hsu, University of Chicago
  • Title: Braverman-Kazhdan-Ngô program over non-Archimedean local fields
  • Abstract:

    The Poisson summation conjecture, initiated by Braverman and Kazhdan, later refined by Lafforgue, Ngô, and many others, and broadened by Sakellaridis to the setting of affine spherical varieties, predicts Poisson summation formulae on affine spherical varieties (and beyond) that generalize classical harmonic analysis on vector spaces. It provides a uniform framework for establishing analytic properties of L-functions and, ultimately, for establishing Langlands functoriality in great generality. In the setting of L-monoids, it is often referred to as the Braverman–Kazhdan–Ngô program.

    Recent work of Getz et al. explains how Fourier transforms for L-monoids can be constructed using the Harish-Chandra Plancherel formulae, assuming enough of tempered local Langlands correspondence. In joint work with HaoYun Yao, we construct the Schwartz spaces over non-Archimedean local fields under the same assumption. With an additional assumption on \(\gamma\)-factors, we also establish the Tate–Godement–Jacquet theory in this setting. Our approach is spectral in nature. In this talk, I will explain how Schwartz spaces and Fourier transforms can be constructed spectrally for general linear groups. If time permits, I will sketch a proof of the Tate–Godement–Jacquet theory for \(\mathrm{GL}_2\).

    (Warmup talk for graduate students at 11:00pm-11:45pm in Krieger 204.)

• September 9: Pranjal Warade, Purdue University
  • Title: TBA
  • Abstract: TBA
• September 16: Luis Garcia, University College London
  • Title: TBA
  • Abstract: TBA
• September 23: TBA
  • Title: TBA
  • Abstract: TBA
• September 30: Salim Tayou, Dartmouth College
  • Title: TBA
  • Abstract: TBA
• October 7: Yan Pan, University of Arizona
  • Title: TBA
  • Abstract: TBA
• October 14: Guy Shtotland , Ben-Gurion University
  • Title: TBA
  • Abstract: TBA
• October 21: Marco Sangiovanni, Columbia University
  • Title: TBA
  • Abstract: TBA
• October 28: TBA
  • Title: TBA
  • Abstract: TBA
• November 4: Yingkun Li, Institute for Advanced Study
  • Title: TBA
  • Abstract: TBA
• November 11: TBA
  • Title: TBA
  • Abstract: TBA
• November 18: Manami Roy, Lafayette College
  • Title: TBA
  • Abstract: TBA
• November 25: Thanksgiving
• December 2: David Roe , MIT
  • Title: TBA
  • Abstract: TBA